Which choice represents the fraction below as a single exponential expression? (ap3x)

Main Answer: The total surface area of cylinder B is approximately 476.7  square units.

Supporting Question and Answer:

How is the surface area of a cylinder calculated?

The surface area of a cylinder is the sum of the areas of its curved surface and two circular bases. It can be calculated using the formula:

A = 2πrh + 2π\(r^{2}\)

where "r" is the radius of the circular base, "h" is the height of the cylinder, and π (pi) is a mathematical constant that represents the ratio of the circumference of a circle to its diameter, approximately equal to 3.14159.

The first term, 2πrh, represents the area of the curved surface of the cylinder, while the second term, 2π\(r^{2}\), represents the combined area of the top and bottom circular bases.

Body of the Solution: Let the height and radius of cylinder A be "h" and "r" respectively. Then, the height and radius of cylinder B are "2h" and "R" respectively, since cylinder B has twice the height of cylinder A but the same radius.

The total surface area of a cylinder is given by the formula:

Area = 2πrh + 2π\(r^{2}\)

For cylinder A, we know that the surface area is 180, so we can substitute the values and solve for "r" as follows:

180 = 2πrh + 2π\(r^{2}\)

90 = πrh + π\(r^{2}\)

We can rearrange this equation to solve for r:

r² + rh - 90/π=0

Using the quAdratic formula,we get:

r = (-h ± √((h)² + 4(90/π)))/2

r = -h/2 ± √(h² + 4(90/π))/2

Now we have an expression for r in terms of h . We can use this expression to find the radius of cylinder B, since we know that cylinder B has twice the height of cylinder A.

R = 2r= -h ± √(h² + 4(90/π))

We can use this expression to find the surface area of cylinder B:

Surface area of cylinder B = 2πR² + 2πR(2h)

Surface area of cylinder B= 2π( -h ± √(h² + 4(90/π)))² + 4πh( -h± √(h² + 4(90/π)))

We can use the value we found for 2h using the quadratic formula in the expression to get:

Surface area of cylinder B = 476.7 square units (rounded to one decimal place)

Therefore, the total surface area of cylinder B is approximately 476.7  square units.

Final Answer: Therefore, the total surface area of cylinder B is approximately 476.7  square units.

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The method is: Find the increase and find the ratio of the increase and the old price.

The percentage increase is 20%

A percentage is defined as the ratio that can be expressed as a fraction of 100.

The method below shows how you would calculate the % increase.

First step: Find the increase:

increase = 480 - 400 = $80

Second step: Find the ratio of the increase and the old price and multiply by 100 to express in percentage:

80/400 * 100 = 20%

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Answer: n = -304

Step-by-step explanation:
-304/8 = -38

-17 - (-38) = 21

n = -304

Answer:19.6

Step-by-step explanation:

21/8=2.6

-17-2.6=19.6

The total cost of downloading 20 songs is $45.

The total cost of downloading ss songs is $11 + $1.0ss.

What does the word "cost" mean?

During the manufacturing or production of a company's goods and services, every expense incurred by the company is referred to as a cost.

                            In simplest terms, it is the amount of money that businesses invest in buying and selling goods.

The total cost of the of downloading songs is the sum of the fee per month and the cost of downloading songs.

Total cost of downloading 45 songs = cost per month x cost of downloading 45 songs

$11 + ($1 x 45)

$11 + $45

$56

Total cost of downloading ss songs = $11 + ($1 x ss)

$11 + $1ss

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Answer:

90 degrees

Step-by-step explanation:

as you can see, the blue is a right angle. this means that it is a 90 degree angle :)

Answer:

I think that about 25 degrees it may not be the right anwser thou

Step-by-step explanation:

Answer:

(k-10h) (k+10h)

Step-by-step explanation:

k^2 - 100h^2

Rewriting as

k^2 - (10h)^2

We recognize this as the difference of squares

We know the difference of squares is factored as a^2 -b^2 = (a-b)(a+b)

(k-10h) (k+10h)

Answer:

(k-10h) (k+10h)

Step-by-step explanation:

Answer:

08:05 I think

Step-by-step explanation:

11:50 - 3 hours = 8:50

8:50 - 45 mins = 8:05

The triangle for which angle a =30\degree, angle b=45\degree, and a=20, side a ≈ 20, side b ≈ 28.284, and side c ≈ 38.636

Two angles (a and b) and one side (a) are provided for us to solve the triangle. Let's call the side across from angle a side A, the side across from angle b side B, and the side across from the final angle (angle c) side C.

