Select the correct answer from each drop-down menu.
Riley is swinging on a swing at the playground. Let t represent time, in seconds, and let represent Riley's horizontal distance, in inches, from
her starting position, as shown in the table.
t
0 0.75 1.5 2.25 3 3.75 4.5 5.25 6 6.75
f(t) 0 38.9 55 38.9 0-28.9 -55 -38.9 0 38.9
Note: When Riley swings in front of the starting position, f (t) is positive, and when Riley swings behind the starting position, f(t) is negative.
From the table, Riley is moving forward on the interval [0,
It takes Riley
Riley reaches a maximum distance of
seconds to swing forward, back, and then return to her starting position.
inches from her starting position.
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Answers
Thus, Riley's maximum distance from the starting position is 55 inches.
Explain about the function:When an input value has a defined output value in reality, functions can be applied. For instance, how long a car has been driving affects how far it has travelled (the output) (the input).
Riley is swaying on a playground swing. As stated in the table, let t denote the passing of time in seconds and let f(t) denote Riley's horizontal displacement from her starting location in inches.
t: 0 ,0.75, 1.5, 2.25, 3, 3.75, 4.5, 5.25, 6, 6.75
f(t): 0 ,38.9, 55, 38.9, 0, -28.9, -55, -38.9, 0, 38.9
Recall that f(t) is positive when Riley swings closest to the starting position and negative when Riley swings in behind starting position.
So,
started from 0 and travelled distance of 55 inches in 1.5 seconds.
She is advancing by up to 1.5 seconds.
Then she begins to move backward, returning to her starting location after 3 seconds, and continuing to do so for an additional 4.5 seconds at a distance of -55.
Then begin to advance and return to the starting position after six seconds
Riley is advancing from the table on the interval [0, 1,5].Riley swings forward, backward, and then back to the starting position in six seconds. A is a few inches from where she started.Riley's maximum distance from the starting position is 55 inches.Know more about the function:
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Related Questions
HELP!!!! 50 POINTS!!!!
Answers
Answer:sorryy if this is late but its 2
Step-by-step explanation:
The number of customers, y, queueing at the payment counter at a given time t, is given by equation:
y=t^3-14t^2+50t,where 0≤t≤8.5,
t is the number of hours after the shop opens at 9 am
Required:
1. Advise the management of the shop as to when they can deploy more cashiers and the number of customers queueing at that time. (6 Marks)
2. Determine the number of man-hours spent per day by shoppers queueing
Answers
Answer: 1. To find the time when the management should deploy more cashiers, we need to find the time when the number of customers queueing is the highest. We can find the maximum value of y by taking the derivative of the equation and setting it equal to zero:
dy/dt = 3t^2 - 28t + 50 = 0
Solving for t, we get:
t = (28 ± sqrt(28^2 - 4350)) / (2*3) = 4.67 or 9.33
Since the time has to be between 0 and 8.5 hours, the maximum occurs at t = 4.67 hours. Therefore, the management should deploy more cashiers around 1:40 pm (9:00 am + 4.67 hours). At this time, the number of customers queueing is:
y = 4.67^3 - 14(4.67)^2 + 50(4.67) = 51.64
So, there will be approximately 52 customers queueing at that time.
2. To find the number of man-hours spent per day by shoppers queueing, we need to integrate the equation for y over the range 0 ≤ t ≤ 8.5:
∫(0 to 8.5) y dt = ∫(0 to 8.5) (t^3 - 14t^2 + 50t) dt
Evaluating the integral, we get:
= [(1/4)t^4 - (14/3)t^3 + 25t^2] from 0 to 8.5
= (1/4)(8.5)^4 - (14/3)(8.5)^3 + 25(8.5)^2
= 1907.81
Therefore, the total number of man-hours spent per day by shoppers queueing is approximately 1908.
Step-by-step explanation:
To determine when the shop should deploy more cashiers, we need to find the maximum point of the function y(t), which corresponds to the peak of the queue. The maximum point of a cubic function is found at its turning point, which is where its derivative equals zero. Therefore, we can find the turning point by taking the derivative of y(t) and setting it equal to zero:
y'(t) = 3t^2 - 28t + 50
0 = 3t^2 - 28t + 50
Using the quadratic formula, we get t = 4.47 or t = 3.19.
