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aleksley [76]
3 years ago
15

Which expression is equivalent to

Mathematics
1 answer:
KonstantinChe [14]3 years ago
6 0
Given the expression:

\sqrt[4]{ \frac{24x^{6}y}{128x^{4}y^{5}}}

Simplifying: 

\sqrt[4]{ \frac{3x^{2}}{16y^{4}}}

Then the answer is:

\frac{ \sqrt[4]{3x^{2}}}{2y}


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How to prove that a shape is a square on the coordinate plane?
Goshia [24]
If a quadrilateral has four congruent sides and four right angles, then it's a square, and also If two consecutive sides of a rectangle are congruent, then it's a square.

Glad I could help, Have a great day!
5 0
3 years ago
Read 2 more answers
A rectangular solid has width w, a length of 7 more than the width, and a height that is equivalent to 15 decreased by 3 times t
dexar [7]

Answer:

For a rectangular solid with:

width = w

length = l

height = h

The volume is equal to:

V = w*l*h

in this case we know that:

width = w.

"length of 7 more than the width"

l = w + 7.

"a height that is equivalent to 15 decreased by 3 times the width."

h = 15 - 3*w

Then the volume will be:

V = w*l*h = w*(w + 7)*(15 - 3w) = (w^2 + 7*w)*(15 - 3*w)

V =  ( -3*w^3 + 15*w^2 + 105*w - 21*w^2)

V = (-3*w^3 - 6*w^2 + 105*w)

Now, the maximum volume will be for the value of w such that:

V'(w) = 0.

and:

V''(W) < 0

Where:

dV/dw = V'(w).

dV'/dw = V''(w)

Then first we need to differentiate the equation for the volume.

V'(w) = dV/dw = ( 3*(-3*w^2) + 2*(-6*w) + 105)

V'(w) = -9*w^2 - 12*w + 105.

Then we need to find the solution for:

-9*w^2 - 12*w + 105 = 0.

We can use the Bhaskara formula, and we will get:

w = \frac{+12 +-\sqrt{(-12)^2 - 4*(-9)*105} }{2*-9}  = \frac{+12 +- 62.6}{-18}

Then the two solutions are:

w₁ = (+12 - 62.6)/(-18) = 2.81

w₂ = (+12 + 62.6)/(-18) = -15.5

But we can not have a negative width, so we can just discard the second solution.

Now let's check the second condition for the maximum, we must have:

V''(2.81) < 0.

V'' = dV'/dw = 2*(-9*w) - 12 = -18*w - 12

V''(2.81) = -18*2.81 - 12 = -62.58 < 0 .

Then the volume is maximized when w = 2.81, and the maximum volume will be:

V(2.81) =  (-3*(2.81)^3 - 6*(2.81)^2 + 105*2.81) = 180.1

 

8 0
3 years ago
Graph each function. State the domain and range.
kondaur [170]

Answer:

Just put it in Geogebra classic. It's an app that helps very much with functions!

7 0
2 years ago
24 students in Jamal's class are wearing tennis shoes. There are 30 students in his class. Jamal says that 70% of his class is w
allsm [11]
No 70 percent is 21 students
7 0
3 years ago
PLEASE HELP!!!!!!!!! WILL MARK BRAINLIEST!!
muminat

Answer:

b=-0.0019a + 215

at 2500 ft, b=210.25 degrees F

Step-by-step explanation:

First find the slope. a=altitude, b = temperature

slope is b2-b1 / a2-a1

points are (8200, 199.42) and (4700, 206.07)

(206.07 - 199.42) / (4700-8200)

= 6.65/ -3500

= - 0.0019

we have b = -0.0019a + intercept

plug in a point to find intercept

199.42 = -0.0019*8200 + intercept

intercept = 199.42 + 15.58 = 215

b=-0.0019a + 215

at a=2500 ft, substitute into equation

b= -0.0019*2500 + 215

= -4.75 + 215

= 210.25 degrees F

please give thanks by clicking heart button :)

4 0
2 years ago
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