So, we can express matrix B as a linear combination of matrices A1 and A2 as shown above.
How do mathematical matrices work?An arrangement of integers into rows and columns is called a rectangular matrix. Every single number in a matrix is referred to as a "matrix element" or "entry." The example matrix, designated as A, has two rows and three columns.
To express matrix B as a linear combination of matrices A1, A2, and A3, we need to find coefficients x, y, and z such that:
B = xA1 + yA2 + z*A3
Substituting the matrices B, A1, A2, and A3 into this equation, we get the following system of linear equations:
x + z = 1
x - y + z = 1
-3x + y + z = 0
x + y + z = 1
Solving this system of equations, we get:
x = 1/2
y = 1/2
z = 0
Therefore, we have:
B = (1/2)*A1 + (1/2)A2 + 0A3
Substituting the values of A1, A2, and A3, we get:
B = (1/2)[1 0] + (1/2)[0 1] + 0*[1 -1]
= [1/2 1/2]
So, we can express matrix B as a linear combination of matrices A1 and A2 as shown above.
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We can write B as a linear cοmbinatiοn οf A1, A2, and A3 as:
B = 2 A2 + A3
What is a linear cοmbinatiοn οf matrices?In linear algebra, a linear cοmbinatiοn οf matrices is a sum οf scalar multiples οf thοse matrices. That is, given matrices A1, A2, ..., An and scalars c1, c2, ..., cn, their linear cοmbinatiοn is defined as:
c1A1 + c2A2 + ... + cnAn
Tο write B as a linear cοmbinatiοn οf A1, A2, and A3, we need tο sοlve the system οf linear equatiοns:
x1 A1 + x2 A2 + x3 A3 = B
where x1, x2, and x3 are the cοefficients οf the linear cοmbinatiοn.
Rewriting the matrix equatiοn, we get:
x1 + x3 = 1
x1 - x3 = 1
-3x1 + x2 + x3 = -3
x2 + x3 = 1
Sοlving this system οf equatiοns, we get:
x1 = 0
x2 = 2
x3 = 1
Therefοre, we can write B as a linear cοmbinatiοn οf A1, A2, and A3 as:
B = 2 A2 + A3
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please answer this question!!
The maximum height of the ball from the maximum compression of the spring is 13.39 m
What is maximum height?Maximum height is the highest displacement of the object.
How to find the maximum height of the ball?Since a spring of spring constant 504 N/m is compressed 7.66 cm by a ball of mass 11.2 g. If the ball is shot straight into the air, we desire the maximum height of the ball.
Using the law of conservation of energy, the elastic potential energy lost by the spring, E equals the gravitational potential energy gained by the ball, E'
So, E = E'
1/2kx² = mgh where
k = spring constant = 504 N/mx = compression of spring = 7.66 cm = 0.0766 mm = mass of ball = 11.2 g = 0.0112 kgg = acceleration due to gravity = 9.8 m/s² and h = maximum height of ballMaking h subject of the formula, we have that
h = kx²/2mg
So, substituting the values of the variables into the equation, we have that
h = kx²/2mg
h = 504 N/m × (0.0766 m)²/(2 × 0.0112 kg × 9.8 m/s²)
= 504 N/m × 0.00586756 m²/(2 × 0.0112 kg × 9.8 m/s²)
= 2.95725024 Nm/(0.21952 kgm/s²)
= 13.47 m
So, the maximum height from the springs compression is H = h - x = 13.47 - 0.0766 m
= 13.3934 m
≅ 13.39 m
So, the maximum height is 13.39 m
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The function that assigns every positive three-digit integer the sum of the largest and the smallest digits.
State the number of elements in the Domain and Range for this part only
Answer:
17 numbers in this range.
Step-by-step explanation:
For this function, the domain consists of all positive three-digit integers. There are 900 such integers, from 100 to 999.
The range consists of all numbers between 2 and 18, inclusive, since the smallest possible sum is 1+0+0 = 1 and the largest possible sum is 9+9+1 = 19, but the function only takes the sum of the largest and smallest digits. There are 17 numbers in this range.
Answer:
Step-by-step explanation:
The domain of this function consists of all positive three-digit integers. There are 900 three-digit integers in total, from 100 to 999 inclusive.