However, we need to make sure that the maximum point lies within the given range of 0 ≤ t ≤ 8.5. Since 3.19 is within this range and 4.47 is not, the maximum point occurs at t = 3.19 hours after the shop opens.
What is the number of man-hours spent per day by shoppers queueing?To find the number of customers queueing at that time, we simply plug in t = 3.19 into the original equation:
y(3.19) = (3.19)^3 - 14(3.19)^2 + 50(3.19) ≈ 30.8
Therefore, the management of the shop should deploy more cashiers at 12:11 pm (9 am + 3.19 hours) when there are approximately 30.8 customers queueing.
To determine the number of man-hours spent per day by shoppers queueing, we need to find the total area under the curve of y(t) from t = 0 to t = 8.5. This area represents the total number of customers queueing during the day.
Using integration, we get:
∫(t^3 - 14t^2 + 50t)dt = (t^4/4) - (14t^3/3) + (25t^2) + C
where C is the constant of integration.
Evaluating this expression at t = 8.5 and t = 0, and subtracting the latter from the former, we get:
(8.5^4/4) - (14(8.5)^3/3) + (25(8.5)^2) - (0^4/4) + (14(0)^3/3) - (25(0)^2) ≈ 2233.1
Therefore, the total number of man-hours spent per day by shoppers queueing is approximately 2233.1. Note that this assumes that each customer spends exactly one hour in the queue, which may not be realistic, but provides a rough estimate of the total time spent.
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The polynomial function f has exactly one positive zero. Approximate the zero correct to two decimal
places.
f(x)=2x-16x³ - 3x² - 8x-2
The positive zero of f is approximately
(Round to two decimal places as needed.)
141
Answers
Answer:
We can use a numerical method such as the Newton-Raphson method or the bisection method to approximate the positive zero of the function f(x) = 2x - 16x³ - 3x² - 8x - 2.
Let's use the Newton-Raphson method to approximate the positive zero of f(x). We start by choosing an initial guess x_0, and then compute successive approximations using the formula:
x_(n+1) = x_n - f(x_n) / f'(x_n)
where f'(x) is the derivative of f(x). We continue this process until we get an approximation that is accurate enough for our needs.
Let's choose an initial guess of x_0 = 1.5. Then we have:
f(x) = 2x - 16x³ - 3x² - 8x - 2
f'(x) = 2 - 48x² - 6x - 8
Using these expressions, we can compute successive approximations as follows:
x_1 = x_0 - f(x_0) / f'(x_0) = 1.5 - (-23.375) / (-73) ≈ 1.320
x_2 = x_1 - f(x_1) / f'(x_1) = 1.320 - (-12.608) / (-50.673) ≈ 1.141
x_3 = x_2 - f(x_2) / f'(x_2) = 1.141 - (-5.364) / (-35.883) ≈ 1.067
x_4 = x_3 - f(x_3) / f'(x_3) = 1.067 - (-1.949) / (-31.120) ≈ 1.042
x_5 = x_4 - f(x_4) / f'(x_4) = 1.042 - (-0.361) / (-30.251) ≈ 1.029
x_6 = x_5 - f(x_5) / f'(x_5) = 1.029 - (-0.012) / (-30.055) ≈ 1.028
So the positive zero of f(x) is approximately 1.028, rounded to two decimal places.
find the length of each leg
Answers
Simplifying this equation, we get: PQ ≈ 6.93 and QR ≈ 8.
What is triangle?
A triangle is a three-sided polygon with three angles. It is a fundamental geometric shape and is often used in geometry and trigonometry. A triangle is defined by its three sides and the three angles formed by those sides.
To find the lengths of PQ and QR in triangle RPQ, we can use the law of sines:
sin(R) / RP = sin(P) / PQ = sin(Q) / QR
We are given R = 30° and P = 60°, so we can find Q:
Q = 180° - R - P
Q = 180° - 30° - 60°
Q = 90°
Now we can use the law of sines:
sin(30°) / 4 = sin(60°) / PQ = sin(90°) / QR
Simplifying this equation, we get:
PQ = (4 * sin(60°)) / sin(30°) ≈ 6.93
QR = (4 * sin(90°)) / sin(30°) = 4 * 2 ≈ 8
Therefore, PQ ≈ 6.93 and QR ≈ 8.
