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3 years ago

What is an equation that models the following situation?

Mathematics

1 answer:

Oksanka [162]3 years ago

5 0

Answer:

Step-by-step explanation:

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If a=2b^3 and b= -1/2c ^-2,express a in terms of c.

ElenaW [278]

Answer:

Part 1) $a=-\frac{1}{4c^6}$

Part 2) $a=-\frac{1}{4c^{-6}}$

Step-by-step explanation:

Part 1) we have

$a=2b^{3}$ ----> equation A

$b=-\frac{1}{2}c^{-2}$ ----> equation B

substitute equation B in equation A

$a=2(-\frac{1}{2}c^{-2})^{3}$

Applying property of exponents

$(x^{m})^{n}=x^{m*n}$

$x^{-m} =\frac{1}{x^{m}}$

$a=2(-\frac{1}{2}c^{-2})^{3}=2(-\frac{1}{2})^3(c^{-2})^{3}=2(-\frac{1}{8})(c^{-6})=-\frac{1}{4c^6}$

therefore

$a=-\frac{1}{4c^6}$

Part 2) we have

$a=2b^{3}$ ----> equation A

$b=-\frac{1}{2c^{-2}}=-\frac{c^{2}}{2}$ ----> equation B

substitute equation B in equation A

$a=2(-\frac{c^{2}}{2})^{3}$

Applying property of exponents

$(x^{m})^{n}=x^{m*n}$

$x^{-m} =\frac{1}{x^{m}}$

$a=2(-\frac{c^{2}}{2})^{3}=2(-\frac{c^{6}}{8})$

simplify

$a=-\frac{c^{6}}{4}$

therefore

$a=-\frac{1}{4c^{-6}}$

6 0

3 years ago

The sides of a rectangle have length x+ 2 and width x -5. Which equation describes the area, A, of the rectangle in terms of x?

Yakvenalex [24]

Answer:

The area in factored form is $A=(x+2)(x-5)$ .

The area in standard form is $A=x^2-3x-10$ .

Step-by-step explanation:

The area of a rectangle is length times width.

So the area here is (x+2)(x-5).

They are probably not looking for A=(x+2)(x-5) because it requires too little work.

They probably want A in standard form instead of factored form.

Let's use foil:

First x(x)=x^2

Outer: x(-5)=-5x

Inner: 2(x)=2x

Last: 2(-5)=-10

---------------------Adding together: $x^2-3x-10$ .

The area in factored form is $A=(x+2)(x-5)$ .

The area in standard form is $A=x^2-3x-10$ .

4 0

3 years ago

Plssss help 30 pointsss<br><br> If your slope is 1/3 how do you move horizontally?

sweet [91]

What is 1/3 as a slope?

The answer is approximately 18.43º. A slope of 1 in 3 means the slope is 1/3. It also means a rise of 1 and a run of 3. On a graph, starting at the origin, go up 1 unit, then from there, go to the right 3 units.

(hope this helps) :)

7 0

3 years ago

Are you cyclist travels at a rate of 1.8 km/min. how far will the cycle is travel in 48 minutes

Tpy6a [65]

Answer:

86.4 km

Step-by-step explanation:

Since the cyclist travels 1.8km in a minute, he will travel 48 times that in 48 minutes:

$48*1.8 = 86.4$

6 0

4 years ago

a box contains 5 plain pencils and 3 pens. a second box contains 4 color pencils and 4 crayons. one item from each box is chosen

kodGreya [7K]

I think it would be 9 out of 16.

4 0

3 years ago

What is an equation that models the following situation?​

What is an equation that models the following situation?