The range of this function consists of all integers between 2 and 18 inclusive, since the smallest and largest digits of a three-digit integer can range from 1 to 9, and their sum can range from 2 (1 + 1) to 18 (9 + 9). So the range has 17 elements in total: {2, 3, 4, ..., 18}.
Sketch the parabola, clearly labelling the points corresponding the vertex, x-intercepts and y-intercepts: (leave the vertex values in the form of a fraction). This may also help with 8a, remember that we want to use graphs to solve non-linear inequalities.
y=6x^2-17x+12
We kindly invite to see the image attached below to know the representation of the parabola according to its features.
How to graph a parabola
A parabola is the graphic representation of any quadratic equation, that is, a polynomial of the form y = a · x² + b · x + c, where a, b, c are real coefficients. An alternative presentation is the vertex form:
y - k = C · (x - h)²
Where:
C - Vertex constanth, k - Coordinates of the vertex.The procedure to sketch the parabola according to its features is described below:
Determine the y-intercept.Determine the x-intercepts.Determine the coordinates of the vertex.Add the points on Cartesian plane.Match the points by a single curve.Step 1 - Determine the y-intercept:
y = 6 · 0² - 17 · 0 + 12
y = 12
Step 2 - Determine the x-intercepts.
6 · x² - 17 · x + 12 = 0
6 · [x² - (17 / 6) · x + 2] = 0
6 · (x - 3 / 2) · (x - 4 / 3) = 0
x = 3 / 2 or x = 4 / 3
Step 3 - Determine the coordinates of the vertex:
y = 6 · x² - 17 · x + 12
y = 6 · [x² - (17 / 6) · x + 2]
y + 6 · (1 / 144) = 6 · [x² - (17 / 6) · x + 2 + 1 / 144]
y + 1 / 24 = 6 · [x² - (17 / 6) · x + 289 / 144]
y + 1 / 24 = 6 · (x - 17 / 12)²
(h, k) = (17 / 12, - 1 / 24)
Steps 4 & 5 - Add the points on Cartesian plane and match the resulting curve.
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At 8am it was -6c the temperature risen 13c what was the temperature by noon
Answer:
7 degress celcius
Step-by-step explanation:
What are the the x-intercepts for the graph of y = cos(x) over the interval [- 2pi, 2pi]
the x-intercepts will be -π/2, -3π/2, π/2, 3π/2.
What is Trigonometric Functions?
Trigonometry uses six fundamental trigonometric operations. Trigonometric ratios describe these operations. The sine function, cosine function, secant function, co-secant function, tangent function, and co-tangent function are the six fundamental trigonometric functions. The ratio of sides of a right-angled triangle is the basis for trigonometric functions and identities. Using trigonometric formulas, the sine, cosine, tangent, secant, and cotangent values are calculated for the perpendicular side, hypotenuse, and base of a right triangle.
The x-intercepts are locations on the coordinate plane where the y-value of the ordered pair is 0.
y = cos(x)
so the x-intercepts will be -π/2, -3π/2, π/2, 3π/2.
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Cómo puedo resolver
-17=x/64
Answer:
x= −1088
Step-by-step explanation:
Answer:
-1088
Step-by-step explanation:
-17 = x/64
*64 *64
-1088 = x
The equation of your model is y=0.122x
'The y -intercept is zero. Should it be? Explain
Yes, The y - intercept is zero because it cannot intercept at any point on y - axis.
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
The equation of your model is,
⇒ y = 0.122x
Here, The y - intercept is zero.
Since, The slope intercept form of equation of line is,
⇒ y = mx + b
Where, 'm' is slope and 'b' is y - intercept.
By comparing with the given equation, We get;
The y - intercept is zero.
And, By graph it cannot intercept at any point on y - axis.
Hence, The y - intercept is zero because it cannot intercept at any point on y - axis.
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Please Someone smart help me with this!!
a) The linear function is defined as follows: y = 1 - 0.2x.
b) The slope and the intercepts are interpreted as follows:
The slope indicates that the power decreases by 20% per hour.The x-intercept indicates that the battery lasts 5 hours.The y-intercept indicates that the battery power is at 100% when you turn on the laptop.c) The battery power is at 75% after 1.25 hours.
How to define a linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
m is the slope, representing the rate of change.b is the intercept, representing the value of y when x = 0.The graph touches the y-axis at y = 1, hence the intercept b is given as follows:
b = 1.