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Given the function f(x) = x, what is the effect of f(x) - 8?
A. The new line is parallel to the original
B. The new line has a smaller rate of change
C. The x intercept decreases
C. The y intercept increases
Answers
If the function f(x) = x, the effect of f(x) - 8 is: is (D) The y intercept decreases.
What is the effect of f(x) - 8?The function f(x) = x is a linear function with a slope of 1, which means that for every increase of 1 in the x-value, the y-value also increases by 1.
If we subtract 8 from the function, we get:
f(x) - 8 = x - 8
This is still a linear function with a slope of 1, but it has been shifted downwards by 8 units.
Therefore, the effect of f(x) - 8 is that the y-intercept decreases by 8 (since the y-intercept of f(x) is 0 and the y-intercept of f(x) - 8 is -8), while the slope remains the same.
So the correct answer is (D) The y intercept decreases.
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How many Cube Cs will fit into Cube A. Enter the max amount.
Answers
Answer:
27 cubes
Step-by-step explanation:
The volume of Cube A is 1 cubic centimeter. The volume of one Cube C is 1/27 of a cubic centimeter. So 27 Cube C's will fit into Cube A.
An individual depositing in a non-IRA account has to pay income taxes on the funds deposited and on interest earned in each year but does not have to pay taxes on withdrawals from the account.
Sarah, who is five years from retirement, receives a $10,000 bonus at work. She is trying to decide whether to save this extra income in an IRA account or in a regular savings account. Both accounts earn 8 percent nominal interest, and Sarah is in the 30 percent tax bracket in every year (including her retirement year)
If Sarah invests in the normal savings account, her net value (after taxes) five years from now will be?:
Answers
The net value of the $10,000 bonus in a normal savings account after taxes and interest in five years will be $9,181.
What is the net value of Sarah's $10,000 bonus in a normal savings account after taxes and interest in five years?Assuming an 8 percent nominal interest rate and a 30 percent tax bracket, the after-tax return on the normal savings account is 5.6 percent. Thus, after five years, the $10,000 bonus will grow to $14,693.
However, since Sarah is in the 30 percent tax bracket in every year, she will owe taxes on the interest income earned each year. This reduces the after-tax return to 3.92 percent. Therefore, in five years, the $10,000 bonus in the normal savings account will be worth $9,181 after taxes.
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15 Points 15 Points 15 Points
(Diversifying Portfolios MC)
Name of Stock Symbol High Low Close
Stock A A 105.19 103.25 103.38
Stock B B 145.18 43.28 144.05
Last year, an investor purchased 120 shares of stock A at $90 per share and 35 shares of stock B at $145 per share. What is the difference in overall loss or gain between selling at the current day's high price or low price?
A The difference in overall gain is $299.30.
B The difference in overall loss is $299.30.
C The difference in overall gain is $293.90.
D The difference in overall loss is $293.90.
Answers
the answer is option C: The difference in overall gain is $293.90.
How to solve the question?
To calculate the difference in overall loss or gain, we need to calculate the current value of the investor's portfolio for both high and low prices and then compare the two values.
First, let's calculate the current value of the investor's holdings for stock A:
High price: 120 shares x $105.19 per share = $12,623.80
Low price: 120 shares x $103.25 per share = $12,390.00
Next, let's calculate the current value of the investor's holdings for stock B:
High price: 35 shares x $145.18 per share = $5,080.30
Low price: 35 shares x $43.28 per share = $1,514.80
Now we can calculate the total current value of the investor's portfolio:
High price: $12,623.80 + $5,080.30 = $17,704.10
Low price: $12,390.00 + $1,514.80 = $13,904.80
The difference between the two values is:
High price: $17,704.10 - ($120 x $90) - ($35 x $145) = $299.30
Low price: $13,904.80 - ($120 x $90) - ($35 x $145) = $293.90
Therefore, the answer is option C: The difference in overall gain is $293.90.
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Select all of the following that are potential roots of
p(x)=x²-9x²
- 4x + 12?
00
00
+2
NI ###
+4
+9
O +3
+6
+12
Answers
The potential roots of the function p(x) = x² - 9x² - 4x + 12 are x = 1, -1.5, and 12.
What is the degree of a polynomial?Degree of a polynomial is the highest power of the variable in that polynomial. For example, in a cubic polynomial, the variable [[tex]\bold{x}[/tex]] has the highest power of 3.
