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3 years ago

I need to know how to simplify these problems.

Mathematics

1 answer:

nalin [4]3 years ago

5 0

You need to factor the radicals into products of radicals, and when factoring you should keep in mind you want to obtain perfect square roots. So √125 = √5*√25 and squareroot 25 has a definite answer of 5, so ∛125=∛5×∛25=5×√5. You want to follow the general pattern of factoring perfect squares to obtain a number outside the radical which can be multiplied by the current coefficient

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What is the volume of the composite figure? (Round to the nearest hundredth. Use 3.14 for x.)

marshall27 [118]

The volume of the composite figure is the third option 385.17 cubic centimeters.

Step-by-step explanation:

Step 1:

The composite figure consists of a cone and a half-sphere on top.

We will have to calculate the volumes of the cone and the half-sphere separately and then add them to obtain the total volume.

Step 2:

The volume of a cone is determined by multiplying $\frac{1}{3}$ with π, the square of the radius (r²) and height (h). Here we substitute π as 3.1415.

The radius is 4 cm and the height is 15 cm.

The volume of the cone :

$V = \frac{1}{3} \pi r^{2} h = \frac{1}{3} (3.1415)(4^{2} )(15) = 251.32$ cubic cm.

Step 3:

The area of a half-sphere is half of a full sphere.

The volume of a sphere is given by multiplying $\frac{4}{3}$ with π and the cube of the radius (r³).

Here the radius is 4 cm. We take π as 3.1415.

The volume of a full sphere $\frac{4}{3} \pi r^{3} = \frac{4}{3} (3.1415) (4^{3}) = 268.07$ cubic cm.

The volume of the half-sphere $=\frac{1}{2} (268.07) = 134.037$ cubic cm.

Step 4:

The total volume = The volume of the cone + The volume of the half sphere,

The total volume $251.32+134.037 = 385.357$ cub cm. This is closest to the third option 385.17 cubic centimeters.

5 0

3 years ago

A worker uses 900 inches of steel wire to make 600 springs of the same size. At this rate how

a_sh-v [17]

Can I get your number and I will help you

7 0

3 years ago

9,000 + 40 + 0.1 + 0.008 I need to put it in standard form. Please help!

Andre45 [30]

Answer:

-12

Step-by-step explanation:

8 0

3 years ago

Which procedure correctly simplifies the expression? ( 4 x − 3 ) − 2 ( x + 5 ) A. Step 1: 4 x − 2 x − 3 + 5 Step 2: 2 x + 2 B. S

olya-2409 [2.1K]

Answer:

Step-by-step explanation:

Given the expression;

(4 x − 3) − 2 (x + 5)

The following steps/ procedure are to be taken when simplifying the expression.

open the parenthesis

(4 x − 3) − 2 (x + 5)

= 4x-3 -2(x)-2(5)

= 4x-3-2x-10

collect the like terms

= 4x-2x-3-10

simplify the resulting expression

= 2x-13

Hence the procedure that correctly simplifies the expression are:

Step 1: 4 x − 3 − 2 x − 10

Step 2: 2 x − 13

6 0

3 years ago

If 4/5 of the population of a certain town is

kkurt [141]

Hi! I'm happy to help!

Our town is composed of 2,000 people. Of those 2,000 people, 4/5 of them are middle class. The word 'of' usually means multiplication when it is in a word problem. So, we will multiply 2,000 by 4/5. When multiplying a whole number, we just multiply it by the numerator (top) and leave the denominator. (bottom)

2,000×4

8,000

8,000/5

Fractions are just a different way of putting division, so we can change this to a division problem:

8,000÷5=

1,600

1,600 of the people are middle class.

I hope this was helpful, keep learning! :D

8 0

2 years ago