From the x-intercept, when x increases by 5, y decays by 1, hence the slope is given as follows:
m = -1/5
m = -0.2.
Hence the function is:
y = -0.2x + 1.
The battery power is of 75% = 0.75 when y = 0.75, as follows:
0.75 = -0.2x + 1
0.2x = 0.25
x = 0.25/0.2
x = 1.25 hours.
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8. The top of a building is 20 feet tall. If a fireman has a ladder that is 24 feet long, how far out
does the ladder need to be placed from the bottom of the wall to reach the top of the
building?
Answer: 480
Step-by-step explanation:
20 times 24 is 480
At the Culver City Trampoline Park, customers leave their shoes in cubbies shaped like rectangular prisms while they jump. Each cubby is 11 inches deep, 6 inches tall, and has a volume of 396 cubic inches.
How wide is each cubby?
At the Culver City Trampoline Park, customers leave their shoes in cubbies shaped like rectangular prisms while they jump. Each cubby is 11 inches deep, 6 inches tall, and has a volume of 396 cubic inches. So, each cubby is 6 inch wide.
What is volume?Three-dimensional space is quantified by volume. It is frequently expressed as a numerical value using SI-derived units, other imperial units, or American customary units.
Every object in three dimensions takes up that space. The volume of that kind of area is the one being measured. The area covered by such an object's boundaries in three-dimensional space generally said to as the volume. Other term for it would be an object's capacity.
Given that,
Each cubby is 11 inches deep,
6 inches tall, and
has a volume of 396 cubic inches.
Volume of rectangular prism = L × W × h
or, 396 = 11 × W × 6
or, W = 396 / 66
or, W = 6 inch
Thus, each cubby is 6 inch wide.
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What is the solution to this question?
Answer:
Step-by-step explanation:
To solve the equation (-1)/(x-5) = 2/(x+4), we can start by cross-multiplying:
(-1)(x+4) = 2(x-5)
Expanding both sides and simplifying, we get:
-x - 4 = 2x - 10
Bringing all the x terms to one side and all the constant terms to the other, we get:
3x = 6
Dividing both sides by 3, we get:
x = 2
So the solution to the equation is x = 2. However, we need to check if this value of x makes the denominators of the original equation non-zero. Plugging x = 2 into the original equation, we get:
(-1)/(2-5) = 2/(2+4)
Simplifying, we get:
1/3 = 1/3
Since both sides are equal, the solution x = 2 satisfies the original equation. Therefore, the only solution to the equation is x = 2.
Answer: x = 2
Step-by-step explanation:
[tex]\boldsymbol{\sf{The\:exercise\:is \longmapsto \ \dfrac{-1}{x-5}=\dfrac{2}{x+4} }}[/tex]
We cross multiply.
-(x + 4) = 2(x - 5)
We apply the multiplicative law of distribution.
-x -4 = 2(x - 5)
-x - 4 = 2x - 10
We rearrange the unknown terms to the left side of the equation.
-x - 2x = -10 + 4 <===Combine as terms===> -3x = -10 + 4
We calculate -10 + 4 = -6.
-3x = -6
We divide both sides of the equation by the coefficient of the variable.
[tex]\boldsymbol{\sf{x=\dfrac{-6}{-3} \iff \ x=\dfrac{6}{3} }}[/tex]
x = 2
4. Aziz grows vegetables in his garden. of the vegetables grow underground. Of these underground vegetables, are potatoes. What fraction of all the vegetables are potatoes? 5 If there are 70 vegetables altogether, how many potatoes are there?
A fraction of [tex]\frac{1}{7}[/tex] of all the vegetables are potatoes.
If there are 70 vegetables altogether, then there are 10 potatoes.
What are Fractions?Fractions are type of numbers which are written in the form p/q, which implies that p parts in a whole of q.
Here p, called the numerator and q, called the denominator, are real numbers.
Some of the values are missing here.
Given that,
Aziz grows vegetables in his garden.
Let the total number of vegetables be x.
Assuming [tex]\frac{1}{2}[/tex] of the vegetables grow underground.
Number of underground vegetables = [tex]\frac{1}{2}[/tex] x
Assuming, [tex]\frac{2}{7}[/tex] of these underground vegetables, are potatoes.
Number of potatoes = [tex]\frac{2}{7}[/tex] × ( [tex]\frac{1}{2}[/tex] x ) = [tex]\frac{1}{7}[/tex] x
So, [tex]\frac{1}{7}[/tex] of all the vegetables are potatoes.
