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3 years ago

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Scorpion4ik [409]3 years ago

4 0

???????????????????????? What are the dots for

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Angle θ is in standard position. if sin(θ) = − 1/3, and π < θ < 3π/2 , find cos(θ).

scoray [572]

Use pythagorean theorem:
sin^2 + cos^2 = 1

(-1/3)^2 + cos^2 = 1
1/9 + cos^2 = 1
cos^2 = 8/9
cos = +- sqrt(8)/sqrt(9) = +- 2sqrt(2)/3

Determine whether cos is positive or negative by looking at which quadrant the angle is in.
pi < theta < 3pi/2 ---> this is 3rd quadrant where x or cos is negative

Therefore cos(theta) = -2sqrt(2)/3

7 0

3 years ago

Read 2 more answers

Consider a uniform distribution created by a random number generator. The distribution looks like a square with a length of 1 an

vekshin1

The rigorous way to do this would be to compute a few integrals, but less work is usually better. Each of these probabilities correspond to the areas of rectangles. Each rectangle will have a height of 1, and the probability of interest will tell you everything you need to know about their lengths.

$\mathbb P(0\le X\le0.4)\implies \text{length}=0.4\implies\mathbb P(0\le X\le0.4)=0.4\times1=0.4$

$\mathbb P(0.4\le X\le1)\implies \text{length}=0.6\implies\mathbb P(0\le X\le0.4)=0.6$

Alternatively, you can use the fact that $\mathbb P(0.4\le X\le 1)=1-\mathbb P(0\le X\le 0.4)$ to get the same result.

$\mathbb P(X>0.6)=\mathbb P(0.60.6)=0.4$

$\mathbb P(X\le0.6)\implies \text{length}=0.6\implies\mathbb P(X\le0.6)=0.6$

$\mathbb P(0.23\le X\le0.76)\implies \text{length}=0.76-0.23=0.53\implies\mathbb P(0.23\le X\le0.76)=0.53$

3 0

3 years ago

Find the slope of the line

Reika [66]

Answer:

7/3

Step-by-step explanation:

We can find the slope of a line given two points by

m = (y2-y1)/ (x2-x1)

= (3--4)/(4-1)

= (3+4)/(4-1)

7/3

5 0

3 years ago

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What is the surface area of the figure below? Round your answer to the nearest whole number.

Strike441 [17]

Answer:

I believe the answer is C. 674 because the surface area of the pyramid is approx. 682.64569.

Step-by-step explanation:

I'm sorry I could be of more help.

3 0

2 years ago

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Vertices A and B of triangle ABC are on one bank of a river, and vertex C is on the opposite bank. The distance between A and B

Anna71 [15]

Answer:

The length of side b is 179 ft

Step-by-step explanation:

Given triangle ABC in which

∠A = 33°, ∠B = 63°, c=200

we have to find the length of b

In ΔABC, by angle sum property of triangle

∠A+∠B+∠C=180°

33°+63°+∠C=180°

∠C=180°-33°-63°=84°

By sine law,

$\frac{\sin \angle A}{a}=\frac{\sin \angle B}{b}=\frac{\sin \angle C}{c}$

$\frac{\sin \angle B}{b}=\frac{\sin \angle C}{c}$

$\frac{\sin 63^{\circ}}{b}=\frac{\sin 84^{\circ}}{200}$

$b=200\times \frac{\sin 63^{\circ}}{\sin 84^{\circ}}=179.182887\sim 179 ft$

The length of side b is 179 ft

Option C is correct.

7 0

3 years ago