All categories

3 years ago

What is the quotient of -8x^6/4x^-3?

Mathematics

1 answer:

olga nikolaevna [1]3 years ago

5 0

Answer: $-2x^{9}$

Step-by-step explanation:

To find the quotient, you need to apply the Quotient of powers property. This is:

$\frac{a^m}{a^n}=a^{(m-n)$

Then given the expression $\frac{-8x^6}{4x^{-3}}$ you can apply the property mentioned before. Then you get:

$\frac{-8x^{(6-(-3))}}{4}$

You should remember the multiplication of signs:

$(-)(-)=+\\(+)(+)=+\\(-)(+)=-$

Therefore, simplifying the expression, you get that the quotient of $\frac{-8x^6}{4x^{-3}}$ is:

$-2x^{9}$

You might be interested in

Suppose 60% of kids like video games. Predict the number of kids that prefer video games out of a group of 200 kids.

myrzilka [38]

Answer:

120 kids prefer video games

Step-by-step explanation:

60% is .60

multiply .60 by 200 to get your answer.

.60 × 200 = 120

4 0

3 years ago

A bin is constructed from sheet metal with a square base and 4 equal rectangular sides. if the bin is constructed from 48 square

kondaur [170]

This is a problem of maxima and minima using derivative.

In the figure shown below we have the representation of this problem, so we know that the base of this bin is square. We also know that there are four square rectangles sides. This bin is a cube, therefore the volume is:

V = length x width x height

That is:

$V = xxy = x^{2}y$

We also know that the bin is constructed from 48 square feet of sheet metal, so:

Surface area of the square base = $x^{2}$

Surface area of the rectangular sides = $4xy$

Therefore, the total area of the cube is:

$A = 48 ft^{2} = x^{2} + 4xy$

Isolating the variable y in terms of x:

$y = \frac{48- x^{2} }{4x}$

Substituting this value in V:

$V = x^{2}( \frac{48- x^{2} }{x}) = 48x- x^{3}$

Getting the derivative and finding the maxima. This happens when the derivative is equal to zero:

$\frac{dv}{dx} = 48-3x^{2} =0$

Solving for x:

$x = \sqrt{\frac{48}{3}} = \sqrt{16} = 4$

Solving for y:

$y = \frac{48- 4^{2} }{(4)(4)} = 2$

Then, the dimensions of the largest volume of such a bin is:

Length = 4 ft
Width = 4 ft
Height = 2 ft

And its volume is:

$V = (4^{2} )(2) = 32 ft^{3}$

8 0

3 years ago

Let logb A= 3; logb C = 2; logb D=5 What is the value of logb D^2/C^3A

Ne4ueva [31]

Answer:

The value of given log function is 1 .

Step-by-step explanation:

Given as :

Logb A = 3

Logb C = 2

Logb D = 5

Now from log property

if , Logb x = c , then x = $b^{c}$

So,

Logb A = 3 , then A = $b^{3}$

Logb C = 2 , then C = $b^{2}$

Logb D = 5 , then D = $b^{5}$

Now, According to question

$Logb\frac{D^{2}}{C^{3}A}$

So, $Logb\frac{(b^{5})^{2}}{(b^{2})^{3}\times b^{3}}$

Or, $Logb\frac{b^{10}}{b^{6}\times b^{3}}$

or, $Logb\frac{b^{10}}{b^{9}}$

Now, since base same So,

$log_{b}b^{10-9}$

∴ $log_{b}b^{1}$

Now log property

$log_{b}b$ = 1

Hence The value of given log function is 1 . answer

5 0

3 years ago

Trail Mix is sold in 1 pound bags. Mary will buy some trail mix and re-package it so that each of the 15 members of her hiking c

Grace [21]

Okay. so we need 15 2/5 pound bags. We'll calculate how many pounds that actually comes to. Our problem is 15x2/5. Using cross simplification, our problem becomes 3x2. 3x2=6. We need 6 pounds. That means that we must have 6 1-pound bags to fit with no leftovers.

3 0

3 years ago

Read 2 more answers

Whats the answer pls can any body say.....

Natalija [7]

I think your equation is on the paper; it’s 2016 A.D + 544 then you’ll get your answer and which is 2560.

5 0

3 years ago