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3 years ago

11

A sphere has a diameter of 8 feet.What is its surface area in square inches?Round your answer to the nearest hundredth.Use 3.14

to approximate pi.

1 answer:

Scilla [17]3 years ago

8 0

The surface area of the sphere in square inches is 28,952.92 in^2 rounded to the nearest hundredth.

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What is the constant of proportionality what does it mean<br>

Alexandra [31]

Answer:

The constant of proportionality is the ratio between numbers that expresses the rate at which the numbers increase or decrease. These two numbers are directly proportional when they increase and decrease at the same rate.

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3 years ago

Find the perimeter of a field that has length 2/x + 1 and width 5/x^2 -1.

Semmy [17]

Answer:

D)4x + 6/(x + 1)(x - 1)

Step-by-step explanation:

A field is basically a rectangle, so to find the perimeter of our field we are using the formula for the perimeter of a rectangle

$p=2(l+w)$

where

$p$ is the perimeter

$l$ is the length

$w$ is the width

We know from our problem that the field has length 2/x + 1 and width 5/x^2 -1, so $l=\frac{2}{x+1}$ and $w=\frac{5}{x^2-1}$ .

Replacing values:

$p=2(l+w)$

$p=2(\frac{2}{x+1} +\frac{5}{x^2-1})$

Notice that the denominator of the second fraction is a difference of squares, so we can factor it using the formula $a^2-b^2=(a+b)(a-b)$ where $a$ is the first term and $b$ is the second term. We can infer that $a=x^2$ and $b=1^2$ . So, $x^2-1=(x+1)(x-1)$ . Replacing that:

$p=2(\frac{2}{x+1} +\frac{5}{x^2-1})$

$p=2(\frac{2}{x+1} +\frac{5}{(x+1)(x-1})$

We can see that the common denominator of our fractions is $(x+1)(x-1)$ . Now we can simplify our fraction using the common denominator:

$p=2(\frac{2(x-1)+5}{(x+1)(x-1)} )$

$p=2(\frac{2x-2+5}{(x+1)(x-1)} )$

$p=2(\frac{2x+3}{(x+1)(x-1)} )$

$p=\frac{4x+6}{(x+1)(x-1)}$

We can conclude that the perimeter of the field is D)4x + 6/(x + 1)(x - 1).

3 0

3 years ago

Nine less than five times a number is equal to -30

disa [49]

To solve this question, we can start to set up an equation using what the question is telling us. Since we don't know what the number is, let's make it equal to x.

The phrase "5 times a number" means that we're multiplying our unknown, x, by 5. That is equal to 5x. 9 less than that would be 5x - 9. Since we know that it's equal to -30, we can solve.

5x - 9 = -30

Get all terms with x on one side and the constants on the other

5x - 9 +9 = -30 + 9

Simplify

5x = -21

Now, we can divide both sides by 5 to get our answer of x = - $\frac{21}{5}$

6 0

3 years ago

Read 2 more answers

A population of 5000 people doubles in size every 10 years. Determine the population

Marrrta [24]

Answer: A quantity grows exponentially when its increase is proportional to what is already there. A common example is compound interest, where $100 invested at 7% per year annual compound interest will double in 10 years. Similarly, if a population grows at 7% per year, it, too, will double in 10 years.

Step-by-step explanation:

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3 years ago

A group of biologists found a total of 15 loggerhead turtle nests along a beach during a certain season. This was 20% of the tot

Andre45 [30]

20% also equals 1/5, right?

So in order to find the total number of turtle nests, just find 5/5, or multiply 15 by 5.

15 x 5 = 75

There were 75 total nests

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3 years ago