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3 years ago

Find the answer to each trigonometric function below.

Mathematics

1 answer:

Airida [17]3 years ago

8 0

Answer:

Sin A = $\frac{opposite}{hypotenuse} =\frac{32}{40} =\frac{4(8)}{5(8)} =\frac{4}{5}$
Cos C = $\frac{adjacent}{hypotenuse} =\frac{16}{34}=\frac{2(8)}{2(17)} =\frac{8}{17}$
Tan A = $\frac{opposite}{adjacent} =\frac{21}{20}$

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A group of college students were asked about their TV watching habits. Of those surveyed, 30 students watch The Walking Dead, 24

Usimov [2.4K]

Answer: 44 students

Step-by-step explanation:

Let Walking dead be denoted as W

Let Blacklist be denoted as B

Let Game of thrones be denoted as G

Total number of students that watch W = 30

W&G&B = 7

W&B only = 13-7 = 6

W&G only = 10-7 = 3

To get the number of people that watch W ONLY, we subtract those that watch W&B only (6), W&G only(3) and W&B&G(7) from 30. Hence,

W Only = 30 - 6- 3 - 7= 14 (14 students watch Walking dead only)

Total number of students that watch B =24

B&G&W = 7

B&W only = 13-7 = 6

B&G only = 16 - 7 = 9

Hence, those that watch B only = 24-6-9-7= 2 students.

Total number of students that watch G = 22

G&W&B = 7

G&B only = 9

G&W only = 3

Hence those that watch G only = 22-9-3-7 = 3 students.

Hence number of students that watch at least one show = W only + B only + G only + W&B only + W&G only + B&G only + W&B&G.

= 14+2+3+6+3+9+7 = 44 students.

3 0

3 years ago

Express each number as a quotient of two integer of 54

inysia [295]

There are many possibilities. For example 108/2, -108/-2, 162/3, -162/-3, 216/4, -216/-4, and so forth....

6 0

3 years ago

(x^2y+e^x)dx-x^2dy=0

klio [65]

It looks like the differential equation is

$\left(x^2y + e^x\right) \,\mathrm dx - x^2\,\mathrm dy = 0$

Check for exactness:

$\dfrac{\partial\left(x^2y+e^x\right)}{\partial y} = x^2 \\\\ \dfrac{\partial\left(-x^2\right)}{\partial x} = -2x$

As is, the DE is not exact, so let's try to find an integrating factor µ(x, y) such that

$\mu\left(x^2y + e^x\right) \,\mathrm dx - \mu x^2\,\mathrm dy = 0$

*is* exact. If this modified DE is exact, then

$\dfrac{\partial\left(\mu\left(x^2y+e^x\right)\right)}{\partial y} = \dfrac{\partial\left(-\mu x^2\right)}{\partial x}$

We have

$\dfrac{\partial\left(\mu\left(x^2y+e^x\right)\right)}{\partial y} = \left(x^2y+e^x\right)\dfrac{\partial\mu}{\partial y} + x^2\mu \\\\ \dfrac{\partial\left(-\mu x^2\right)}{\partial x} = -x^2\dfrac{\partial\mu}{\partial x} - 2x\mu \\\\ \implies \left(x^2y+e^x\right)\dfrac{\partial\mu}{\partial y} + x^2\mu = -x^2\dfrac{\partial\mu}{\partial x} - 2x\mu$

Notice that if we let µ(x, y) = µ(x) be independent of y, then ∂µ/∂y = 0 and we can solve for µ :

$x^2\mu = -x^2\dfrac{\mathrm d\mu}{\mathrm dx} - 2x\mu \\\\ (x^2+2x)\mu = -x^2\dfrac{\mathrm d\mu}{\mathrm dx} \\\\ \dfrac{\mathrm d\mu}{\mu} = -\dfrac{x^2+2x}{x^2}\,\mathrm dx \\\\ \dfrac{\mathrm d\mu}{\mu} = \left(-1-\dfrac2x\right)\,\mathrm dx \\\\ \implies \ln|\mu| = -x - 2\ln|x| \\\\ \implies \mu = e^{-x-2\ln|x|} = \dfrac{e^{-x}}{x^2}$

The modified DE,

$\left(e^{-x}y + \dfrac1{x^2}\right) \,\mathrm dx - e^{-x}\,\mathrm dy = 0$

is now exact:

$\dfrac{\partial\left(e^{-x}y+\frac1{x^2}\right)}{\partial y} = e^{-x} \\\\ \dfrac{\partial\left(-e^{-x}\right)}{\partial x} = e^{-x}$

So we look for a solution of the form F(x, y) = C. This solution is such that

$\dfrac{\partial F}{\partial x} = e^{-x}y + \dfrac1{x^2} \\\\ \dfrac{\partial F}{\partial y} = e^{-x}$

Integrate both sides of the first condition with respect to x :

$F(x,y) = -e^{-x}y - \dfrac1x + g(y)$

Differentiate both sides of this with respect to y :

$\dfrac{\partial F}{\partial y} = -e^{-x}+\dfrac{\mathrm dg}{\mathrm dy} = e^{-x} \\\\ \implies \dfrac{\mathrm dg}{\mathrm dy} = 0 \implies g(y) = C$

Then the general solution to the DE is

$F(x,y) = \boxed{-e^{-x}y-\dfrac1x = C}$

5 0

3 years ago

WILL MARK BRAINLIEST . PLEASE HELP . Pigeons can fly at a rate of 168ft every 6 minutes, and ravens can fly at a rate of 472ft e

Mila [183]

Answer:

2,265.60 ft/hr

Step-by-step explanation:

168ft/6min = 28ft/min * 60min= 1,680ft/hr

472ft/12.5min= 37.76ft/min * 60min= 2,265.60ft/hr

3 0

3 years ago

Given that a randomly chosen customer likes cake, what is the probability that the customer also likes pie? two-sevenths two-fif

Alex

Using it's concept, it is found that the probability that the customer also likes pie is of $\frac{2}{7}$

<h3>What is a probability?</h3>

A probability is given by the number of desired outcomes divided by the number of total outcomes.

Researching the problem on the internet, it is found that of the 14 students that like cake, 4 also like pie, hence the probability is given by:

p = 4/14 = 2/7.

More can be learned about probabilities at brainly.com/question/14398287

#SPJ4

6 0

2 years ago

Find the answer to each trigonometric function below. ​

Find the answer to each trigonometric function below.