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3 years ago

the thickness of a cd is about 1/20 inch. if carrie has a stack of 52 cds,what is the height of the stack

Mathematics

1 answer:

SVETLANKA909090 [29]3 years ago

7 0

The answer would be 26 because you're multiplying .5 times 52

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Sin(A+B) sin(A-B) /sin^A Cos^B=1-cot^A Tan^B

telo118 [61]

In order to prove

$\dfrac{\sin(x+y)\sin(x-y)}{\sin^2(x)\cos^2(x)}=1-\cot^2(x)\tan^2(y)$

Let's write both sides in terms of $\sin(x),\ \sin^2(x),\ \cos(x),\ \cos^2(x)$ only.

Let's start with the left hand side: we can use the formula for sum and subtraction of the sine to write

$\sin(x+y)=\cos(y)\sin(x)+\cos(x)\sin(y)$

and

$\sin(x-y)=\cos(y)\sin(x)-\cos(x)\sin(y)$

So, their multiplication is

$\sin(x+y)\sin(x-y)=(\cos(y)\sin(x))^2-(\cos(x)\sin(y))^2\\=\cos^2(y)\sin^2(x)-\cos^2(x)\sin^2(y)$

So, the left hand side simplifies to

$\dfrac{\cos^2(y)\sin^2(x)-\cos^2(x)\sin^2(y)}{\sin^2(x)\cos^2(y)}$

Now, on with the right hand side. We have

$1-\cot^2(x)\tan^2(y)=1-\dfrac{\cos^2(x)}{\sin^2(x)}\cdot\dfrac{\sin^2(y)}{\cos^2(y)} = 1-\dfrac{\cos^2(x)\sin^2(y)}{\sin^2(x)\cos^2(y)}$

Now simply make this expression one fraction:

$1-\dfrac{\cos^2(x)\sin^2(y)}{\sin^2(x)\cos^2(y)}=\dfrac{\sin^2(x)\cos^2(y)-\cos^2(x)\sin^2(y)}{\sin^2(x)\cos^2(y)}$

And as you can see, the two sides are equal.

6 0

4 years ago

Which expression use the associative property and make it easier to evaluate 6 (3/2 x 1/5)

k0ka [10]

Answer:

Step-by-step explanation:

Associative property moves the parentheses, but the numbers stay in the same order.

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3 years ago

Choose the equation and the slope of the line that passes through (4,-2) and is perpendicular to the X-axis.

Tanya [424]

Answer:

C. Equation: x=4

D. Slope: undefined

Step-by-step explanation:

If a line is perpendicular to the x-axis, then it is a vertical line because the x-axis is horizontal.

The slope of a vertical line is undefined.

The equation of a vertical line through $(x_1,y_1)$ is $x=x_1$

Since the vertical line passes through (4,-2), its equation is

$x=4$

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1'7" + 3'7" ‾‾‾‾‾‾ ' "

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Answer:

Step-by-step explanation:

4'7"<3

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