Given is the following function with degree of 2 as -
We will plot the graph and find the roots of this function. The number of x - intercepts [coordinates where the graph cuts the x axis] will give us the roots or zeroes of the polynomials. Refer to the graph attached, it shows that the graph intercepts the x - axis at three different coordinates which are → x = 1, x = -1.5, and x = 12. Hence, these three values of [x] are the potential roots of the function p(x) = x² - 9x² - 4x + 12.
Therefore, the potential roots of the function p(x) = x² - 9x² - 4x + 12 are x = 1, -1.5, and 12.
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The potential roots of the given polynomial equation are +4 and -3. These roots are found by factoring the equation, setting each factor equal to zero and solving for x.
Explanation:To find the potential roots of the polynomial equation p(x) = x² - 9x - 12, we can set the equation to zero and solve for x: 0 = x² - 9x - 12.
Next, we look for the factors of 12 which when multiplied would give you -12 and when subtracted would give you 9. There we have -4 and +3. Therefore the factors of the equation are (x - 4)(x + 3) = 0.
So, Final answer:
The potential roots of the given polynomial equation are +4 and -3. These roots are found by factoring the equation, setting each factor equal to zero and solving for x.
Explanation:To find the potential roots of the polynomial equation p(x) = x² - 9x - 12, we can set the equation to zero and solve for x:
0 = x² - 9x - 12.
Next, we look for the factors of 12 which when multiplied would give you -12 and when subtracted would give you 9. There we have -4 and +3. Therefore the factors of the equation are (x - 4)(x + 3) = 0.
So, potential roots of the equation are x = 4 and x = -3 if we set each factor equal to zero and solve for x. This means that from the given options, the potential roots to the equation would be +4 and -3 (though -3 is not mentioned). of the equation are x = 4 and x = -3 if we set each factor equal to zero and solve for x. This means that from the given options, the potential roots to the equation would be +4 and -3 (though -3 is not mentioned).
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[4x2+(5+1)] devide 2 =
Answers
Answer:
7
Step-by-step explanation:
[4x2+(5+1)] ÷ 2
[8+(6)] ÷ 2
14 ÷ 2
7
Is (-1, -3) a solution to this system of equations?
16x - 7y = 5
x = -1
yes
no
Answers
Answer:
Yes, it is
Step-by-step explanation:
The volume of a cube is increasing at a rate of 56 in∧3/sec. At what rate is the length of each edge of the cube changing when the edges are 6 in. long? (Recall that for a cube,
V = x∧3.)
Answers
Answer: The rate at which the length of each edge is changing is approximately 0.5185 inches per second when the edges are 6 inches long.
Step-by-step explanation:
Let's denote the volume of the cube as V and the length of each edge as x. Given that the volume of a cube is V = x^3, we can find the rate at which the length of each edge is changing.
We're given that the rate of change of the volume is dV/dt = 56 in³/sec. We want to find the rate of change of the length of each edge, which is dx/dt, when the length of each edge is 6 inches.
First, we differentiate the volume equation with respect to time t:
V = x^3
dV/dt = d(x^3)/dt
Using the chain rule:
dV/dt = 3x^2 * (dx/dt)
Now, we know that dV/dt = 56 in³/sec and x = 6 in. Plugging these values into the equation, we get:
56 = 3 * (6)^2 * (dx/dt)
Solving for dx/dt:
56 = 108 * (dx/dt)
dx/dt = 56 / 108
dx/dt ≈ 0.5185 in/sec (rounded to four decimal places)
So, the rate at which the length of each edge is changing is approximately 0.5185 inches per second when the edges are 6 inches long.
A rectangle has a length of x + 4 cm and a width of 2x − 7 cm.
(a) If the perimeter is 36cm, what is the value of x?
(b) What is the area of this rectangle
Answers
Answer:
the value of x is 7
Step-by-step explanation:
First, find the half of the perimeter that is 36 divided by 2 which is 18
Next, write like this
18= l+w( length = width)
which means you have to get the sum of 18
so try sums of 18 randomly like
17 + 1
11 + 7
16+2 etc
but the thing is the value of x must be the same it must not be different so
11 + 7 will be suitable because
11 = 7 + 4
7 = 2 x 7 - 7 = 7
and to find the area which is l x b
11 x 7= 77sq. cm
please mark me the brainliest and a thanks too
Answer:
x=7
Step-by-step explanation:
7+4=11(2)=22
2(7)-7= 14-7= 7(2)=14
22+14=36
The base of a triangle is 6 inches more than 4 times the height. If the area of the triangle is 90 square
inches, find the base and height.
