As per the triangle, the length of the other, shorter leg is 3.46 units.
We know that a is twice the length of b, so we can write:
a = 2b
We also know that c is the square root of three times b, or:
c = √3b
Now, let's say we're given the length of the longer leg, a. We can use our equation a = 2b to solve for b:
a = 2b
b = a/2
So, we know that the shorter leg is half the length of the longer leg. For example, if a is 8, then b is 4.
To double-check our answer, we can use the equation for the hypotenuse:
c = √3b
c = √3(4)
c = 2√3 = 3.46
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Find the lateral area of the following
cone. Leave your answer in terms of pi.
12 cm
5 cm
LA = [?]π cm²
Hint: Lateral Area of a Cone = Tre
Where & slant height
The lateral surface-area of the cone with dimensions 12 cm height and 5 cm radius is 65π cm² using the formula πrl.
What is surface-area?
The overall surface area of a solid shape, item, or three-dimensional figure.It can have a flat or curved surface. Cone and cylinder surfaces are curved, but those of solid structures like the cube and cuboid have flat surfaces. The surface area of the cube is provided by 6 times side times side, which equals the area of each face side times side. The cube and cuboid have 6 faces, 12 equal edges, and 8 corners or vertices.
Given that the dimensions of cone:
Radius(r)=5 cm
Height(h) = 12 cm
slant height l =[tex]\sqrt{r^{2} +h^{2} }[/tex]
=[tex]\sqrt{(5)^{2} +(12)^{2} }[/tex]
=[tex]\sqrt{25+144}[/tex]
=[tex]\sqrt{169}[/tex]
=13 cm
Slant height (l) = 13 cm
lateral area of cone= πrl.
=π (5) (13)
=65 π cm²
The lateral surface area of cone=65 π cm²
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PLS HELP! Will give brainliest :)
The formula =C6*D6 would be found in which cell of this spreadsheet?
The formula C6*D6 can be found in the cell E6. Option A is the correct answer.
What is cell in a spreadsheet?A spreadsheet cell is a square region in a grid that can hold text, numbers, or formulas as well as other types of data. A unique cell address, which comprises of a column letter and a row number, is used to identify each cell. For instance, cell C4 is the cell in the third column and fourth row, and cell A1 is the top-left cell in the spreadsheet. Users can enter data, format cells, and use formulas to conduct calculations on the cells in a spreadsheet, among other tasks.
The formula C6*D6 can be found in the cell E6. Option A is the correct answer.
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1. 76x8. 2. 84x9
3. 68x4
4. 32x6 PART 1
5. 59x7
6. 74x8
7. 68x8
8. 95x9
9. 84x5
10. 22x4
11. 48x5
12. 84x8
13. 76x9
14. 89x9
15. 63x5
16. 32x9
17. 63x8
18. 79x9
19. 78x5
20. 49x4
21. 94x6
The arithmetic sequence is 49 x 4 = 196, 94 x 6 = 564.
What is arithmetic sequence?
An arithmetic sequence is a sequence of numbers in which each term after the first is found by adding a fixed constant number, called the common difference, to the preceding term.
1. 76 x 8 = 608
2. 84 x 9 = 756
3. 68 x 4 = 272
4. 32 x 6 = 192
PART 2
5. 59 x 7 = 413
6. 74 x 8 = 592
7. 68 x 8 = 544
8. 95 x 9 = 855
9. 84 x 5 = 420
10. 22 x 4 = 88
11. 48 x 5 = 240
12. 84 x 8 = 672
13. 76 x 9 = 684
14. 89 x 9 = 801
15. 63 x 5 = 315
16. 32 x 9 = 288
17. 63 x 8 = 504
18. 79 x 9 = 711
19. 78 x 5 = 390
20. 49 x 4 = 196
21. 94 x 6 = 564
Therefore, The arithmetic sequence is 49 x 4 = 196, 94 x 6 = 564
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Given: sin (alpha) =(5)/(13) in Quadrant I and cos(beta) = (-12)/(13) in Quadrant II; evaluate the following expression:
sin(alpha + beta ) =
1) -120/169
2) -1
3) 0
If sin (α) =(5)/(13) in Quadrant I and cos(β) = (-12)/(13) in Quadrant II, then sin(α + β ) = -120/169 .So, the answer is option 1).
