Ask question

Ask question

All categories

3 years ago

5

A cube has a valume 1000 cubic feet .what is the length of an edge of the cube?show how you found your answer

1 answer:

Stells [14]3 years ago

3 0

<h2><u>Solution</u> :-</h2>

Given : A cube has a valume 1000 cubic feet.

We know that,

Volume of a cube = (edge)³ cubic unit

=> 1000 = (edge)³

=> 10³ = (edge)³

=> 10 = edge

<u>Hence</u>,

The length of an edge of the cube = 10 feet

You might be interested in

identify the coordinates of four points on the line with each given slope and y-intercept. slope=5 and that y-intercept =-1

mezya [45]

Well given these 2 pieces of information, we can easily obtain the equation for the line which would be the following :

Y = 5x - 1.

The 4 points including the y intercept:

(0,-1)
(1,4)
(2,9)
(3,14).

5 0

3 years ago

Read 2 more answers

Can anybody help plzz?? 65 points

Yakvenalex [24]

Answer:

$\frac{dy}{dx} =\frac{-8}{x^2} +2$

$\frac{d^2y}{dx^2} =\frac{16}{x^3}$

Stationary Points: See below.

General Formulas and Concepts:

<u>Pre-Algebra</u>

Equality Properties

<u>Calculus</u>

Derivative Notation dy/dx

Derivative of a Constant equals 0.

Stationary Points are where the derivative is equal to 0.

1st Derivative Test - Tells us if the function f(x) has relative max or mins. Critical Numbers occur when f'(x) = 0 or f'(x) = undef
2nd Derivative Test - Tells us the function f(x)'s concavity behavior. Possible Points of Inflection/Points of Inflection occur when f"(x) = 0 or f"(x) = undef

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Quotient Rule: $\frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}$

Step-by-step explanation:

<u>Step 1: Define</u>

$f(x)=\frac{8}{x} +2x$

<u>Step 2: Find 1st Derivative (dy/dx)</u>

Quotient Rule [Basic Power]: $f'(x)=\frac{0(x)-1(8)}{x^2} +2x$
Simplify: $f'(x)=\frac{-8}{x^2} +2x$
Basic Power Rule: $f'(x)=\frac{-8}{x^2} +1 \cdot 2x^{1-1}$
Simplify: $f'(x)=\frac{-8}{x^2} +2$

<u>Step 3: 1st Derivative Test</u>

Set 1st Derivative equal to 0: $0=\frac{-8}{x^2} +2$
Subtract 2 on both sides: $-2=\frac{-8}{x^2}$
Multiply x² on both sides: $-2x^2=-8$
Divide -2 on both sides: $x^2=4$
Square root both sides: $x= \pm 2$

Our Critical Points (stationary points for rel max/min) are -2 and 2.

<u>Step 4: Find 2nd Derivative (d²y/dx²)</u>

Define: $f'(x)=\frac{-8}{x^2} +2$
Quotient Rule [Basic Power]: $f''(x)=\frac{0(x^2)-2x(-8)}{(x^2)^2} +2$
Simplify: $f''(x)=\frac{16}{x^3} +2$
Basic Power Rule: $f''(x)=\frac{16}{x^3}$

<u>Step 5: 2nd Derivative Test</u>

Set 2nd Derivative equal to 0: $0=\frac{16}{x^3}$
Solve for <em>x</em>: $x = 0$

Our Possible Point of Inflection (stationary points for concavity) is 0.

<u>Step 6: Find coordinates</u>

<em>Plug in the C.N and P.P.I into f(x) to find coordinate points.</em>

x = -2

Substitute: $f(-2)=\frac{8}{-2} +2(-2)$
Divide/Multiply: $f(-2)=-4-4$
Subtract: $f(-2)=-8$

x = 2

Substitute: $f(2)=\frac{8}{2} +2(2)$
Divide/Multiply: $f(2)=4 +4$
Add: $f(2)=8$

x = 0

Substitute: $f(0)=\frac{8}{0} +2(0)$
Evaluate: $f(0)=\text{unde} \text{fined}$

<u>Step 7: Identify Behavior</u>

<em>See Attachment.</em>

Point (-2, -8) is a relative max because f'(x) changes signs from + to -.

Point (2, 8) is a relative min because f'(x) changes signs from - to +.

When x = 0, there is a concavity change because f"(x) changes signs from - to +.

3 0

3 years ago

Triangle PQR and triangle QRS have vertices P(-9,7) , Q(4,7) , R(4,-3), and S(-10,3) What is the area in square units of the qua

larisa [96]

Answer:

3.7

Step-by-step explanation:

.

7 0

3 years ago

A housepainter mixed 5 gal of blue paint with every 9 gal of yellow paint in order to make a green paint. What is

ella [17]

Answer:

A

Step-by-step explanation:

5:9 is the original ratio.

we know that anything times 5 would have the ones place of either 5 or 0 so we can eliminate c and d. Then we test out the other two choices.

25/5=5

45/9=5

A is correct.

15/5=3

45/9=5

Option B is incorrect.

so, the ratio is 25:45

The answer is A!

4 0

3 years ago

Use the binomial theorem to show that 7^n + 2 is divisible by 3, where n is a positive integer.

masha68 [24]

By the binomial theorem,

$7^n=(6+1)^n=6^n+n6^{n-1}+\dbinom n26^{n-2}+\cdots+\dbinom n{n-2}6^2+n6^1+1$

Each term containing a factor 6 is divisible by 3, since 3 divides 6. The remaining 1 and 2 sum to 3, which is also divisible by 3.

7 0

3 years ago