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EleoNora [17]
3 years ago
7

Susan has 3 shirts ; red, blue, and green; jeans and khakis; and 3 shoes; white, black, and tan , to choose from for her school

outfit. How many different outfits can she create

Mathematics
1 answer:
Veronika [31]3 years ago
8 0
Get outfit can only be 1 outfit
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Suppose Z Varies directly with x and inversely with y, where x = 16, y = 4, when z = 32...............
Greeley [361]
A.)
Z = kx/y where k is a constant.
32 = 16k/4
k = 128/16
k = 8

z = 8x/y

b.)
Z = 8(21)/6
Z = 28

c.)
4 = 8x/48
x = 192/8
x = 24
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2x +8= 3x-4 what is x equal two
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Is the graph of y = sin(x^4) increasing or decreasing when x = 10? Is it concave up or concave down?
Tanzania [10]
y=\sin(x^4)
\implies y'=4x^3\cos(x^4)
\implies y'=12x^2\cos(x^4)-16x^6\sin(x^4)

At x=10, you have

y'(10)=4000\cos(10^4)

The trick to finding out the sign of this is to figure out between which multiples of \dfrac\pi2 the value of 10^4 lies.

We know that \cos x>0 whenever -\dfrac\pi2+2n\pi, and that \cos x whenever \dfrac\pi2+2n\pi, where n\in\mathbb Z.

We have

10^4=\dfrac{k\pi}2\implies k=\dfrac{2\times10^4}\pi\approx6366.2

which is to say that \dfrac{6366\pi}2, an interval that is equivalent modulo 2\pi to the interval \left(\pi,\dfrac{3\pi}2\right).

So what we know is that 10^4 corresponds to the measure of an angle that lies in the third quadrant, where both cosine and sine are negative.

This means y'(10), so y is decreasing when x=10.

Now, the second derivative has the value

y'=12\times10^2\cos(10^4)-16\times10^6\sin(10^4)

Both \cos(10^4) and \sin(10^4) are negative, so we're essentially computing the sum of a negative number and a positive number. Given that \sin x>\cos x for \pi, and \cos x>\sin x for \dfrac{5\pi}4, we can use a similar argument to establish in which half of the third quadrant the angle 10^4 lies. You'll find that the sine term is much larger, so that the second derivative is positive, which means y is concave up when x=10.
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