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3 years ago

What is the volume of a sphere with a radius of 3 inches?

Mathematics

1 answer:

Vilka [71]3 years ago

3 0

Answer:

36π cubic inches

Step-by-step explanation:

V = 4/3 πr³

radius (r): 3

= 4/3π(3)³

= 4/3π (27)

= 36π

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a rectangle has a perimeter of 76 cm. Its length is 5 more that twice its width. The system of equation below can be use to fine

Juliette [100K]

Answer:

$l=27cm$ and $w=11cm$

Step-by-step explanation:

the perimeter of a rectangle is given by the following equation:

$p=2(l+w)=2l+2w$

if a rectangle has a perimeter of 76cm and its length is 5 plus the double of its width we can use a system of equations to find the length $l$ , and the width $w$ .

For the perimeter of the rectangle

$2l+2w=76$ where $l$ is its length, and $w$ is its width, 76 is the perimeter of the rectangle in cm.

We know that the lengh of the rectangle is 5 plus the double of its width, writing the equation:

$l=5+2w$

Substituting the equation above in $2l+2w=76$

$2(5+2w)+2w=76\\10+4w+2w=76\\6w=76-10\\w=66/6\\w=11$

We got that the rectangle width is w=11cm

Substituting w in the equation $2l+2w=76$

$2l+2(11)=76\\2l+22=76\\l=(76-22)/2=54/2\\l=27$

We got that the rectangle length is l=27cm

Verifying the values obtained

$2l+2w=76$ with l=27 and w=11

$2(27)+2(11)=76$

$54+22=76$

Satisfying the equation

5 0

3 years ago

Simplify 6(x + 3). 6x + 3 6x + 18 6x + 9 x + 18

lilavasa [31]

6x+18 because of distribution.

6*x = 6x
6*3 = 18
6x+18

3 0

3 years ago

Read 2 more answers

For the curve with equation y = <img src="https://tex.z-dn.net/?f=x%5E%7B2%7D" id="TexFormula1" title="x^{2}" alt="x^{2}" align=

bixtya [17]

Answer:

Below.

Step-by-step explanation:

a) First we find the derivative of the function, which gives us the gradient in terms of x:-

y = x^2 + 4x + 3

Gradient at x = dy/dx = 2x + 4.

When the curve cuts the x-axis, y = 0:

x^2 + 4x + 3 = 0

(x + 1)(x + 3) = 0

so x = -1 and -3 where the curve cuts the x axis.

The gradients at these point are therefore:

At x = -1 gradient = 2(-1) + 4 = 2

at x = -3 gradient = 2(-3) + 4 = -2.

b) (i) Where the tangent is parallel to x axis the gradient = 0

so 2x + 4 = 0 giving x = -2.

We now need to substitute x = -2 into the original function to find the y coordinate.

So the coordinates are (-2, (-2)^2 + 4(-2) +3))

= (-2, -1)

(ii) First find the slope of the line 6x + 3y = 7:

3y = -6x + 7

y = -2x + 7/3.

So the slope is -2.

Thus -2 = 2x + 4

2x = -6

x = -3

So the coordinates are (-3, (-3)^2 + 4(-3) + 3)

= (-3, 0).

7 0

3 years ago

Find the distance between -6 and eight what is an expression that represents the distance complete the expression

Amanda [17]

Answer: The distance between the two numbers is 14 because to get to zero from -6 you will add 6 to get zero then you will add eight to get 14.

5 0

4 years ago

Simplify the radical expression. show all your steps. √363- 3√27

HACTEHA [7]

All you have to do is take the square root of 363=11√3

11√3-3√27

8 0

3 years ago