If there are 70 vegetables altogether,
Number of potatoes = [tex]\frac{1}{7}[/tex] x = [tex]\frac{1}{7}[/tex] × 70 = 10
Hence of the total vegetables of 70, 10 are potatoes.
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Find the indicated measure in parallelogram ABCD m
In the parallelogram ABCD the measure of ∠BEC is obtained as 113°.
What is a parallelogram?
A quadrilateral with two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Additionally, the interior angles that are additional to the transversal on the same side.
It is given that ABCD is a parallelogram.
The measure of ∠EAD = 30°.
The measure of ∠EDA = 37°.
In the parallelogram ∠EBC = ∠EDA as they form alternate interior angles pair.
Similarly, ∠ECB = ∠EAD as they form alternate interior angles pair.
The measure of ∠ECB = 30°.
The measure of ∠EBC = 37°.
Since EBC forms a triangle, so the sum of the angles of a triangle is 180°.
The equation is -
∠ECB + ∠EBC + ∠BEC = 180°
Substitute the values into the equation -
30° + 37° + ∠BEC = 180°
67° + ∠BEC = 180°
∠BEC = 180° - 67°
∠BEC = 113°
Therefore, the measure of ∠BEC = 113°.
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The population of Placerville grew from 4360 a decade ago to 6590 today.
Answer: To find the percent increase in population, I used the following formula:
percent increase = (new value - old value) / old value * 100
In this case, the old value was the population from a decade ago (4360), and the new value was the current population (6590). So plugging these values into the formula, we get:
percent increase = (6590 - 4360) / 4360 * 100
percent increase = 51.38%
So the population of Placerville increased by approximately 51.38% over the past decade. The population of Placerville has increased by (6590 - 4360) = 2230 people over the past decade.
Step-by-step explanation:
- Corey has a piece of teak wood that is three times as long as his piece of oak wood. He
says that he can use two different equations to find out how long his piece of teak wood is
compared to his piece of oak wood. Is he correct? Explain your reasoning.
The equation and solution to find the length of mis teak wood piece is x/3=8 and 24;
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas;
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely;
We are given:
The length of oak wood is 8inches
Teak wood/3= oak wood
So,
Let the length of teak wood be x;
Now,
x/3=8
x=3x8
x=24
Therefore, by algebra the length of teak wood will be 24;
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please help me
here is the picture I need step by step
Hence, the graph of g is upward than the graph of f.
What is the function?Functions are often defined by a formula that describes a combination of arithmetic operations and previously defined functions; such a formula allows computing the value of the function from the value of any element of the domain.
Here given that,
The functions are
f(x) = 2^x
g(x) = f(x) + 6
so, g(x) = 2^x + 6
Draw the graphs of both the equation
The graph of the g is differ from f because in the graph of g it is upward than the graph of f .
Hence, the graph of g is upward than the graph of .
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Question
Write "negative one and two thousandths" as a decimal.
Provide your answer below:
Y=4x-22 substitution method
2x+3y=4
The x and y values are x=5 and y= -2
What is the solution to an equation?
In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.
y=4x-22 ----(1)
2x+3y=4------(2)
Substitute (1) into (2)
=> 2x+3(4x-22)=4
=> 2x+12x-66 = 4
=> 14x = 4+66
=> 14x = 70
=> x=70/14 = 5
(1) => y=4*5-22 = 20 - 22 = -2
So, the x and y values are x=5 and y= -2
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One of the lamp posts at a shopping center has a motion detector on it, and the equation (x+16)2 + (y-13)² = 36 describes the boundary within which motion can be sensed. What is the greatest distance, in feet, a person could be from the lamp and be detected? A. 6 ft B. 12 ft C. 36 ft D. 72 ft
The greatest distance, in feet, a person could be from the lamp and be detected is: B. 12 ft
How to find the greatest distance?The equation (x+16)² + (y-13)² = 36 describes a circle with center (-16,13) and radius 6. The motion detector on the lamp post can detect motion within this circle.
To find the greatest distance a person could be from the lamp and still be detected, we need to find the diameter of the circle, which is equal to twice the radius. Therefore, the greatest distance a person could be from the lamp and still be detected is 2(6) = 12 feet.
Therefore, the correct answer is B) 12 ft.