Answers
The height of the triangle is 6 inches and the base of the triangle is 30 inches.
How can we find the height of the triangle ?Let's denote the height of the triangle as h inches. According to the given information, the base of the triangle is 6 inches more than 4 times the height, which can be expressed as 4h + 6 inches.
The formula for the area of a triangle is given by the formula A = (1/2) * base * height. Substituting the given values, we have:
90 = (1/2) * (4h + 6) * h
To solve for h, we can first multiply both sides of the equation by 2 to eliminate the fraction:
180 = (4h + 6) * h
Next, we can distribute the h on the right-hand side:
[tex]180 = 4h^2 + 6h[/tex]
Rearranging the equation to form a quadratic equation in standard form:
[tex]4h^2 + 6h - 180 = 0[/tex]
Now, we can solve this quadratic equation for h using factoring, completing the square, or the quadratic formula. Let's use the quadratic formula:
The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions for x are given by:
[tex]x = (-b ± \sqrt{(b^2 - 4ac)) / (2a)}[/tex]
In our equation, a = 4, b = 6, and c = -180. Plugging in these values, we get:
[tex]h = (-6 ± \sqrt{(6^2 - 4 * 4 * -180)} ) / (2 * 4)[/tex]
Simplifying further:
[tex]h = (-6 ± \sqrt{(36 + 2880)} ) / 8h = (-6 ± \sqrt{(2916)} ) / 8[/tex]
h = (-6 ± 54) / 8
Now we can find the two possible values for h:
h1 = (-6 + 54) / 8 = 48 / 8 = 6
h2 = (-6 - 54) / 8 = -60 / 8 = -7.5
Since height cannot be negative in this context, we discard the solution h2 = -7.5.
So, the height of the triangle is 6 inches.
Now, we can use this value of h to find the base of the triangle:
Base = 4h + 6 = 4 * 6 + 6 = 24 + 6 = 30 inches.
So, the height of the triangle is 6 inches and the base of the triangle is 30 inches.
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What is the slope of the line
Answers
Step-by-step explanation:
Look at the points (0,-3) and ( 3,0)
slope, m = rise / run = 3 / 3 = 1
Answer:
1
Step-by-step explanation:
y=x+3
PLS HELP DUE AT 11:59PM TODAY
Math mugshot….probability
Answers
The probability of spinning a number less than 5 is P =70%
How to find the probability?To find the probability just take the quotient between the number of numbers that are smaller than 5, and the total amount in the spinner. That is because we assume that all the regions have the same individual probability of being spun.
There are 10 in total, and of these, 7 are smaller than 5, then the probability is:
P= 7/10 = 0.7
And to write as a percent, multiply it by 100%
0.67*100% = 70%
That is the probability.
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100 Points! Two multiple choice algebra questions. Photo attached. Thank you!
State the domain and range of the function.
Stats the end behavior of the function.
Answers
Answer:
7.D
8.A
Step-by-step explanation:
For the function f(x) = √x+2+5:
(D) D= {x|x≥2}, R= {y|y≥5}
The domain is restricted to x values greater than or equal to 2 because the function contains the square root of x+2, which cannot be negative. The range starts at y = 5 because the lowest possible output of the function is √2+2+5 = 5.
(A) f(x)+∞o as x→ +∞o; f(x) +∞ as x――∞
As x approaches positive infinity, the output of the function approaches infinity as well. As x approaches negative infinity, the function is undefined since it involves taking the square root of negative numbers. However, the limit of the function as x approaches negative infinity from the right is positive infinity.
Find the value of x. Then find the area of the triangle.
