MATHEMATICS HIGH SCHOOL

A sports ball has a diameter of 16 cm. Find the volume of the ball.

Answers

Answer 1
Answer:

Answer:

4/3 pi radius cubed

Step-by-step explanation:

4/3 pi x (8x8x8)

512 x 4/3 pi

2144.660585

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A beach has to enclose a rectangular area, because some endangered species are nesting there. They have 200 feet of rope to rope off the area with. What is the maximum area that they can rope off?

Answers

Area is equal to length times width. The perimeter (the amount of rope) has to equal twice the length added to twice the width so we're left with:
A = l * w
200 = 2l + 2w
solve for either l or w
l = 100 - w
plug into the area equation to get one equation with two variables
A = w(100 - w)
A = -w^2 + 100w
take the derivative
A' = -2w + 100
set the derivative equal to zero
0 = -2w + 100
2w = 100
w = 50
This is the width that maximizes the area
with a width of 50, the length must also be 50 to have a perimeter of 200
therefore, they can rope up to 50 * 50 = 2500 ft^2

Final answer:

The maximum area that can be roped off with 200 feet of rope is 2500 square feet by making the roped off area a square.

Explanation:

The question deals with the optimization of area given a fixed perimeter, which involves the principles of geometry and algebra. Since the area needs to be roped off is a rectangle, and you have 200 feet of rope, your rectangle will have dimensions length (L) and width (W) such that 2L + 2W = 200.

To maximize the area of a rectangle given a fixed perimeter, the rectangle should be a square. So, for a maximum area, the length and width should be equal. Thus, each dimension (length and width) would be 200/4 = 50 feet.

Finally, to find the maximum area, we multiply the length by the width: 50 feet * 50 feet = 2500 square feet. So, the maximum area that they can rope off with 200 feet of rope is 2500 square feet.

Learn more about Optimization of Area here:

brainly.com/question/29759875

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To increase an amount by 3% what single multiplier would you use

Answers

The multiplier would be 1.03 because 1 is a whole and you are increasing by 3 therefore the answer would be 1.03

If you were decreasing an amount then you would take that amount away from 100. Eg - decrease an amount by 50%. What multiplier would you use? The answer to this would be 0.50 because you are taking away 50 from 100.

Hope this helps :)
Multiply by 1.03 to get an amount + 3% of that amount

A certain forest covers an area of 2,000 square kilometers. Suppose that each year this area decreases by 6%. What is the function that best represents the area of the forest each year and how much area remains after 12 years? Round your answer to the nearest square kilometer.Hint: Use the formula, f(x) = P(1 + r)x.

f(x) = 2,000(0.94)x, 952 square kilometers
f(x) = 2,000(1.06)x, 4,204 square kilometers
f(x) = 2,000(0.06)x, 1,239 square kilometers
f(x) = 2,000(0.94)x, 1,432 square kilometers

Answers

Given:
2,000 square kilometers
decreases by 6% per year
12 years.

f(x) = P(1+r)^x

The fact that the term decreases is used, (1+r) will become (1-r)

f(12) = 2,000(1-0.06)^12
f(12) = 2,000(0.94)^12
f(12) = 2,000(0.4759)
f(12) = 951.80

Answer is:
f(x) = 2,000(0.94)^x, 952 square kilometers.

A 15 foot ladder is leaning against a wall. The foot of the ladder is 7 feet from the wall. How high up the wall is the ladder? Round to the nearest tenth if necessary.

Answers

Answer:

13.26

Step-by-step explanation:

The computation of the height should be computed by using the Pythagoras theorem

As we know that

Hypothenuse^2 = base^2 + height^2

where,

Hypothenuse is 15 foot

And, the foot of the ladder i.e base is 7

So now placing these values

The height is

15^2 = 7^2 + height^2

225= 49 + height^2

After solving this, the height is 13.26

What is the absolute value of -10

Answers

absolute value is basically made everything positive, so it is 10! :)
the absolute value of -10 is 10 because that is the opposite number.

3/10 off the normal price 400

Answers

Answer: 120

Step-by-step explanation: 3/10=0.3

0.3*400=120
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