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Step2247 [10]
3 years ago
6

Find the exact value, without a

Mathematics
1 answer:
Ghella [55]3 years ago
4 0

Answer:

√(2 + √3)/4

Step-by-step explanation:

Sine 5π/12 = Sine (5π/6)/2

Recall

π = 180°

Thus,

Sine (5π/6)/2 = Sine (5×180 /6)/2

= Sine 150/2

Recall

Sine θ/2 = √(1 – Cos θ)/2

Thus,

Sine 150/2 = √(1 – Cos 150)/2

But, Cosine is negative in the 2nd quadrant. Thus,

Cos 150 = – Cos 30 = –√3/2

Thus,

√(1 – Cos 150)/2 = √(1 – –√3/2 )/2

= √(1 + √3/2 )/2

= √[(2 + √3)/2 ÷ 2]

= √[(2 + √3)/2 × 1/2]

= √(2 + √3)/4

Therefore,

Sine 5π/12 = √(2 + √3)/4

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Express the integral as an iterated integral in six different ways, where E is the solid bounded by y=4-x^2-4z^2 and y=0
zmey [24]
Assuming you need the integral expressing the volume of E, the easiest setup is to integrate with respect to y first.

This is done with either

\displaystyle\iiint_E\mathrm dV=\int_{-2}^2\int_{-2}^2\int_0^{4-x^2-z^2}\mathrm dy\,\mathrm dx\,\mathrm dz
\displaystyle\iiint_E\mathrm dV=\int_{-2}^2\int_{-2}^2\int_0^{4-x^2-z^2}\mathrm dy\,\mathrm dz\,\mathrm dx

Thanks to symmetry, integrating with respect to either x or z first will be nearly identical.

First, with respect to x:

\displaystyle\iiint_E\mathrm dV=\int_{-2}^2\int_0^4\int_{-\sqrt{4-y-z^2}}^{\sqrt{4-y-z^2}}\mathrm dx\,\mathrm dy\,\mathrm dz
\displaystyle\iiint_E\mathrm dV=\int_0^4\int_{-2}^2\int_{-\sqrt{4-y-z^2}}^{\sqrt{4-y-z^2}}\mathrm dx\,\mathrm dz\,\mathrm dy

Next, with respec to z:

\displaystyle\iiint_E\mathrm dV=\int_{-2}^2\int_0^4\int_{-\sqrt{4-y-z^2}}^{\sqrt{4-y-x^2}}\mathrm dz\,\mathrm dy\,\mathrm dx
\displaystyle\iiint_E\mathrm dV=\int_0^4\int_{-2}^2\int_{-\sqrt{4-y-z^2}}^{\sqrt{4-y-x^2}}\mathrm dz\,\mathrm dx\,\mathrm dy
5 0
3 years ago
What is the answer to 1/7(x+3/4)=1/8
ivolga24 [154]

Answer:

<h3>x = 1/8</h3>

Step-by-step explanation:

1/7(x+3/4) = 1/8

Multiply 1/7 with x and 3/4

1/7x + 3/28 = 1/8

Multiply everything by 7, so x is a whole number

x + 21/28 = 7/8

Convert 21/28 into a similar like denominator to 7/8

x + 6/8 = 7/8

x = 7/8 -6/8

x = 1/8

<em>If this helped you, and this is the correct answer, make sure to give me the brainliest answer as it is greatly appreciated. Thank You!</em>

3 0
3 years ago
You have $30 dollars saved up. Every week you spend $6 at the arcade. Write an equation in slope intercept form that shows how m
Colt1911 [192]

Answer:

y = -6x + 30

Step-by-step explanation:

The inicial value you have is $30, so this will be the value of y after 0 weeks, that is, x = 0

After one week, you spend $6, so you will have y = 30 - 6 = 24 when x = 1.

With these pair of values, we can find the linear equation:

y = ax + b

for x = 0, y = 30:

30 = a*0 + b

b = 30

for x = 1, y = 24:

24 = a*1 + 30

a = 24 - 30 = -6

So, our equation is:

y = -6x + 30

7 0
3 years ago
Calculate the first and second
LenKa [72]

Answer:

Hi,

Step-by-step explanation:

\begin{array}{|c|c|c|c|}x&3x^2+5&\Delta_1x&\Delta_2x\\--&--&--&--\\0&5&-&-\\1&8&3&-\\2&17&9&6\\3&32&15&6\\4&53&21&6\\--&--&--&--\\\end{array}

3 0
2 years ago
Find the missing angle.
hammer [34]

Answer:

Linear pair angle of 40 is

=180-40

=140

If, the two rays are parallel

Therefore, the two rays are parallel and the straight line is transversal

Therefore, (?) angle =140 corrosponding angle

Your answer is 140

4 0
2 years ago
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