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saw5 [17]
3 years ago
6

Find the x-values that are solutions of the equation 5cot^2x-15=0

Mathematics
1 answer:
julia-pushkina [17]3 years ago
3 0
First solve for the trig function 'cot'
cot^2 x = \frac{15}{5} = 3

Next take the sqrt of both sides (include plus/minus)
cot x = \pm \sqrt{3}

Now take reciprocal of both sides, this will change trig function to 'tan'
(cot = 1/tan)

tan x = \pm \frac{1}{\sqrt{3}} = \pm \frac{\sqrt{3}}{3}

Finally use the unit circle or inverse tan on your calculator to find x.
There will be 4 solutions, one for each quadrant.

x = \frac{\pi}{6}, \frac{5\pi}{6}, \frac{7\pi}{6}, \frac{11\pi}{6}
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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
Human hair grows at the average rate of 1/3 inch per month. Sara wants her hair to grow 4 2/3 inches longer. About how many mont
SVETLANKA909090 [29]

Answer:

14 months

Step-by-step explanation:

1/3 x 12 = 4.

1/3 x 2 = 2/3.

12 + 2 = 14.

It will take her 14 months.

Hope this helps! :)

6 0
2 years ago
Suppose that the regression equation y = 16.99 + 0.32 x1 + 0.41 x2 + 5.31 x3 predicts an adult’s height (y) given the individual
umka21 [38]

Answer:

Step-by-step explanation:

It is given that the regression equation

y = 16.99 + 0.32 x_1 + 0.41 x_2 + 5.31 x_3

predicts an adult’s height (y) given the individual’s mother’s height (x1), his or her father’s height (x2), and whether the individual is male (x3 = 1) or female (x3 = 0).

The coefficient of x1 = 0.32 represents the increase in height of the child due to one inch increase in mother.

Similarly coefficient of x2 = 0.42 represents the increase in height of the child due to one inch increase in father.

and coefficient of x3 = 5.31 represents the increase in height of the child due to being a male than a female.

8 0
3 years ago
Each day, Karen makes 45 loaves of bread at the bakery where she works. Each loaf of bread requires 5 cups of flour. One pound o
xxTIMURxx [149]

Answer: 5cups of flour = 1 loaf of bread

45 loaves of bread multiplied by 5 cups of four = 225 cups of flour to make 45 loaves of bread.

225 cups of flour divided by 4 = 56.25 pounds of flour.

6 0
3 years ago
Read 2 more answers
Help please :) I'd greatly appreciate it
azamat
= 4i (2i) <span>√6
= 8i^2 </span><span>√6 but i^2 = -1
= - 8</span><span>√6</span><span>

</span>
6 0
3 years ago
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