Answers
Step-by-step explanation:
first of all, remember, the sum of all angles in a triangle is always 180°.
now, we see that both bottom angles are 45°.
that means
180 = 45 + 45 + top-angle
90° = top-angle
aha ! we are dealing with a right-angled triangle, that is also isoceles (both legs are equally long, because the angles with the baseline are equal).
via Pythagoras
c² = a² + b²
where "c" is the Hypotenuse (the side opposite of the 90° angle), "a" and "b" are the legs.
in our case both legs are 7×sqrt(2) units long.
so,
baseline² = (7×sqrt(2))² + (7×sqrt(2))² = 49×2 + 49×2 =
= 98 + 98 = 196
baseline = sqrt(196) = 14 units
x is now the height of this triangle, and because of the isoceles form, it splits the baseline exactly in half.
so, one side of the baseline from x is 14/2 = 7 units.
and now Pythagoras for that sub-triangle :
(7×sqrt(2))² = 7² + x²
98 = 49 + x²
49 = x²
x = sqrt(49) = 7 units
the area of the triangle is
baseline × height / 2
in our case
14 × 7 / 2 = 7×7 = 49 units²
100 POINTS + BRAINLIEST
A teacher hires a coach for a school trip. The cost is worked out using the
formula C =
m
3 + 40, where C is the cost in pounds and m is the number of
miles the coach travels.
(a) Calculate how much it would cost to hire the coach to travel a distance of
42 miles.
b) If the cost of the hire is £75,how many miles does the coach travel?
Answers
C = (42/3) + 40
C = 14 + 40
C = 54
Therefore, it would cost £54 to hire the coach to travel a distance of 42 miles.
(b) To calculate the number of miles the coach travels for a cost of £75, we need to rearrange the formula to make m the subject:
C = m/3 + 40
m/3 = C - 40
m = 3(C - 40)
Now we can substitute C = £75 into the formula:
m = 3(75 - 40)
m = 3(35)
m = 105
Therefore, the coach would travel 105 miles for a cost of £75.
Answer:
(a) To calculate how much it would cost to hire the coach to travel a distance of 42 miles, we can substitute m = 42 into the formula and solve for C:
C = (42/3) + 40
C = 14 + 40
C = 54
Therefore, it would cost £54 to hire a coach to travel 42 miles.
(b) To find how many miles the coach travels if the cost of the hire is £75, we can set the formula equal to 75 and solve for m:
75 = (m/3) + 40
35 = m/3
m = 105
Therefore, the coach travels 105 miles if the cost of the hire is £75.
What is the numerical coefficient in the expression 2x³y?
Answers
Answer:
2
Step-by-step explanation:
The numerical coefficient is the number that is multiplied to a variable.
Example.
2x^2 + 7y^3
The numerical coefficients would be 2 and 7.
So for your problem it would be 2 since 2 is the number being multiplied to x and y.
Elijah is using a ladder to hang decorations for the holidays outside. He places the ladder 4 feet from the base of tree so he can reach a branch that is 12 feet from the ground. What is the angle of elevation of the ladder?
Round to the nearest tenths place if necessary.
Answers
The angle of elevation of the ladder is approximately 71.6 degrees.
What is the angle of elevation?To find the angle of elevation of the ladder, we can use trigonometry. The ladder forms a right triangle with the ground and the tree.
The base of the triangle is 4 feet, the height is 12 feet, and the hypotenuse is the length of the ladder.
Using the trigonometric function tangent (tan), we can write:
tan(angle) = opposite/adjacent
In this case, the opposite side is the height of the tree (12 feet) and the adjacent side is the base of the triangle (4 feet).
Therefore, we can calculate the angle of elevation as follows:
tan(angle) = 12/4
angle = arctan(12/4)
Using a calculator or a trigonometric table, we can find that arctan(12/4) is approximately 71.6 degrees.
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NO LINKS!! URGENT HEL PLEASE!!!
Use tests for symmetry to determine which graphs from the lists below are symmetric with respect to the y-axis, the x-axis, and the origin. (Select all that apply)
a. symmetric with respect to the y-axis
Answers
Using the tests for symmetry, the following are symmetric with respect to y-axis:
y = - x + 7y = - 7x²x = - y² + 9How to determine symmetricity?A graph is symmetric with respect to the y-axis if replacing x with -x produces an equivalent equation.
A graph is symmetric with respect to the x-axis if replacing y with -y produces an equivalent equation.
A graph is symmetric with respect to the origin if replacing x with -x and y with -y produces an equivalent equation.
