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schepotkina [342]
3 years ago
15

Find the primary solution of cosθ=−0.3 ⁡

Mathematics
1 answer:
Agata [3.3K]3 years ago
4 0

The solution of cos θ = −0.3 is θ = 107.45760312 degrees

<em><u>Solution:</u></em>

Given that we have to find the primary solution of cos \theta = -0.3

To solve this equation, you must find the unknown (theta)

cos \theta = -0.3

Use the inverse of cosine (Arccos) to find the angle measurement (in degrees) of theta

\theta = arccos (-0.3)

We know that arccos (-0.3) = 107.45760312 degrees

[ If you reference a unit circle or use a calculator ]

\theta = 107.45760312^{\circ}

Therefore solution of cos θ = −0.3 is θ = 107.45760312 degrees

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Question is attached
rodikova [14]

9514 1404 393

Answer:

  x = 12

  perimeter = 124

Step-by-step explanation:

The midline RS is half the length of MN, so we have ...

  2×RS = MN

  2(x +3) = 5x -30

  2x +6 = 5x -30

  36 = 3x . . . . . . . . . add 30-2x

  12 = x . . . . . . . . . . divide by 3

__

The length RS is then ...

  RS = x +3 = 15

and the perimeter of QRS is ...

  P(QRS) = QR +RS +SQ = 25 +15 +22 = 62

The perimeter of QRS is half the perimeter of MNP, so ...

  P(MNP) = 2×P(QRS) = 2×62 = 124

The perimeter of ΔMNP = 124.

8 0
2 years ago
Find the particular solution to y'=2sin(x) given the general solution is y=C-2cos(x) and the initial condition y(pi/3)=1
mezya [45]

ANSWER

The particular solution is:

y=2-2 \cos(x)

EXPLANATION

The given Ordinary Differential Equation is

y'=2 \sin(x)

The general solution to this Differential equation is:

y=C-2 \cos(x)

To find the particular solution, we need to apply the initial conditions (ICs)

y( \frac{\pi}{3} ) = 1

This implies that;

C-2 \cos( \frac{\pi}{3} ) = 1

C-2( \frac{1}{2} )= 1

C-1= 1

C= 1 + 1 = 2

Hence the particular solution is

y=2-2 \cos(x)

4 0
3 years ago
H(n)=-4n-5<br> g(n)=n-1<br> Find h(g(n)) =
Delicious77 [7]

Answer:

h(g(n))=4n-9

Step-by-step explanation:

h(g(n))=4*g(n)-5 ( we replace n in the formule of h(n) by g(n).

h(g(n))=4(n-1)-5

h(g(n))=4n-4-5

h(g(n))=4n-9

Hope you understand it

3 0
3 years ago
A ferry departs from a port along the Sands River at 10:00 am. The ferry travels at a speed of 15 mph in still water and returns
jek_recluse [69]

Answer:

Speed of river's current = 5 mph

Step-by-step explanation:

Let 'd' be the distance covered  

 Let x be the speed of the rivers current

Speed upstream = 15-x

speed downstream = 15+x

Time = distance / speed

time upstream = \frac{d}{15-x}

time downstream = \frac{d}{15+x}

the ferry trip upstream takes twice as long as its return trip downstream

\frac{d}{15-x}= \frac{2d}{15+x}

divide both sides by d

\frac{1}{15-x}= \frac{2}{15+x}

cross multiply

15+x= 2(15-x)

15+x= 30-2x

Add 2x on both sideds

15+3x= 30

subtract 15 from both sides and divide by 3

3x=15

x=5

Speed of river's current = 5 mph

8 0
3 years ago
What is the answer to 5+5(x+4)≤20?
Nata [24]
5+5\left( x+4 \right) \le 20\\ \\ 5\left\{ 1+\left( x+4 \right)  \right\} \le 20\\ \\ \frac { 1 }{ 5 } \cdot 5\left\{ 1+\left( x+4 \right)  \right\} \le 20\cdot \frac { 1 }{ 5 }

\ \\ 1+\left( x+4 \right) \le 4\\ \\ 1+x+4\le 4\\ \\ x+5\le 4\\ \\ x\le 4-5\\ \\ x\le -1
7 0
3 years ago
Read 2 more answers
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