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vagabundo [1.1K]
3 years ago
12

I would really appreciate help with the following, along with work shown so I can understand how these were solved.

Mathematics
1 answer:
Alja [10]3 years ago
6 0

First, you have to know the double angle formula:

sin 2A  =  2 sin A cos A

cos 2A  =  cos² A − sin² A  =  2 cos² A − 1  =  1 − 2 sin² A

tan 2A<span> = 2 tan </span>A<span> / (1 − tan² </span>A)


Next, find the other leg: 17^2-15^=64, √64 is 8, so the unknown leg length is 8.

sinα=15/17, cosα=8/17, tanα=15/8

sinβ=8/17, cosβ15/17, tanβ=8/15

Plug these values in the above formula, you'll have your answers.


For the half angles, know the half-angle formula:

sin(B/2) = ± √<span>(1 − cos B)/2</span>

cos(B/2) = ± √<span>(1 + cos B)/2</span>

tan(B/2)  =  (1 − cos B) / sin B<span>  =  sin </span>B<span> / (1 + cos </span>B)

refer to this website for details:

<span>https://brownmath.com/twt/double.htm
</span>


For the power reduction formula, please search for it. I tried to copy and paste here, but it wouldn't paste. 

for number 4, factor the quadratic equation into (cscx-8)(cscx+1)=0

cscx=8 or cscx=-1

You may not have the csc button on your calculator. Recall that csc is 1/sin, so sinx=1/8 or sinx=-1, so x is either 7.18 or 270 degrees



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Please I need help with differential equation. Thank you
Inga [223]

1. I suppose the ODE is supposed to be

\mathrm dt\dfrac{y+y^{1/2}}{1-t}=\mathrm dy(t+1)

Solving for \dfrac{\mathrm dy}{\mathrm dt} gives

\dfrac{\mathrm dy}{\mathrm dt}=\dfrac{y+y^{1/2}}{1-t^2}

which is undefined when t=\pm1. The interval of validity depends on what your initial value is. In this case, it's t=-\dfrac12, so the largest interval on which a solution can exist is -1\le t\le1.

2. Separating the variables gives

\dfrac{\mathrm dy}{y+y^{1/2}}=\dfrac{\mathrm dt}{1-t^2}

Integrate both sides. On the left, we have

\displaystyle\int\frac{\mathrm dy}{y^{1/2}(y^{1/2}+1)}=2\int\frac{\mathrm dz}{z+1}

where we substituted z=y^{1/2} - or z^2=y - and 2z\,\mathrm dz=\mathrm dy - or \mathrm dz=\dfrac{\mathrm dy}{2y^{1/2}}.

\displaystyle\int\frac{\mathrm dy}{y^{1/2}(y^{1/2}+1)}=2\ln|z+1|=2\ln(y^{1/2}+1)

On the right, we have

\dfrac1{1-t^2}=\dfrac12\left(\dfrac1{1-t}+\dfrac1{1+t}\right)

\displaystyle\int\frac{\mathrm dt}{1-t^2}=\dfrac12(\ln|1-t|+\ln|1+t|)+C=\ln(1-t^2)^{1/2}+C

So

2\ln(y^{1/2}+1)=\ln(1-t^2)^{1/2}+C

\ln(y^{1/2}+1)=\dfrac12\ln(1-t^2)^{1/2}+C

y^{1/2}+1=e^{\ln(1-t^2)^{1/4}+C}

y^{1/2}=C(1-t^2)^{1/4}-1

I'll leave the solution in this form for now to make solving for C easier. Given that y\left(-\dfrac12\right)=1, we get

1^{1/2}=C\left(1-\left(-\dfrac12\right)^2\right))^{1/4}-1

2=C\left(\dfrac54\right)^{1/4}

C=2\left(\dfrac45\right)^{1/4}

and so our solution is

\boxed{y(t)=\left(2\left(\dfrac45-\dfrac45t^2\right)^{1/4}-1\right)^2}

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3 years ago
Find f ′(x) for f(x) = sin (3x2).
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Answer:

  f'(x) = cos(3x^2)(6x)

Step-by-step explanation:

(d/dx)(sin u) = cos(u)·du/dx . . . . . chain rule

For f(x) = sin(3x^2), this means ...

  f'(x) = cos(3x^2)(6x)

3 0
3 years ago
What is the value of (x+1) in 13(6x − 5) − x = 13 − 2(x + 1)
yKpoI14uk [10]
The answer is -2x+11 for sure is the answer
5 0
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The number of newly reported crime cases in a county in New York State is shown in
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Answer is answer

Step-by-step explanation:The number of newly reported crime cases in a county in New York State is shown in

the accompanying table, where x represents the number of years since 2007, and y

represents number of new cases. Write the linear regression equation that represents

this set of data, rounding all coefficients to the nearest hundredth. Using this

equation, find the projected number of new cases for 2016, rounded to the nearest

whole number

Years since 2007 (x) New Cases (y)

0

1156

1

1167

2

1230

3

1215

4

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5

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Alex placed a classified ad in the local newspaper to sell his used Nissan Sentra. He plans to write a 9 line ad. The newspaper
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Answer:

$67 total

Step-by-step explanation:

9-3= 6

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49.50+17.50= $67

7 0
3 years ago
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