(a) symmetric with respect to the y-axis:
y = 7x - 4 (no)
y = - x + 7 (yes)
y = - 7x² (yes)
y = 6x² - 9 (no)
x = 1/4 × y² (no)
x = - y² + 9 (yes)
y = - 1/6 × x³ (no)
y = x³ - 1 (no)
y = √(x) (no)
y = √(x) - 6 (no)
Therefore, the graphs that are symmetric with respect to the y-axis are:
y = - x + 7
y = - 7x²
x = - y² + 9
None of the graphs are symmetric with respect to the x-axis or the origin.
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The measure of an angle formed by two tangents to a circle is 80°. The radius of the circle is 8
centimeters. How far is the vertex of the angle from the center of the circle to the nearest centimeter?
Answers
Answer: So the vertex of the angle is located at the center of the circle, which is 8 centimeters away from the nearest centimeter.
Step-by-step explanation:
Let O be the center of the circle, and let A and B be the points of tangency of the two tangents with the circle. Since OA and OB are radii of the circle, they have the same length of 8 centimeters.
Let C be the vertex of the angle formed by the two tangents. Since the tangents are perpendicular to the radii at the points of tangency, we have that angle AOC = angle BOC = 90 degrees.
Since the measure of the angle formed by the two tangents is 80 degrees, we have that angle AOB = 180 - 80 - 80 = 20 degrees.
Let D be the foot of the perpendicular from C to line AB. Then angle OCD = 90 - 20/2 = 80 degrees, so triangle OCD is an isosceles triangle. Therefore, we have that OD = OC = 8 centimeters.
Finally, since triangle OCD is a right triangle, we can use the Pythagorean theorem to find the length of CD. We have:
CD^2 = OD^2 - OC^2 = 8^2 - 8^2 = 0
Therefore, CD = 0 centimeters.
So the vertex of the angle is located at the center of the circle, which is 8 centimeters away from the nearest centimeter.
100 Points! Algebra question, only looking for an answer to B. Photo attached. Please show as much work as possible. Thank you!
Answers
F/g • x
Fx/g is the answer.
Apply the fraction rule:
[tex]\text{a}\times\dfrac{\text{b}}{\text{c}} =\dfrac{\text{a}\times\text{b}}{\text{c}}[/tex]
Answer:
[tex]\longrightarrow\boxed{\bold{\frac{\text{fx}}{\text{g}}}}[/tex]
if h(x)=x+2/x-2, then dy/dx=? A. x-2 B. -5/2 C. 1/(x-2)². D. none
Answers
1/(x-2)². The correct option is C
What is quotient rule ?The quotient rule is a formula used in calculus to find the derivative of a function that is the quotient of two other functions. Specifically, it gives the formula for finding the derivative of a function of the form f(x) = g(x) / h(x), where g(x) and h(x) are both functions of x.
We can use the quotient rule to find the derivative of h(x):
h(x) = (x+2)/(x-2)
h'(x) = [ (x-2)(1) - (x+2)(1) ] / (x-2)^2 (apply quotient rule)
Simplifying the numerator, we get:
h'(x) = [ x-2 - x-2 ] / (x-2)^2
h'(x) = -4 / (x-2)^2
Therefore, the answer is (C) 1/(x-2)².
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You need to cut the strongest beam out of a log with a diameter of 18 in. The strength of a wooden beam is directly proportional to the product of its width and the square of its height. What are the dimensions of the strongest beam? Find the exact value and then round your answer to the nearest hundredth.
Need answers ASAP
Answers
The dimensions of the strongest beam are 27 inches x 13.5 inches.
What is a dimension?In general, dimension refers to a measurable extent of a physical quantity, such as length, width, height, depth, or time. These dimensions provide a framework for describing and measuring objects and events in the physical world. In geometry, dimension are refers to the number of coordinates needed to specify a point in a space. In physics, the concept of dimension is used to describe the properties of space and time.
We know that the strength of the beam is directly proportional to its width multiplied with the square of its height. Let's call the width of the beam "w" and the height "h". Then we can write the strength of the beam as:
S = kwh², where "k" is the constant of proportionality.
We want to find the dimensions of the strongest beam, which means we want to find the values of "w" and "h" that will maximize the strength "S". To do this, we need to find the maximum value of the function S = kwh² subject to the constraint that the diameter of the log is 18 inches.
