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3 years ago

If sin (13y-5) = cos (2y+5), then what is the value of y?

Mathematics

1 answer:

Xelga [282]3 years ago

3 0

Given sin (13y-5) = cos (2y+5)

We have a formula regarding complementary angles that is given as follows :-

If sin(A) = cos(B), then A + B = 90 degrees.

where A and B are complementary angles.

Comparing it with given information, we get A = (13y-5) and B = (2y+5).

So the sum of two angles A = (13y-5) and B = (2y+5) would be 90 degrees.

(13y-5)° + (2y+5)° = 90°

13y + 2y - 5 + 5 = 90°

15y = 90°

y = 6°

Hence, final answer is y = 6 degrees.

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Express the equation in rectangular form a) r = 2sin(2Θ) b) r = 4cos(3Θ)

Dafna11 [192]

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a. sqrt(x^2+y^2) * (x^2+y^2) = 4xy

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Step-by-step explanation:

a) r = 2sin(2Θ)

r* = 2 sin 2 theta

We know sin 2theta = 2 sin theta cos theta

r = 2 * 2 sin theta cos theta

sin theta = y/r and cos theta = x/r

r = 4 y/r * x/r

r = 4xy / r^2

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r * r^2 = 4xy

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sqrt(x^2+y^2) * (x^2+y^2) = 4xy

b) r = 4cos(3Θ)

we know that cos 3 theta = cos^3(theta) - 3 sin^2(theta) cos(theta)

r = 4 *cos^3(theta) - 3 sin^2(theta) cos(theta)

Factor out a cos theta

r = 4 *cos(theta){ cos^2 (theta) - 3 sin^2(theta) }

We know that sin theta = y/r and cos theta = x/r

r = 4 (x/r) { (x/r)^2 - 3 (y/r)^2}

r = 4 *(x/r) { (x^2/r^2 - 3 y^2/r^2}

Multiply by r

r^2 = 4x { (x^2/r^2 - 3 y^2/r^2}

Multiply by r^2

r^2 *r^2 = 4x { (x^2 - 3 y^2}

r^4 = 4x{ (x^2 - 3 y^2}

We know r^2 = (x^2+y^2)

(x^2+y^2)^2 = 4x{ (x^2 - 3 y^2}

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3 years ago

One grocery clerk can stock a shelf in 20 min. A second clerk requires 45 min to stock the same shelf. How long would it take to

Lorico [155]

Answer:

clerk A and clerk B can simultaneously stock a shelf in $\frac{180}{13}$ minutes

Explanation:

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A can stock a shelf in 20 min

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Consider the complete work to be W

A’s rate of stocking = $\frac{W}{20}$ per minute

B’s rate of stocking = $\frac{W}{45}$ per minute

When, A and B work simultaneously, rate of work done = $\frac{W}{20}+\frac{W}{45}$

Total work done simulatenously = $\frac{W}{\frac{W}{20}+\frac{w}{45}}$

= $\frac{20 * 45}{20+45}$

Therefore, clerk A and clerk B can simultaneously stock a shelf in $\frac{180}{13}$ minutes

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