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pshichka [43]
3 years ago
8

PLEASE HELP OMG IM ON MY FINAL!!! If z varies inversely as w, and z=4 when w=9, find z when w=12

Mathematics
1 answer:
Drupady [299]3 years ago
4 0

z=3. If z varies inversely as w, and z=4 when w=9, then when w=12 the value of z is 3.

The key to solve this problem is using reverse proportionality, in which two magnitudes a and b are inversely proportional when there is a constant k such that

a⋅b=k, where constant k is called the proportionality constant.

Then if z varies inversely as w, and z=4 when w=9

z.w=k -------> 4.9=k -------> k=36

So, let's find z when w = 12. With k = 36

z.w=K, clear z from the equation

z=k/w -------> z=36/12 -----> z=3

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He rode 2 miles since 4 can go into eight 2 times

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3 years ago
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Find the general solution of the given differential equation. cos^2(x)sin(x)dy/dx+(cos^3(x))y=1 g
eimsori [14]

If the given differential equation is

\cos^2(x) \sin(x) \dfrac{dy}{dx} + \cos^3(x) y = 1

then multiply both sides by \frac1{\cos^2(x)} :

\sin(x) \dfrac{dy}{dx} + \cos(x) y = \sec^2(x)

The left side is the derivative of a product,

\dfrac{d}{dx}\left[\sin(x)y\right] = \sec^2(x)

Integrate both sides with respect to x, recalling that \frac{d}{dx}\tan(x) = \sec^2(x) :

\displaystyle \int \frac{d}{dx}\left[\sin(x)y\right] \, dx = \int \sec^2(x) \, dx

\sin(x) y = \tan(x) + C

Solve for y :

\boxed{y = \sec(x) + C \csc(x)}which follows from [tex]\tan(x)=\frac{\sin(x)}{\cos(x)}.

7 0
1 year ago
What is the midpoint of a segment with endpoints at(-4,-8) and (8, 10)?
vekshin1

Answer:

The answer is

<h2>( 2 , 1)</h2>

Step-by-step explanation:

The midpoint M of two endpoints of a line segment can be found by using the formula

M = ( \frac{x1 + x2}{2}  , \:  \frac{y1 + y2}{2} )

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

(-4,-8) and (8, 10)

The midpoint is

M = ( \frac{ - 4 + 8}{2}  , \:  \frac{ - 8 + 10}{2} ) \\  = ( \frac{4}{2} ,  \frac{2}{2} )

We have the final answer as

<h3>( 2 , 1)</h3>

Hope this helps you

4 0
3 years ago
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slavikrds [6]

Answer:

15=2x

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3 0
3 years ago
Whats the surface area of the prism below,and please explain how you got the answer :)
nevsk [136]
Answer: 480 units^2



IN DEPTH EXPLANATION TO HELP YOU FOR FUTURE PROBLEMS:

Front:
b*h/2 = sa
12*5/2 = 30
Front = 30 units^2

Back:
b*h/2 = sa
12*5/2 = 30
Back = 30 units^2

Right:
w*l = sa
14*13 = 182 units^2
Right: 182 units*2
(figures out the length by using
pythagorean theorem)

Left:
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Left: 70 units^2

Bottom:
w*l = sa
12*14 = 168 units^2

ADD ALL THE UNITS:
168 + 70 + 182 + 30 + 30 = 480

4 0
3 years ago
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