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Orlov [11]
3 years ago
15

If cos(x)cos(π/7)+sin(x)sin(π/7)= - (√2)/2, then x can equal:

Mathematics
1 answer:
r-ruslan [8.4K]3 years ago
8 0

\bf \textit{Sum and Difference Identities} \\\\ sin(\alpha + \beta)=sin(\alpha)cos(\beta) + cos(\alpha)sin(\beta) \\\\ sin(\alpha - \beta)=sin(\alpha)cos(\beta)- cos(\alpha)sin(\beta) \\\\ cos(\alpha + \beta)= cos(\alpha)cos(\beta)- sin(\alpha)sin(\beta) \\\\ cos(\alpha - \beta)= cos(\alpha)cos(\beta) + sin(\alpha)sin(\beta) \\\\[-0.35em] ~\dotfill\\\\

\bf cos(x)cos\left( \cfrac{\pi }{7} \right)+sin(x)sin\left( \cfrac{\pi }{7} \right)=-\cfrac{\sqrt{2}}{2}\implies cos\left( x-\cfrac{\pi }{7} \right)=-\cfrac{\sqrt{2}}{2} \\\\\\ x-\cfrac{\pi }{7}=cos^{-1}\left( -\cfrac{\sqrt{2}}{2} \right)\implies x-\cfrac{\pi }{7}= \begin{cases} \frac{3\pi }{4}\\\\ \frac{5\pi }{4} \end{cases} \\\\[-0.35em] ~\dotfill

\bf x-\cfrac{\pi }{7}=\cfrac{3\pi }{4}\implies x=\cfrac{3\pi }{4}+\cfrac{\pi }{7}~\hfill \stackrel{n ~\in~ \mathbb{Z}}{x=\cfrac{3\pi }{4}+\cfrac{\pi }{7}~~~~+2\pi n} \\\\[-0.35em] ~\dotfill\\\\ x-\cfrac{\pi }{7}=\cfrac{5\pi }{4}\implies x=\cfrac{5\pi }{4}+\cfrac{\pi }{7}~\hfill \stackrel{n ~\in~ \mathbb{Z}}{x=\cfrac{5\pi }{4}+\cfrac{\pi }{7}~~~~+2\pi n}

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A car travels 17 miles on one gallon of gas
zmey [24]

When x =170, y =10, when x = 187, y = 1, when x = 204, y = 12, when x = 221, y = 13, when x = 238, y = 14, when x = 255, y = 15, when x = 272, y = 16, when x = 289, y = 17, when x = 306, y = 18, when x = 323, y = 19, when x = 340, y = 20,

Step-by-step explanation:

Step 1; Assume y is the gallons in the tank while x is the range of the car. We need to determine the equation relating the y to the x values in the given coordinates. x is the dependent value whereas y is the independent value i.e. the value of x depends on the value of y.

Step 2; As y increases, x also increases. For every extra gallon in the tank, the car can go another 17 miles. So with y as the amount of gas in the tank in gallons and x as the range of vehicle, we get;

x = 17y, this represents the relation between x and y.

To find the gallons in the tank, y = \frac{x}{17},

For x = 170, y = \frac{170}{17} = 10,

Similarly equating the values we get that when x = 187, y = 11,

when x = 204, y = 12,

when x = 221, y = 13,

when x = 238, y = 14,

when x = 255, y = 15,

when x = 272, y = 16,

when x = 289, y = 17,

when x = 306, y = 18,

when x = 323, y = 19,

when x = 340, y = 20,

8 0
3 years ago
Please help Simplify the following expression.
Whitepunk [10]

Answer:

răspuns corect :a 2x -8y +3

Step-by-step explanation:

dami coroana te rog

4 0
2 years ago
PLS HELP ME NOW ITS PYTHAGOREAN THEOREM
rusak2 [61]

Answer:

a =2.2

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean theorem

a^2+b^2 = c^2

where a and b are the legs and c is the hypotenuse

a^2+2^2 = 3^2

a^2 +4 = 9

a^2 = 9-4

a^2 = 5

Taking the square root of each side

sqrt(a^2) = sqrt(5)

a = sqrt(5)

a=2.236067977

To the nearest tenth

a =2.2

3 0
3 years ago
Given that LM and LN are tangent to the circle and that the measure of angle MLN = 75.86, find the measure of arc MN.
siniylev [52]

we know that

The measure of the external angle is the semidifference of the arcs that it covers

so

∠MLN=(1/2)*(mayor arc MN-minor arc MN)

Let

x------> minor arc MN

major arc MN=360-x

substitute in the formula above

∠MLN=(1/2)*(mayor arc MN-minor arc MN)

75.86=(1/2)*(360-x-x)------> 151.72=(360-2x)------>360-151.72=2x

x=104.14°

therefore

the answer is

the measure of arc MN (minor arc) is 104.14°

7 0
3 years ago
Choose two angles that are each separately corresponding angles with 5
netineya [11]
2 and 12 both correspond with angle 5
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3 years ago
Read 2 more answers
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