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2 years ago

6

HOW DO YOU FIND THE SINE, COSINE, AND TANGENT VALUES GIVEN A POINT ON A CIRCLE

1 answer:

Arte-miy333 [17]2 years ago

7 0

When the circle is centered at the origin and the angle of interest (α) is measured counterclockwise from the positive x-axis, the trig functions can be determined from the coordinates of the point (x, y) and the radius of the circle (r) (which can also be determined from the coordinates of the point).

The radius is
r = √(x² +y²)

The trig functions are (remember SOH CAH TOA?)
sin(α) = y/r
cos(α) = x/r
tan(α) = y/x

These ratios hold regardless of quadrant.

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Answer:

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If f(x) =2x²-x, find f(-4)-f(9)

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A particular sale involves four items randomly selected from a large lot that is known to contain 9% defectives. Let X denote th

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Answer:

The expected repair cost is $3.73.

Step-by-step explanation:

The random variable <em>X</em> is defined as the number of defectives among the 4 items sold.

The probability of a large lot of items containing defectives is, <em>p</em> = 0.09.

An item is defective irrespective of the others.

The random variable <em>X</em> follows a Binomial distribution with parameters <em>n</em> = 9 and <em>p</em> = 0.09.

The repair cost of the item is given by:

$C=3X^{2}+X+2$

Compute the expected cost of repair as follows:

$E(C)=E(3X^{2}+X+2)$

$=3E(X^{2})+E(X)+2$

Compute the expected value of <em>X</em> as follows:

$E(X)=np$

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The expected value of <em>X</em> is 0.36.

Compute the variance of <em>X</em> as follows:

$V(X)=np(1-p)$

$=4\times 0.09\times 0.91\\=0.3276\\$

The variance of <em>X</em> is 0.3276.

The variance can also be computed using the formula:

$V(X)=E(Y^{2})-(E(Y))^{2}$

Then the formula of $E(Y^{2})$ is:

$E(Y^{2})=V(X)+(E(Y))^{2}$

Compute the value of $E(Y^{2})$ as follows:

$E(Y^{2})=V(X)+(E(Y))^{2}$

$=0.3276+(0.36)^{2}\\=0.4572$

The expected repair cost is:

$E(C)=3E(X^{2})+E(X)+2$

$=(3\times 0.4572)+0.36+2\\=3.7316\\\approx 3.73$

Thus, the expected repair cost is $3.73.

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