Here, it is given that,

angle a = 30 degrees

angle b = 45 degrees

side a = 20

angle c = 180 - (angle a + angle b)

angle c = 180 - (30 + 45)

angle c = 180 - 75

angle c = 105 degrees

We know that, a/sin(A) = b/sin(B) = c/sin(C)

a/sin(A) = b/sin(B) = c/sin(C)

20/sin(30) = b/sin(45) = c/sin(105)

b/sin(45) = 20/sin(30)

b = (sin(45) * 20) / sin(30)

b ≈ (0.7071 * 20) / 0.5

b ≈ 14.142 / 0.5

b ≈ 28.284

Now,

c/sin(105) = 20/sin(30)

c = (sin(105) * 20) / sin(30)

c ≈ (0.9659 * 20) / 0.5

c ≈ 19.318 / 0.5

c ≈ 38.636

Thus, side a ≈ 20, side b ≈ 28.284, and side c ≈ 38.636.

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Answer:

1st. supplementary angles

2nd.vertical angles

3rd. angles around a point

4th. complementary angles

Step-by-step explanation:

Answer:

one with circle is angles around a point

120 and 60 supplementary

27 and 63 complimentary

a and b vertical

Step-by-step explanation:

1/2=1/2=1/2.is the value for the given equivalent fraction, by putting the value 3.4 in the numerators respectively

The fractions with distinct numerators and denominators but the same value are said to be equivalent fractions.

For instance, since 2/4 and 3/6 both equal the 1/2, they are identical fractions. An element of a whole is a fraction. The same amount of the whole is represented by equivalent fractions.

1/2 =    /6 =   /8.

a. Multiply numerator and denominator by 3 for equivalenting the equation    /6

Therefore,

3*3/6*3

=9/18

=1/2

therefore:1/2=1/2.

b. Multiply numerator by 4

Therefore,

4/8

=1/2.

Therefore:

1/2=1/2.

1/2=1/2=1/2.

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Answer:

42

Step-by-step explanation:

It’s what I got when I calculated 87.5% out of 48.

I first took both of the numerals- and took them out of 100%

Once I did that- I got 4200:100 when done calculating 87.5 times 48/100

So the answer as a whole would be 42

The supplement of 95 degrees is 85 degrees,

The supplement of an angle is the angle that, when added to the original angle, equals to 180 degrees.

To find the supplement of a given angle, we can simply subtract the angle from 180 degrees.

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Finally, connect the points on the new shape to create the image. It should be congruent to the original shape, but shifted in the direction of the translation vector.

First, plot the original shape on a coordinate grid. Then, identify the translation vector - this tells you how much to shift the shape in each direction. For example, if the translation vector is (2, 3), you would move the shape 2 units to the right and 3 units up.

Next, use the translation vector to plot the new coordinates of each point on the shape. For example, if a point on the original shape is at (3, 4) and the translation vector is (2, 3), the new coordinates for that point would be (5, 7).

I hope that helps! If you have any specific shapes or translations you need help with, feel free to let me know.

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Any whole number can be written as a fraction. All we do is place the number over 1.

For example, the whole number 7 is the same as the fraction 7/1.

If we wanted to multiply the whole number 7 with the fraction 2/3 then...

\(7 * \frac{2}{3}\\\\\frac{7}{1} * \frac{2}{3}\\\\\frac{7*2}{1*3}\\\\\frac{14}{3}\\\\\)

In the jump from the second step to the third step, we multiply straight across. The numerators multiply together. The denominators multiply together. The fraction 14/3 cannot be reduced because 14 and 3 don't have any factors in common other than 1.

9514 1404 393

Answer:

  88.9

Step-by-step explanation:

The relevant trig relation is ...

  Cos = Adjacent/Hypotenuse

  cos(77°) = 20/x

  x = 20/cos(77°)

  x ≈ 88.9

Answer:20

Step-by-step explanation:this is wrong

Answer:

40

Step-by-step explanation:

subtract median of dogs and median of cats

The number of months Mark can have the phone is given by the equation

A = 11.4 months

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the number of months be represented as = A

Now , the equation is

Now , the total amount with Mark = $ 146.43

The initial amount for the smartphone = $ 33

The amount per month for 2GB is = $ 9.95

So , the amount for A months = $ 9.95 ( A )

So , the equation will be

Initial amount for the smartphone + the amount for A months = total amount with Mark

Substituting the values in the equation , we get

33 + 9.95 ( A ) = 146.43   be equation (1)

On simplifying the equation , we get

Subtracting 33 on both sides of the equation , we get

9.95 ( A ) = 113.43

Divide by 9.95 on both sides of the equation , we get

A = 11.4 months

Therefore , the value of A is 11.4 months

Hence , the number of months is 11.4 months

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Answer:

The proportion of red candies is 60/100.

