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morpeh [17]
3 years ago
7

. Write the equation in slope intercept form for the line that goes through point (−10, 8) with slope =6.

Mathematics
1 answer:
Doss [256]3 years ago
4 0
Y = mx + b is slope intercept form

x = -10
y = 8
m = 6

1. Solve for b

8 = (6)(-10) + b
b = 68

2. Plug m and b back into your slope intercept equation

y = 6x + 68
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Save me the headache
maxonik [38]

(9\sin2x+9\cos2x)^2=81

Taking the square root of both sides gives two possible cases,

9\sin2x+9\cos2x=9\implies\sin2x+\cos2x=1

or

9\sin2x+9\cos2x=-9\implies\sin2x+\cos2x=-1

Recall that

\sin(\alpha\pm\beta)=\sin\alpha\cos\beta\pm\cos\alpha\sin\beta

If \alpha=2x and \beta=\dfrac\pi4, we have

\sin\left(2x+\dfrac\pi4\right)=\dfrac{\sin2x+\cos2x}{\sqrt2}

so in the equations above, we can write

\sin2x+\cos2x=\sqrt2\sin\left(2x+\dfrac\pi4\right)=\pm1

Then in the first case,

\sqrt2\sin\left(2x+\dfrac\pi4\right)=1\implies\sin\left(2x+\dfrac\pi4\right)=\dfrac1{\sqrt2}

\implies2x+\dfrac\pi4=\dfrac\pi4+2n\pi\text{ or }\dfrac{3\pi}4+2n\pi

(where n is any integer)

\implies2x=2n\pi\text{ or }\dfrac\pi2+2n\pi

\implies x=n\pi\text{ or }\dfrac\pi4+n\pi

and in the second,

\sqrt2\sin\left(2x+\dfrac\pi4\right)=-1\implies\sin\left(2x+\dfrac\pi4\right)=-\dfrac1{\sqrt2}

\implies2x+\dfrac\pi4=-\dfrac\pi4+2n\pi\text{ or }-\dfrac{3\pi}4+2n\pi

\implies2x=-\dfrac\pi2+2n\pi\text{ or }-\pi+2n\pi

\implies x=-\dfrac\pi4+n\pi\text{ or }-\dfrac\pi2+n\pi

Then the solutions that fall in the interval [0,2\pi) are

x=0,\dfrac\pi4,\dfrac\pi2,\dfrac{3\pi}4,\pi,\dfrac{5\pi}4,\dfrac{3\pi}2,\dfrac{7\pi}4

5 0
3 years ago
Read 2 more answers
From her eye, which stands 1,61 meters above the ground, Savannah measures the
Cloud [144]

Answer:

152.99 m

Step-by-step explanation:

Using the solution diagram attached below :

We can obtain the height, h of skyscraper to the position of her eye level using trigonometry ;

Tan θ = opposite / Adjacent

Tan 24 = h / 340

h = tan 24 * 340

h = 151.37775

Hence, the height will be (h + distance from eyelevel to ground)

151.37775 + 1.61

= 152.98775

= 152.99 m

4 0
2 years ago
PLEASE HELP WILL GIVE BRAINLIEST
vekshin1

Answer:

Step-by-step explanation:

Tod did not want the answer?

3 0
2 years ago
what is the height of a rectangular prism that has a volume of 2880 cubic inches and a base of 240 inches
Sergeu [11.5K]

Answer:

h = 12 in

Step-by-step explanation:

To find the height, divide the volume by the base:

              2880 in^3

height:  ------------------ = 12 in

                  240 in

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2 years ago
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the sales tax rate in a city is 8%. Find the sales tax charged on a purchase of $800. Then find the total cost.
Svetradugi [14.3K]
64 dollars is the tax, the total cost would be $864.
Use this for percentages.
https://percentagecalculator.net/

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3 years ago
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