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1 year ago

Find the number of positive factors of 540

Mathematics

1 answer:

Elden [556K]1 year ago

8 0

$540=2^2 \times 3^3 \times 5$

So, there are (3)(4)(2)=24 positive factors.

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1. The science club constructed a pyramid with a square base out of paper clips. The height of the pyramid is 2.5 feet. One side

elena-14-01-66 [18.8K]

Answer:

Part 1) The slant height of the pyramid is $2.80\ ft$

Part 2) The length of the third side of the window is $20.78\ in$

Part 3) The building's slant height is $53.85\ ft$

Step-by-step explanation:

Part 1) we know that

To find out the slant height of the pyramid, apply the Pythagorean Theorem

Let

l ----> the slant height of the pyramid

h ---> the height of the pyramid

b ---> the length side of the square base

$l^2=h^2+(b/2)^2$

we have

$h=2.5\ ft\\b=2.5\ ft$

substitute the given values

$l^2=2.5^2+(2.5/2)^2$

$l^2=2.5^2+(1.25)^2$

$l^2=7.8125$

$l=2.80\ ft$

Part 2) Let

c ----> the hypotenuse of a right triangle (the greater side)

a ---> the measure of one leg of the right triangle

b ---> the measure of the other leg of the right triangle

Applying the Pythagorean Theorem

$c^2=a^2+b^2$

we have

$c=24\ in\\a=12\ in$

substitute the given values and solve for b

$24^2=12^2+b^2$

$b^2=24^2-12^2$

$b^2=432$

$b=20.78\ in$

Part 3) Let

l ----> the building's slant height

h ---> the height of the building

r ---> the radius of the base of the building

Applying the Pythagorean Theorem

$l^2=h^2+r^2$

we have

$h=50\ ft\\r=20\ ft$

substitute the given values

$l^2=50^2+20^2$

$l^2=2,900$

$l=53.85\ ft$

4 0

3 years ago

Haydn made a scale model of a building. The actual height of the building is 75 feet. Haydn's model used a scale in which 1.5 in

vfiekz [6]

Answer:

3.75

Step-by-step explanation:

1.5 equals 30 ft so x2 equals 60 then 15 is half of 20 so half of 1.5 in is .75 so 3 plus .75

7 0

3 years ago

Find the simple interest on an investment of $3500 for 2.5 years at

aleksklad [387]

Answer:

$481.25

Step-by-step explanation:

The formula for simple interest is i = p*r*t, in which p is the principal, r is the interest rate as a decimal fraction, and t is the time in years.

Here p = $3500, r = 0.055 and t =2.5 yrs, and so the simple interest is

i = ($3500.00)(0.055)(2.5 yr), or

i = $481.25

5 0

3 years ago

Mr. endres wants to put fencing around his rectangular shaped backyard. the width of the backyard is 42 feet and the length is t

Anna71 [15]

The the number of feet needed for the fence of the rectangular garden = its perimeter = 252 ft.

<h3>What is the Perimeter of a Rectangle?</h3>

Perimeter = 2(length + width).

The number of feet needed for the fence around the rectangular garden = perimeter of teh rectangular garden.

Given the following:

Width = 42 ft.
Length = 2(42) = 84 ft.

Plug the values into Perimeter = 2(length + width):

Perimeter of the rectangular garden = 2(42 + 84)

Perimeter of the rectangular garden = 252 ft

Therefore, the the number of feet needed for the fence of the rectangular garden = its perimeter = 252 ft.

Learn more about perimeter of rectangle on:

brainly.com/question/24571594

7 0

2 years ago

How many ways can Caroline choose 6 courses of any type?

Zanzabum

Answer:

6 times she can choose courses

4 0

2 years ago

Find the number of positive factors of 540​

Find the number of positive factors of 540