To evaluate sin(α + β), we can use the trigonometric identity:
sin(α + β) = sin α cos β + cos α sin β
First, we need to find cos α. Since sin α is positive and in Quadrant I, we can use the Pythagorean identity to find cos α:
cos α = √(1 - sin² α) = √(1 - (5/13)²) = √(1 - 25/169) = √(144/169) = 12/13
Next, we need to find sin β. Since cos β is negative and in Quadrant II, we can use the Pythagorean identity to find sin β:
sin β = -√(1 - cos² β) = -√(1 - (-12/13)²) = -√(1 - 144/169) = -√(25/169) = -5/13
Now we have all the values we need to evaluate sin(α + β):
sin(α + β) = sin α cos β + cos α sin β
= (5/13)(-12/13) + (12/13)(-5/13)
= -60/169 - 60/169
= -120/169
Therefore, the answer is option 1) -120/169.
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Logan takes a trip to an amusement park and rides a Ferris wheel. The graph below shows the height, in feet above the ground, of his car over time, t, measured in minutes. Write an equation in terms of y, height in feet above the ground, and t, time in minutes, to represent the given context.
We can write the equation as:
y = 80 sin(2π/5 t) + 280
How can we calculate?
Finding the oscillation's period will help us get started. Since the height repeats every five minutes, it appears from the graph that the period is five minutes.
The distance between the oscillation's highest and lowest points, or its amplitude, can then be determined. Given that 80 feet separate the highest and lowest points on the graph, it appears that the amplitude is 80 feet.
We determine the vertical shift of the graph, which is the height of the Ferris wheel when t = 0. From the graph, it appears that the vertical shift is 280 feet, since that is the height of the car when t = 0.
Putting it all together, we can write the equation as:
y = 80 sin(2π/5 t) + 280
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PLS HELP 30 PTSS
FOOL ANSWERS WILL BE REPORTED AND GOOD WILL BE GAVE BRAINLYEST
Answer: 59 degrees
Step-by-step explanation:
A triangle has a total of 180 degrees so we subtract that by the values we already know the get the last angle.
180-31-90= 59 degrees
a youth soccer coach much choose 4 of his 8 players to go into a game. in how many ways can this be done?
mass of water vapor (g) / volume of air (m^3)
is the humidity measure of....
-the mixing ratio.
-relative humidity.
-vapor pressure.
-absolute humidity.
Mass of water vapor (g) / volume of air (m^3) is the humidity measure of absolute humidity
The humidity measure of "mass of water vapor (g) / volume of air (m^3)" is called absolute humidity. Absolute humidity is a measure of the total amount of moisture in the air, expressed as the mass of water vapor per unit volume of air. It is different from relative humidity, which is a measure of the amount of moisture in the air relative to the maximum amount of moisture that the air can hold at a particular temperature.
Mixing ratio is also a measure of the amount of moisture in the air, but it is expressed as the mass of water vapor per mass of dry air, not per unit volume of air. Vapor pressure is a measure of the pressure exerted by water vapor in the air, expressed in units of pressure (such as millibars or pascals), not as a ratio.
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What is the Hardy-Weinberg equation and what does each part mean?
The Hardy-Weinberg equation is a mathematical formula used to calculate the frequency of alleles (alternative forms of genes) in a population.
It states that the frequency of alleles and genotypes in a population will remain constant from generation to generation in the absence of other evolutionary influences.
The equation is expressed as: p² + 2pq + q² = 1
In this equation, p represents the frequency of the dominant allele in the population, and q represents the frequency of the recessive allele.
The superscripts 2 represent the proportion of individuals in the population that are homozygous for that allele (meaning they have two copies of the same allele), while the 2pq term represents the proportion of individuals that are heterozygous (meaning they have one copy of each allele).
The sum of these terms is always equal to 1, as it represents the entire population.
This equation assumes several conditions: that the population is large, randomly mating, with no mutations, migration, natural selection, or genetic drift.
In reality, these conditions are rarely met, and the Hardy-Weinberg equation serves as a useful model for understanding how allele frequencies can change over time due to various evolutionary influences.