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Nolan Arenado has 593 at-bats in the 2021 season. He had 151 hits and 81 runs. Which of the following shows the correct calculation of his batting average
The correct calculation of the average is given as 0.2546
How to solve for the averageThe average is a measure of central tendency that represents the typical value in a set of data. It is also known as the arithmetic mean and is calculated by adding up all the values in a set of data and then dividing the sum by the total number of values in the set.
The calculation of the average would be gotten by the number of hits / by the total bats that he had
This is given as
151 / 593
= 0.2546
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PLEASE HELP THIS IS DUE IN AN HOUR
an art supplies store sells boxes that contain colored pencils and markers.
Each box has a colored pencil to marker ratio of 5 to 2. Complete the table
or the missing number of colored pencils, markers, or total number of
colored pencils and markers in each box for sale.
*it's in box like | blank | 20 | blank |.... so on so fourth. also the blanks are what I need to figure out*
Boxes for sale
||||||||||||||||||||||||||||||||||||||||||
Number of Colored | blank | 20 | blank |
Pencils | | | |
||||||||||||||||||||||||||||||||||||||||||
Number of Markers | 6 | blank | blank |
| | | |
Total Number of ||||||||||||||||||||||||||||||||||||||||||||
Colored Pencils and | blank | blank | 70 |
Markers in the Box |||||||||||||||||||||||||||||||||||||||||||||
Answer:
Using the ratio given, we know that for every 5 colored pencils, there are 2 markers in each box.
Therefore:
The first blank represents the number of colored pencils in the box. Since the ratio of colored pencils to markers is 5 to 2, we can calculate that there are 5 colored pencils for every 2 markers. This means that for each box, there are 5/7 of the total number of items are colored pencils. So the missing value in the first row is 35.
The second row indicates that there are 20 items in the box. We know that the first row (colored pencils) has 35 items, and since the total number of items in the box is 20, the missing value in the second row (markers) is 20 - 35/7 = 15.
The third row represents the total number of colored pencils and markers in each box. We know that there are 35 colored pencils and 15 markers in each box, so the total number of items in each box is 50.
Therefore, the completed table would be:
Boxes for sale
||||||||||||||||||||||||||||||||||||||||||
Number of Colored | 35 | 20 | 35 |
Pencils | | | |
||||||||||||||||||||||||||||||||||||||||||
Number of Markers | 6 | 15 | 6 |
| | | |
Total Number of ||||||||||||||||||||||||||||||||||||||||||||
Colored Pencils and | 41 | 35 | 50 |
Markers in the Box |||||||||||||||||||||||||||||||||||||||||||||
11) If the time is now 14:46pm. What time will it be in 2 hours and 24 minutes from now?
Answer: 17:20pm
Step-by-step explanation: If you add 24 minutes to 14:46, that gives you 15:20pm. Add the 2 hours. So your answer is 17:20pm
What is the height of the statue?
SEE ATTACHED.
Answer:
x ≈ 2.7 m
Step-by-step explanation:
since the 2 triangles are similar then the ratios of corresponding sides are in proportion, that is
[tex]\frac{x}{1.6}[/tex] = [tex]\frac{4}{2.4}[/tex] ( cross- multiply )
2.4x = 4 × 1.6 = 6.4 ( divide both sides by 2.4 )
x = [tex]\frac{6.4}{2.4}[/tex] = 2.6666...
height of statue x ≈ 2.7 m ( to 1 decimal place )
A mail-order computer business has six telephone lines. Let X denote the number of lines in use at a specified time. Suppose the pmf of X is as given in the accompanying table.
x 0 1 2 3 4 5 6
p(x) 0.12 0.18 0.20 0.20 0.20 0.07 0.03
Calculate the cdf F(x).
x 0 1 2 3 4 5 6
f(x)
Use the graph to calculate the probabilities of the events given below.
(a) {at most three lines are in use}
(b) {fewer than three lines are in use}
(c) {at least three lines are in use}
(d) {between two and five lines, inclusive, are in use}
The probability of the event between two and five lines, inclusive, are in use is 0.85.
What is the probability?Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.
Given that,
x 0 1 2 3 4 5 6
p(x) 0.12 0.18 0.20 0.20 0.20 0.07 0.03
a) At most three lines are in use
Here we need to find the probability for x≤3.
