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Archy [21]
2 years ago
12

Given the universal set U = {v, w, x, y, z), and subsets A = {v, w, z} and B = {x, y, z), indicate the roster

Mathematics
1 answer:
lukranit [14]2 years ago
8 0

If U = {v, w, x, y, z} and A = {v, w, z}, then

A' = {x, y}

(A' is the complement of A - it's the set containing all elements of U that are not in A)

If B = {x, y, z}, then

B' = {v, w}

Their their union is

A' U B' = {v, w, x, y}

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What are the ratios for sin A and cos A? The triangle is not drawn to scale.
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Answer:

SinA = \frac{84}{85}  and  CosA=\frac{13}{85}

Step-by-step explanation:

The ratios of sine and cos are defined as follows:

Sin A = \frac{Opposite}{Hypotenuse} , and

CosA = \frac{Adjacent}{Hypotenuse}

The hypotenuse is always the side opposite of the 90 degree angle (for the given triangle, the hypotenuse is 85)

Since we are looking at the angle A, the opposite side with respect to A would be the side length of 84. That leaves the side 13 as the adjacent side.

Thus, we can now write:

Sin A = \frac{Opposite}{Hypotenuse}\\SinA = \frac{84}{85}

CosA = \frac{Adjacent}{Hypotenuse}\\CosA=\frac{13}{85}

The correct answer is  the first answer choice.

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A ball is launched straight up in the air from a height of 6 feet. Its velocity (feet/second) t seconds after launch is given by
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Step-by-step explanation:

A ball is launched straight up in the air from a height of 6 feet. The velocity as a function of time t is given by :

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Height of the ball is :

h(t)=\int\limits{f(t){\cdot} dt}\\\\h(t)=\int\limits{(-32t+285){\cdot} dt}\\\\h(t)=-16t^2+285t+C

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h(t)=-16t^2+285t+6

At t = 2 s, h(t)=-16(2)^2+285(2)+6=512\ m

At t = 9 s, h(t)=-16(9)^2+285(9)+6=1275\ m

Between 2 s and 9 s, the ball's height changed is : 1275 - 512 = 763 m.

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