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bixtya [17]
3 years ago
5

If sin theta = cos theta then find the value of theta

Mathematics
1 answer:
Ksenya-84 [330]3 years ago
4 0

Step-by-step explanation:

\because \sin  \theta =  \cos  \theta  \\   \\ \therefore \: \sin  \theta =  \sin(90 \degree -   \theta)  \\   \\ \therefore \:  \theta =  90 \degree -   \theta \\   \\ \therefore \:   \theta + \theta=  90 \degree \\  \\ \therefore \:  2\theta =  90 \degree \\  \\\therefore \:  \theta =   \frac{90 \degree }{2} \\  \\ \huge \orange{\boxed{\therefore \:   \theta =   45 \degree}}\\  \\

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Identify an equation in point-slope form for the line parallel to y=-2/3x+8 that
UNO [17]

Answer:

\large\boxed{y+5=\dfrac{2}{3}(x-4)}

Step-by-step explanation:

The point-slope form of an equation of a line:

y-y_1=m(x-x_1)

m - slope

Parallel lines have the same slope.

We have the equation in the slope-intercept form (y = mx + b)

y=-\dfrac{2}{3}x+8\to m=\dfrac{2}{3}

Put to the point-slope equation value of the slope and the coordinates of the point (4, -5):

y-(-5)=\dfrac{2}{3}(x-4)\\\\y+5=\dfrac{2}{3}(x-4)

7 0
3 years ago
What are two ways that you can find the surface area of a prism
3241004551 [841]

Answer:


Step-by-step explanation:


4 0
3 years ago
Consider the sequence 8, 14, 20, 26, . . .. (a) What is the next term in the sequence? 2.2 Exercises 98 (b) Find a formula for t
omeli [17]

Answer:

Step-by-step explanation:

Each term of the given arithmetic sequence is 6 more than the previous one.  Thus, the next term is 26+6, or 32.

a(n) = 8 + 6(n-1)

3 0
3 years ago
Sketch the domain D bounded by y = x^2, y = (1/2)x^2, and y=6x. Use a change of variables with the map x = uv, y = u^2 (for u ?
cluponka [151]

Under the given transformation, the Jacobian and its determinant are

\begin{cases}x=uv\\y=u^2\end{cases}\implies J=\begin{bmatrix}v&u\\2u&0\end{bmatrix}\implies|\det J|=2u^2

so that

\displaystyle\iint_D\frac{\mathrm dx\,\mathrm dy}y=\iint_{D'}\frac{2u^2}{u^2}\,\mathrm du\,\mathrm dv=2\iint_{D'}\mathrm du\,\mathrm dv

where D' is the region D transformed into the u-v plane. The remaining integral is the twice the area of D'.

Now, the integral over D is

\displaystyle\iint_D\frac{\mathrm dx\,\mathrm dy}y=\left\{\int_0^6\int_{x^2/2}^{x^2}+\int_6^{12}\int_{x^2/2}^{6x}\right\}\frac{\mathrm dx\,\mathrm dy}y

but through the given transformation, the boundary of D' is the set of equations,

\begin{array}{l}y=x^2\implies u^2=u^2v^2\implies v^2=1\implies v=\pm1\\y=\frac{x^2}2\implies u^2=\frac{u^2v^2}2\implies v^2=2\implies v=\pm\sqrt2\\y=6x\implies u^2=6uv\implies u=6v\end{array}

We require that u>0, and the last equation tells us that we would also need v>0. This means 1\le v\le\sqrt2 and 0, so that the integral over D' is

\displaystyle2\iint_{D'}\mathrm du\,\mathrm dv=2\int_1^{\sqrt2}\int_0^{6v}\mathrm du\,\mathrm dv=\boxed6

4 0
3 years ago
Please answer fully​
Andrews [41]

Answer:

There is a 1/6 chance of rolling a certain number and 1/2 chance of getting a heads.

1/6 x 1/2 = 1/12 so C.

1 is the chance of getting the wanted number / 6 is all the numbers in total

When there are multiple chances you just multiply the fractions

Step-by-step explanation:

4 0
3 years ago
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