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3 years ago

For the right triangle shown, the lengths of two sides are given. Find the third side. Leave your answer in simplified,

Mathematics

1 answer:

liberstina [14]3 years ago

4 0

Answer:

<u>a = 5√7 units</u>

Step-by-step explanation:

Let's find the value of a, using the Pythagorean Theorem, this way:

c = Hypotenuse = 16

a² = c² - b²

a² = 16² - 9²

a² = 256 - 81

a² = 175

√a² = √175

a = √25 * 7

<u>a = 5 √7 units</u>

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The radius of the base of the cylinder is 2x cm and the height of the cylinder is h cm.

valentina_108 [34]

Answer:

h = 9x

Step-by-step explanation:

Given: i. for the cylinder, base radius = 2x cm, height = h cm

ii. for the sphere, radius = 3x cm

iii. volume of the cylinder = volume of the sphere

volume of a cylinder is given as;

volume = $\frac{1}{3}$ $\pi$ $r^{2}$ h

where: r is its base radius and h the height

volume of the given cylinder = $\frac{1}{3}$ $\pi$ x $(2x)^{2}$ x h

= $\frac{1}{3}$ $\pi$ x 4 $x^{2}$ x h

= $\frac{4}{3}$ $\pi$ $x^{2}$ h

volume of a sphere = $\frac{4}{3}$ $\pi$ $r^{3}$

where r is the radius.

volume of the given sphere = $\frac{4}{3}$ $\pi$ x $(3x)^{3}$

= $\frac{4}{3}$ $\pi$ x 9 $x^{3}$

= 12 $\pi$ $x^{3}$

Since,

volume of the cylinder = volume of the sphere

Then we have;

$\frac{4}{3}$ $\pi$ $x^{2}$ h = 12 $\pi$ $x^{3}$

4 $\pi$ $x^{2}$ h = 36 $\pi$ $x^{3}$

subtract $x^{2}$ from both sides

4 $\pi$ h = 36 $\pi$ x

divide both sides by 4 $\pi$

h = $\frac{36\pi x}{4\pi }$

= 9x

h = 9x

5 0

3 years ago

What is the simplified form of the equation 4/5n - 1/5 = 2/5n ?

Gnoma [55]

we are given

$\frac{4}{5}n -\frac{1}{5} =\frac{2}{5}n$

Firstly , we will multiply both sides by 5

$5*\frac{4}{5}n -5*\frac{1}{5} =5*\frac{2}{5}n$

now, we can simplify it

$4n-1 =2n$

$2n =1$

now, we can solve for n

$n =\frac{1}{2}$ .............Answer

8 0

4 years ago

The following are the annual salaries of 15 chief executive officers of major companies. (The salaries are written in thousands

Alisiya [41]

Answer:

The 25th percentile is 248.

The 70th percentile is 700.

Step-by-step explanation:

The pth percentile is a data value such that at least p% of the data-set is less-than or equal to this data value and at least (100-p)% of the data-set are more-than or equal to this data value.

Arrange the data set in ascending order as follows:

S = {75 , 157 , 224 , 248 , 271 , 381 , 472 , 495 , 586 , 676 , 700 , 723 , 743 , 767 , 1250}

The formula to compute the position of the pth percentile is:

$p^{th} \text{Percentile}=\frac{(n+1)\cdot p}{100}$

Compute the 25th percentile as follows:

$25^{th} \text{Percentile}=\frac{(15+1)\cdot 25}{100}=4^{th}obs.$

The 4th observation from the arranged data set is 248 .

Thus, the 25th percentile is 248.

Compute the 70th percentile as follows:

$70^{th} \text{Percentile}=\frac{(15+1)\cdot 70}{100}\approx 11^{th}obs.$

The 11th observation from the arranged data set is 700.

Thus, the 70th percentile is 700.

4 0

3 years ago

The area of the square rug is 121 square feet. what is the length of the side of the rug

hram777 [196]

Answer:

11 feet

Step-by-step explanation:

Squares have the same length and width. So you just take the square root of teh area to find both.

√121 = 11

7 0

3 years ago

Steve received three payments for a total of $45 how much was each payment

defon

Answer:

$15

Step-by-step explanation:

Assuming all the payments are the same, simply divide the total with the amount of payments:

45/3 = 15

$15 each payment.

5 0

4 years ago

Read 2 more answers