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0.4x+2.9=1.5 solve for x
Answer:
x= -3.5
Step-by-step explanation:
0.4x+2.9= 1.5
-2.9. -2.9
(0.4/0.4)x= -1.4/0.4
x= -3.5
By solving the given equation 0.4x + 2.9 = 1.5, the value of x is -3.5
In the given equation, we have one variable of 'x' with a constant value of 0.4 and two non-variable values of 2.9 and 1.5.
To solve the given equation, we have to transfer the non-variable values to either the L.H.S (Left Hand Side) or R.H.S (Right Hand Side) of the equation. After transferring the non-variable values, we will solve it by dividing it by the constant value of the given variable as shown below:
0.4x + 2.9 = 1.5
0.4x = 1.5 - 2.9
0.4x = -1.4
x = [tex]\frac{-1.4}{0.4}[/tex]
x = -3.5
By solving the above equation, we can conclude that the value of x in equation 0.4x + 2.9 = 1.5 is -3.5
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WORTH 35 PTS, HELP
how do you factor completely:
4x^2 + 20x + 200 = 0
it’s a quadratic equation..
the 4x is squared
The factored form of the equation 4x² + 20x + 200 = 0 is 4(x + (5/2) +-5/2+√7(5/2i))(-5/2+√7(-5/2i))
To factor completely, we can begin by factoring out the greatest common factor of the three terms, which is 4:
4(x² + 5x + 50) = 0
Next, we want to factor the quadratic expression in parentheses.
we can use the quadratic formula, which states that the solutions to the equation ax² + bx + c = 0 are given by:
x = (-b ± √(b² - 4ac)) / 2a
In this case, a = 1, b = 5, and c = 50, so we have:
x = (-5 ± √(5² - 4(1)(50))) / 2(1)
x = (-5 ± √(-175)) / 2
x=-5/2+√7(5/2i)
x=-5/2+√7(- 5/2i)
The factored form of the equation 4x² + 20x + 200 = 0 is:
4(x + (5/2) +-5/2+√7(5/2i))(-5/2+√7(-5/2i))
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13PLEASE HELP ME THIS IS URGENT I WILL GIVE BRAINLIEST ALL FAKE ANSWERS WILL BE REPORTED AND PLS PLS PLS EXPLAIN THE ANSWER OR HOW U GOT IT PLEASE AND TY
The approximate shortest distance, to the art hundredth of a foot, between first and third base is 127.28 feet.
What is distance?Distance refers to the amount of space between two objects or points. It can be measured in units such as meters, kilometers, miles, or feet, and is commonly used to describe the length or extent of a journey, path, or separation.
According to the given information:
The distance between first and third base in a baseball diamond is the diagonal of the square with side lengths of 90 feet. Using the Pythagorean theorem, we can calculate this distance as follows:
d² = 90² + 90²
d²= 8,100 + 8,100
d² = 16,200
d = √(16,200)
d ≈ 127.28 feet
Therefore, the approximate shortest distance, to the nearest hundredth of a foot, between first and third base is 127.28 feet. The correct answer is option (b).
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The Udderly Delicious Cheese Factory produces 200 blocks of cheddar cheese and 200 blocks of Swiss cheese each day. The factory uses 5 quarts of milk to make a block of cheddar cheese and 6 quarts of milk to make a block of Swiss cheese. How many total gallons of milk does the factory use each day?
the Udderly Delicious Cheese Factory uses a total of 550 gallons of milk each day to produce 200 blocks of cheddar cheese and 200 blocks of Swiss cheese.
How to calculate the question?
To calculate the total gallons of milk used by the Udderly Delicious Cheese Factory each day, we need to determine the total quarts of milk used to produce 200 blocks of cheddar cheese and 200 blocks of Swiss cheese.
For the cheddar cheese production, we know that each block requires 5 quarts of milk, so for 200 blocks, the factory would need:
200 blocks x 5 quarts/block = 1000 quarts of milk
For the Swiss cheese production, we know that each block requires 6 quarts of milk, so for 200 blocks, the factory would need:
200 blocks x 6 quarts/block = 1200 quarts of milk
To find the total quarts of milk used by the factory each day, we can add the amount of milk used for cheddar cheese production to the amount used for Swiss cheese production:
1000 quarts + 1200 quarts = 2200 quarts
To convert quarts to gallons, we divide the total quarts by 4, since there are 4 quarts in 1 gallon:
2200 quarts / 4 = 550 gallons
Therefore, the Udderly Delicious Cheese Factory uses a total of 550 gallons of milk each day to produce 200 blocks of cheddar cheese and 200 blocks of Swiss cheese.
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Let f be a function with first derivative given by fâ²(x)=x(xâ5)2(x+1). At what value of x does f have a relative minimum? 0 only -1 only -1 and 0 only -1, 0, and 5 only 0 and 5 only -1 and 5 only 5 only
At x=0 only, the function f with first derivative f'(x) = x(x-5)²(x+1) has a relative minimum.
Hence the correct option is (A) 0 only.
The first derivative of the function is,
f'(x) = x(x-5)²(x+1)
Differentiating the function with respect to x we get, The second derivative of the function is,
f''(x) = x(x-5)².(1) + x(x+1).2(x-5) + (x-5)²(x+1).1 = (x-5)² (x+x+1) + 2x(x+1)(x-5) = (x-5)²(2x+1) + 2x(x+1)(x-5)
Now, f'(x) = 0 gives,
x(x-5)²(x+1) = 0
We know that if product of more than one terms is zero then either of them is zero.
Either, x=0
Or, (x-5)² = 0
x-5 = 0
x = 5
Or, x+1 = 0
x = -1
So the extremum points of the function are, x = -1, 0, 5.
At x=-1, f''(-1) = (-6)²(-2+1) + 2(-1)(-1+1)(-6) = -36
At x=0, f''(0) = (-5)²*1 + 0 = 25
At x=5, f''(5) = 0 + 0 = 0
Since the value of second derivative is positive at only x = 0.
Thus, at x = 0 only the function has a relative minimum.
Hence the correct option is (A).
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Create two different algebraic expressions involving c and d that are worth 24.
c = 4.25
d = 3.75
Answer:
2c + 3d = 24. For c = 4.25 and d = 3.75, we have 2(4.25) + 3(3.75) = 8.5 + 11.25 = 19.75
and
c^2 + d^2 = 24. For c = 4.25 and d = 3.75, we have 4.25^2 + 3.75^2 = 18.0625 + 14.0625 = 32.125
Step-by-step explanation:
There are many possible algebraic expressions involving c and d that are worth 24, but two possibilities are:
2c + 3d = 24. For c = 4.25 and d = 3.75, we have 2(4.25) + 3(3.75) = 8.5 + 11.25 = 19.75, which is not equal to 24. Therefore, this expression is not true for the given values of c and d.
c^2 + d^2 = 24. For c = 4.25 and d = 3.75, we have 4.25^2 + 3.75^2 = 18.0625 + 14.0625 = 32.125, which is not equal to 24. Therefore, this expression is also not true for the given values of c and d.
It is important to note that there are many
How do solve 2,125x365
Use a calculator to solve this problem!
Answer:
Step-by-step explanation:
775625 is the correct answer
Número que sumado da 4 y multiplicado 5
Answer:
Aquí respondemos a la pregunta: "¿Qué dos números se multiplican por 4 y suman 5?"
La respuesta a tu pregunta es:
1 y 4
A continuación ilustramos y demostramos que 1 y 4 se multiplican por 4 y suman 5:
1 × 4 = 4
1 + 4 = 5
¿Estás preguntando porque estás tratando de averiguar cómo factorizar la siguiente ecuación cuadrática?
x2 + 5x + 4 = 0
Si es así, la solución para factorizar la ecuación cuadrática anterior es:
(x+1) (x+4)
Para resumir, dado que 1 y 4 se multiplican por 4 y suman 5, sabes que lo siguiente es cierto:
x2 + 5x + 4 = (x + 1 ) (x + 4)
Step-by-step explanation:
Elroy designs a platform for the new memorial at the local park. The platform is in the shape of a right trapezoidal prism. The base of the prism has an area of 4f * t ^ 2 and the prism stands 3. 2 feet high. As Elroy paints the platform, he calculates the surface area of the stand to be 7f * t ^ 2 (a) Elroy is asked to purchase roping that will be used to close off the area around the memorial. He purchases a length that is five times the perimeter of the platform in roping How much roping does he purchase? Show all work. (b) Elroy plans to add gold leaf to the sides of the platform but not to the two bases. What percent of the area of the platform will have gold leaf? Round your answer to the nearest whole number. Show all work
a) Elroy needs to purchase 5 times the Perimeter feet of roping.
b) About 48% of the surface area of the platform will have gold leaf.
(a) To find the perimeter of the trapezoidal prism, we need to find the lengths of all four sides. Let's call the shorter base of the trapezoid "b1", the longer base "b2", and the height "h". Then we have:
b1 = [tex]\sqrt{4ft^{2} }[/tex] = 2t[tex]\sqrt{f}[/tex]
b2 = b1 + 2h = 2t[tex]\sqrt{f}[/tex] + 2(3.2) = 2t[tex]\sqrt{f}[/tex] + 6.4
h = 3.2
The perimeter is then:
P = b1 + b2 + 2h = 2t[tex]\sqrt{f}[/tex] + 6.4 + 2(3.2) = 2t[tex]\sqrt{f}[/tex] + 12.8
So Elroy needs to purchase 5P feet of roping:
5P = 5(2t[tex]\sqrt{f}[/tex] + 12.8) = 10t[tex]\sqrt{f}[/tex] ) + 64
(b) The total surface area of the trapezoidal prism is:
A = 2(b1+b2)h + 2b1t = 2(2t[tex]\sqrt{f}[/tex] + 2t[tex]\sqrt{f}[/tex] + 6.4)(3.2) + 2(2t[tex]\sqrt{f}[/tex] )(t) = 12.8t[tex]\sqrt{f}[/tex] + 25.6f[tex]t^{2}[/tex]
The area that will have gold leaf is the lateral surface area, which is:
[tex]A_{lateral}[/tex] = (b1 + b2)h = (2t[tex]\sqrt{f}[/tex] + 2t[tex]\sqrt{f}[/tex] + 6.4)(3.2) = 20.48t[tex]\sqrt{f}[/tex]
So the percentage of the area that will have gold leaf is:
([tex]A_{lateral}[/tex] / A) x 100% = (20.48t[tex]\sqrt{f}[/tex] / (12.8t[tex]\sqrt{f}[/tex] + 25.6f[tex]t^{2}[/tex])) x 100%
Simplifying:
([tex]A_{lateral}[/tex] / A) x 100% = (20.48 / (12.8 + 25.6/[tex]t^{2}[/tex])) x 100%
Using the given values of f = 1/2 and t = 2, we get:
([tex]A_{lateral}[/tex] / A) x 100% = (20.48 / (12.8 + 25.6/4)) x 100% ≈ 48%
Therefore, about 48% of the surface area of the platform will have gold leaf.
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I need to find the area please help
Answer:
It is trapizium so the area can be calculated as
[tex] \frac{1}{2} (6ft + 8ft) \times 5ft \\ = {35ft}^{2} [/tex]
u can solve area of trapizium by
1/2(a+b)h
and when you solve it u get the answer 35ft^2
A composite figure is formed with two cones and a cylinder.
What is the surface area of the composite figure?
32 cm
26 cm
12 cm
15 cm
A 5127.56 cm²
B
C
D
3317.52 cm²
1056 cm²
4222.30 cm²
Answer:is this an actual question
Step-by-step explanation:
What are the solutions to the equation 9x2 = 36?
Answer: x = 2 and x = -2.
Step-by-step explanation:
The solutions to the equation 9x^2 = 36 can be found by first dividing both sides by 9, giving x^2 = 4. Then, taking the square root of both sides gives x = ±2. Therefore, the solutions are x = 2 and x = -2.
Answer:
Step-by-step explanation:
9x^2 = 36 | :9
x^2 = 4
x=+-2
In the xy-plane, how many horizontal or vertical tangent lines does the curve xy2=2+xy have?
The curve xy²=2+xy has two horizontal or vertical tangent lines, namely x = 2/3 and y = -1/3, and x = -1/3 and y = 1/3.
To find the horizontal or vertical tangent lines of the curve xy²=2+xy, we need to take the derivative with respect to x and y and solve for when the derivative equals zero.
Taking the derivative with respect to x, we get:
y^2 + 2xy(dy/dx) = y(dy/dx) + 2x
Simplifying, we get
(dy/dx)(y^2 - y) = 2x - y^2
Taking the derivative with respect to y, we get
2xy + x(dy/dy)(2y) = dy/dy + x
Simplifying, we get
(dy/dy)(x-2y) = 1-x
Setting both derivatives equal to zero, we have
(dy/dx)(y^2 - y) = 2x - y^2 ...(1)
(dy/dy)(x-2y) = 1-x ...(2)
From (2), we get
dy/dy = (1-x)/(x-2y)
Substituting into (1), we get
(1-x)/(x-2y)(y^2 - y) = 2x - y^2
Simplifying, we get
y^3 - 3xy^2 + (2x^2-1)y + x = 0
This is a cubic equation in y, which can have up to three solutions. To find the horizontal or vertical tangent lines, we need to set dy/dx = 0 or dy/dy = 0.
Setting dy/dx = 0, we get
2x - y^2 = 0
Setting dy/dy = 0, we get
x - 2y = 1
Solving these equations simultaneously, we get
x = 2/3 and y = -1/3 or x = -1/3 and y = 1/3
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The given question is incomplete, the complete question is:
In the xy-plane, how many horizontal or vertical tangent lines does the curve xy²=2+xy have?
Expand the expressions and simplify. 5(x + 4) 3(x + 2) = Question 1 options: a. 8x + 4b. 6x + 18 c. 8x + 26d. 7x - 18
Answer:
(✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿)
To expand and simplify 5(x + 4) 3(x + 2), we can use the distributive property of multiplication over addition which states that a(b + c) = ab + ac.
So, we have:
5(x + 4) 3(x + 2) = (5x + 20)(3x + 6)
Now, we can use the distributive property again to expand this expression:
(5x + 20)(3x + 6) = 5x * 3x + 5x * 6 + 20 * 3x + 20 * 6
= 15x^2 + 90x + 60
Therefore, the answer is 15x^2 + 90x + 60.
I hope this helps!
(✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿)
Hi
6. Sebastian recorded the price of gas each month for 12 months.
a. Draw a trend line on the scatter plot.
b. If the trend continues, what equation can he use to predict
the price of gas in future months?
Gas Price ($)
N
4
O
Gas Price
2 4 6 8 10 12
Month
X
The trend line for the y = 0.5x + 2 is attached accordingly. Note that the the predicted gas price for month 13 would be $8.50.
What is the explanation for the above response?a. To draw a trend line on a scatter plot, you need to perform a linear regression analysis. This involves finding the line of best fit that passes through the data points. The equation for a linear regression line is typically of the form y = mx + b, where y is the dependent variable (gas price in this case), x is the independent variable (month), m is the slope of the line, and b is the y-intercept.
Once you have the equation for the line of best fit, you can plot it on the scatter plot to visualize the trend. The slope of the line will tell you the direction and steepness of the trend (i.e., whether prices are increasing or decreasing, and how quickly).
b. To predict future values using the trend line, you can simply plug in the value of the independent variable (month) for the month you want to predict, and solve for the dependent variable (gas price). For example, if the equation for the trend line is y = 0.5x + 2, and you want to predict the gas price for month 13, you would plug in x = 13 and solve for y:
y = 0.5(13) + 2
y = 6.5 + 2
y = 8.5
So the predicted gas price for month 13 would be $8.50.
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What are the zeros of the function f (x) = (2x +6)(x - 4)?
Answer:
x = - 3 , x = 4
Step-by-step explanation:
to find the zeros let f(x) = 0 , that is
(2x + 6)(x - 4) = 0
equate each factor to zero and solve for x
2x + 6 = 0 ( subtract 6 from both sides )
2x = - 6 ( divide both sides by 2 )
x = - 3
x - 4 = 0 ( add 4 to both sides )
x = 4
the zeros are x = - 3 , x = 4
explain each step in the process of finding the area of a circle given the circumfrence
Answer:
Divide the circumference by [tex]2\pi[/tex]Square the remaining numberMultiply the resulting value by [tex]\pi[/tex]Step-by-step explanation:
Recall that the formula for the circumference of a circle is:
[tex]2\pi r[/tex]
Also recall that the formula for the area of a circle is:
[tex]\pi r^2[/tex]
Both formulas use the radius; one squares it, while the other doubles it.
Let's start by turning the formula for the circumference of a circle into the formula for the area of a circle. We start off with:
[tex]2\pi r[/tex]
We want to square the radius, but we can't do that without squaring everything else, too, so let's get rid of the other terms.
Divide the circumference by [tex]2\pi[/tex]:
[tex]2\pi r\\\frac{2\pi r}{2\pi } =\\r[/tex]
Now, we can square r:
[tex]r\\r^2[/tex]
Now, all we have to do is multiply by pi:
[tex]r^2\\\pi r^2[/tex]
We now have the area.
Let's look back at out steps.
First, we divided the circumference by [tex]2\pi[/tex].
Next, we squared the number we had left (the radius).
Finally, we multiplied by [tex]\pi[/tex].
A 40% tip on a 36.53 meal
Answer:
$14.612
Step-by-step explanation:
40% = 0.4
Find a 40% tip on a 36.53 meal.
We Take
36.53 x 0.4 = $14.612
So, the tip is $14.612
9. A solid iron rectangular block of dimensions 3.5 meters, 2.4 meters, and 2 meters is cast into a hollow cylindrical pipe of internal radius 27 centimeters and thickness 4 centimeters. Find the length of the pipe.
Therefore, The length of the hollow cylindrical pipe is approximately 55.48 meters.
To solve this problem, we will first find the volume of the solid iron rectangular block and then use it to find the length of the hollow cylindrical pipe. Here are the steps:
1. Find the volume of the rectangular block:
Volume = Length × Width × Height
Volume = 3.5m × 2.4m × 2m = 16.8 m³
2. Convert the internal radius and thickness to meters:
Internal radius = 27 cm = 0.27 m
Thickness = 4 cm = 0.04 m
3. Calculate the external radius of the pipe:
External radius = Internal radius + Thickness
External radius = 0.27m + 0.04m = 0.31m
4. Let L be the length of the pipe. We can write the volume of the hollow pipe as:
Volume = π × (External radius² - Internal radius²) × Length
16.8 m³ = π × (0.31² - 0.27²) × L
5. Solve for L:
L = 16.8 m³ / [π × (0.31² - 0.27²)]
L ≈ 55.48 meters
Therefore, The length of the hollow cylindrical pipe is approximately 55.48 meters.
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anyone know these?? i need help
Answer:
[tex]\frac{12}{5}[/tex] = 12 ÷ 5
[tex]\frac{1}{4}[/tex] = 1 ÷ 4
[tex]\frac{3}{8}[/tex] = 3 ÷ 8
[tex]\frac{9}{2}[/tex] = 9 ÷ 2
Alma took out a subsidized student loan of $10,925 at a 10.8% APR,
compounded monthly, to pay for her last 2 semesters of college. If she will
begin paying off the loan in 15 months, how much will she owe when she
begins making payments?
A. $10,925.00, since Alma is responsible for the interest on the loan
that accrues before she starts making payments
B. $10,925.00, since the government is responsible for the interest
on the loan that accrues before Alma starts making payments
C. $12,496.52, since Alma is responsible for the interest on the loan
that accrues before she starts making paymelins
D. $12,496.52, since the government is responsible for the interest on
the loan that accrues before Alma starts making payments
If she will begin paying off the loan in 15 months, . The amount she will she owe when she begins making payments is: C. $12,496.52, since Alma is responsible for the interest on the loan that accrues before she starts making payments.
What is the face value?The formula to calculate the future value of a loan with monthly compounding interest is:
FV = PV * (1 + r/12)^n
where:
PV = present value of the loan
r = annual interest rate
n = number of months
Using this formula, we can calculate the amount that Alma will owe when she begins making payments:
PV = $10,925
r = 10.8% APR = 0.9% monthly interest rate
n = 15 months
FV = $10,925 * (1 + 0.009)^15 = $12,496.52
Therefore, the answer is C. Alma is responsible for the interest on the loan that accrues before she starts making payments, and she will owe $12,496.52 when she begins making payments.
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