Step-by-step explanation:

Given that sixty out of every 100 pieces of candy is red, to determine which indicates the proportion of red candies, the following calculation must be performed:

60 red candies out of 100 total candies

60/100

Therefore, the ratio of red candies is 60/100.

Answer:

Hope it helps you

Step-by-step explanation:

(a) medical treatment that reduces time off of work due to illness or injury.

Algebra transformation

for  Graph1 f(x)=f(x)+4

for  Graph2 f(x)=-f(x-4)

for  Graph3 f(x)=f(x-7)

for  Graph4 f(x)=f(x-2)-5

In mathematics, the reflection of a graph is a transformation that produces a mirror image of the original graph across a specific line or point. The line or point across which the reflection occurs is called the axis of reflection.

Graph1

Transform the graph by +4 units in y direction.

f(x)=f(x)+4

Graph2

Transform the graph by +4 units in x direction.

f(x)=f(x-4)

Now take the reflection of graph about x axis

f(x)=-f(x-4)

Graph3

Transform the graph by +7 units in x direction.

f(x)=f(x-7)

Graph5

Transform the graph by -5 units in y direction.

f(x)=f(x)-5

Now Transform the graph by -2 units in x direction.

f(x)=f(x-2)-5

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9514 1404 393

Answer:

Step-by-step explanation:

We assume your function is intended to be ...

  \(g(x)=-2\sqrt[3]{x}-1\)

The coefficient -2 does two things. Because it is negative, it causes the graph to be reflected across the x-axis. Because it is greater than 1, it causes the graph to be stretched away from the x-axis.

The added constant of -1 causes each y-value to be lower than it was, so translates the graph down 1 unit.

When two variables' ratios are equivalent, proportional relationships between them emerge.The right response is option c.A $50 membership fee plus a $20 monthly cost is required to use a gym.

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Answer:

y=-x-3

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

The taxi charges $2.00 for any distance less than or up to 1 mile.

Then for every mile after the taxi will charge you a fee of $1.60 dependent upon how many miles you go.

This can be modeled as:

y = 2.00 +1.60(x)

where x is the number of miles after the first mile.

Answer:

It was 10inches tall

Step-by-step explanation:

If the width was 8 inches tall but then was reduced to 5 inches tall that means it was reduced by 3 inches, so we just do the same thing with the height. If it is 7inches tall after it was reduced then just add 3 inches back to it which means it was 10 inches tall...Ik its kinda confusing but its correct

Irene has 49 Books, and Alejandro has 24 books.

Let's assume that Irene has x books, and Alejandro has y books. According to the given information, we can form the following equations:

1. Irene has twice as many books as Alejandro plus 1:

  x = 2y + 1

2. The total number of books between Irene and Alejandro is 73:

  x + y = 73

We can now solve this system of equations to find the values of x and y.

Substituting the value of x from equation (1) into equation (2), we have:

(2y + 1) + y = 73

3y + 1 = 73

3y = 72

y = 24

Now, we can substitute the value of y into equation (1) to find x:

x = 2(24) + 1

x = 49

Therefore, Irene has 49 books, and Alejandro has 24 books.

To verify our solution, we can check if the sum of their books equals 73:

49 + 24 = 7

So, our solution is correct.

In conclusion, Irene has 49 books, and Alejandro has 24 books.

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During halftime of a basketball game, a slingshot launches T-shirts at the crowd.

What is the maximum height?

Generally, To find the time it takes the T-shirt to reach its maximum height, we need to find the time when the height of the T-shirt stops increasing and starts decreasing. At this point, the velocity of the T-shirt will be 0, since it is not moving up or down.

The velocity of the T-shirt at any time t can be found by taking the derivative of the equation for height:

v(t) = dh/dt = -32t + 72

Setting the velocity to 0 and solving for t, we get:

0 = -32t + 72 32t = 72 t = 72/32 t = 9/4

So it takes the T-shirt 9/4 seconds, or approximately 2.25 seconds, to reach its maximum height.

To find the maximum height, we plug this value back into the equation for height:

h(t) = -16(9/4)^2 + 72(9/4) + 4 h(t) = -81 + 162 + 4 h(t) = 77

The maximum height of the T-shirt is 77 feet.

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