The diameter of the log is equal to the width of the beam plus twice the height of the beam:
d = w + 2h
Since the diameter of the log is 18 inches, we can write:
w + 2h = 18
or
w = 18 - 2h
Substituting this expression for "w" into the equation for the strength of the beam, we get:
S = k × w(18-2h) × h²
Expanding and simplifying this expression, we get:
S = 36kh³ - 2kh⁴
To find the maximum value of S, we take the derivative of S with respect to h and set it equal to zero:
dS/dh = 108kh² - 8kh³ = 0
Simplifying this expression, we get:
h²(108 - 8h) = 0
This equation has two solutions: h = 0 and h = 13.5.
Since a beam with height equal to zero would have zero strength, we reject the solution h = 0. Therefore, the maximum strength is achieved when h = 13.5 inches.
To find the corresponding width, we can use the equation we derived earlier:
w = 18 - 2h = 18 - 27 = -9
Since the width of the beam cannot be negative, we reject this solution as well.
Therefore, the required dimensions of the strongest beam are:
Width = 2h = 2(13.5) = 27 inches
Height = h = 13.5 inches
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A sphere has a volume of approximately 1332 cubic feet.
What is the radius of the sphere?
Round your answer to the nearest tenth if needed.
1
feet
Answers
Answer:
[tex] \frac{4}{3} \pi {r}^{3} = 1332[/tex]
[tex]r = \sqrt[3]{ \frac{1332}{ \frac{4}{3}\pi } } = 6.8[/tex]
The radius of this sphere is about 6.8 feet
100 points! Algebra question, photo attached. Please show as much work as possible. Thank you!
Answers
Given:
[tex]\sqrt{z+5}+4\leq 13[/tex]
Move 4 to the right side:
[tex]\sqrt{z+5}\leq 9[/tex]
Simplify
[tex]z+5 \leq 81[/tex]
Move 5 to the right side:
[tex]z\leq 76[/tex]
Find singularity points
Find non-negative values for radicals: [tex]z\geq -5[/tex]
Combine the intervals
[tex]z\leq 76 \ \text{and} \ z\geq -5[/tex]
Merge overlapping intervals
[tex]-5\leq z\leq 76[/tex]
Answer:
[tex]\longrightarrow \boxed{\bold{-5\leq z\leq 76}}[/tex]nasim is working two summer jobs making $9 per walking dogs and $8 per hour cleaning tables. Nasim must earn no less than $130 this week. Write an inequality that would represent the possible values for the number of hours walking dogs d and the hours cleaning tables c that nasim can work in a given week
Answers
The inequality that would represent the possible values for the number of hours walking dogs is 9d + 8c ≥ 130
How can the inequality be written?Inequalities in mathematics can be described as one that is been used in the expression of the relationship between two values that are not equal
It should be noted thed that Inequality implies not equal with the symbol (≠)” symbols ≥ < > ≤. From the question , number of hours walking dogs (d) Let number of hours clearing tables an be represented by( c) Hence the appropriate inequality is 9d + 8c ≥ 130.
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Select the expression that represents this real-world situation.
There are p people on the bus. At the next stop, 8 people get off and 5 more get on. Write an expression to show how many people are on the bus.
p − 8 + 5
p + 8 − 5
p x (8 + 5)
p ÷ (8 − 5)
Answers
The expression that represents the real-world situation is "p - 8 + 5". It simplifies to "p - 3" and represents the final number of people on the bus.
What is an expression?An expression is a combination of numbers, symbols, and/or operators that represents a quantity, a value, or a computation. Expressions can include variables, which are letters that represent unknown values, and can be manipulated and evaluated using mathematical operations like addition, subtraction, multiplication, and division. Expressions can be simple or complex, and they are used in various areas of mathematics, including algebra, calculus, and geometry, as well as in many other fields such as physics, engineering, and economics.
According to the given information:The expression that represents the real-world situation is:
p - 8 + 5
Explanation:
Initially, there are p people on the bus. Then, 8 people get off, which is represented by the subtraction of 8 from p (p - 8). After that, 5 more people get on the bus, which is represented by adding 5 to p - 8, giving us the final expression: p - 8 + 5. This expression simplifies to p - 3, which represents the final number of people on the bus.
Therefore, The expression that represents the real-world situation is "p - 8 + 5". It simplifies to "p - 3" and represents the final number of people on the bus.
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