P(x≤3)=P(x=0)+P(x=1)+P(x=2)+P(x=3)
= 0.12+0.18+0.20+0.20
= 0.70
b) Fewer than three lines are in use
Here we need to find the probability for x<3.
P(x<3)=P(x=0)+P(x=1)+P(x=2)
= 0.12+0.18+0.20
= 0.50
c) At least three lines are in use
Here we need to find the probability for x≥3.
P(x≥3)=P(x=3)+P(x=4)+P(x=5)+P(x=6)
= 0.20+0.20+0.07+0.03
= 0.50
d) Between two and five lines, inclusive, are in use
Here we need to find the probability for 2≤x≤5.
P(2≤x≤5)= P(x=2)+P(x=3)+P(x=4)+P(x=5)
= 0.18+0.20+0.20+0.20+0.07
= 0.85
Therefore, the probability of the event between two and five lines, inclusive, are in use is 0.85.
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The point (-5, -10) is reflected across the x-axis. What are the coordinates of this reflection?
(Impossible) Twelve men are on a desert island. They all have identical weights except for one of them, who is either slightly lighter or slightly heavier than the others.
The only other thing on the island is a seesaw. There are no scales or means to measure weight otherwise. Can you determine which man has the different weight? You only get to use the seesaw three times.
Answer:
Yes, it is possible to determine which man has the different weight by using the seesaw three times. Here is one possible method
Divide the 12 men into three groups of four: A, B, and C.
Weigh group A against group B on the seesaw. (First use)
If the seesaw balances, then the odd man is in group C. Otherwise, he is in the heavier or lighter group (A or B).
Take two men from group C and weigh them against two men from group A or B that were balanced. (Second use)
If the seesaw balances again, then the odd man is one of the remaining two men from group C. Otherwise, he is one of the two men from group C that were weighed.
Weigh one of the suspected men against any other man. (Third use)
If the seesaw balances, then the odd man is the other one. Otherwise, he is the one that was weighed.
This method works because it eliminates half of the possible candidates at each step and identifies whether the odd man is heavier or lighter by comparing him with known balanced men.
Step-by-step explanation:
2. Answer the following questions:
a. Determine the exact value of the expression: tan (cos-¹ (-16/19)). Make sure your answer is in simplified
radical form.
b. Explain why sin-¹ (tan 2π/3) does not have an answer.
Answer:
a. The exact value of tan(cos⁻¹(-16/19)) in simplified radical form is -3/16.
b. sin⁻¹(tan(2π/3)) is undefined and does not have an answer.
Tan and Sine Identities.a. We know that cos(cos⁻¹(x)) = x and hence cos(cos⁻¹(-16/19)) = -16/19.
Let θ = cos⁻¹(-16/19), then we have
cos(θ) = -16/19 and
sin(θ) = √(1 - cos²(θ))
= √(1 - (16/19)²)
= 3/19 (using the Pythagorean identity).
Now, we can use the identity tan(θ) = sin(θ)/cos(θ) to find the value of tan(cos⁻¹(-16/19)):
tan(cos⁻¹(-16/19))
= sin(θ)/cos(θ)
= (3/19) / (-16/19)
= -3/16.
Therefore, the exact value of tan(cos⁻¹(-16/19)) is -3/16 in simplified radical form.
b. The range of the function tan(x) is (-∞, ∞), which means that it can take any value. However, the range of the function sin⁻¹(x) is [-π/2, π/2], which means that it can only take values between -π/2 and π/2. In particular, sin⁻¹(x) is not defined for |x| > 1, since there is no angle whose sine is greater than 1 or less than -1.
Let's consider sin⁻¹(tan(2π/3)). We know that tan(2π/3) is undefined, since the tangent function has vertical asymptotes at odd multiples of π/2 (including 2π/3).
Therefore, sin⁻¹(tan(2π/3)) is also undefined and does not have an answer.
Learn more on trigonometry identities here https://brainly.com/question/24496175
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Solve (x – 3)2 = 49. Select the values of x.
Answer:
27.5
Step-by-step explanation:
(x – 3)2 = 49
(x – 3) = 49/2
(x – 3) = 24.5
x = 27.5
A grocery store buys soda at wholesale price for $1.25. The retail price has a 20% markup. Find the retail price.
Answer: 48%
Step-by-step explanation:
Draw a graph for f(x)= 2^x-3
Answer:
graph linked
Step-by-step explanation: