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Serga [27]
3 years ago
14

What is the area of this circle?

Mathematics
1 answer:
Ilia_Sergeevich [38]3 years ago
4 0

Answer:

12.57

Step-by-step explanation:

Not rounded it would be 12.56637

If you are just replacing pi with 3.14. than your answer would be exactly 12.56.

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Suppose matrix D is the inverse of matrix C. Which of the following is equal to D?
mr Goodwill [35]

Answer: (A) CDD

if D=C^-1

then

C D D = (C C^-1) D = I D = D

(where I is the identity matrix)

6 0
3 years ago
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It took Shane 2 hours to drive 120 miles. If she continues at this rate, how far will she travel in 4 hours and 30 minutes?
vodomira [7]

Answer:

270 miles

Step-by-step explanation:

If she drove 120 miles in 2 hours, that means she drives at 60 miles per hour. 4 hours and 30 minutes can be seen as 4.5, since 30 minutes is half an hour. So then you multiply 60 by 4.5 and get 270.

6 0
2 years ago
Three times the difference of a number and nine.​
Nikitich [7]

Answer:

3*x-9

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6 0
3 years ago
For 0 ≤ ϴ < 2π, how many solutions are there to tan(StartFraction theta Over 2 EndFraction) = sin(ϴ)? Note: Do not include va
Black_prince [1.1K]

Answer:

3 solutions:

\theta={0, \frac{\pi}{2}, \frac{3\pi}{2}}

Step-by-step explanation:

So, first of all, we need to figure the angles that cannot be included in our answers out. The only function in the equation that isn't defined for some angles is tan(\frac{\theta}{2}) so let's focus on that part of the equation first.

We know that:

tan(\frac{\theta}{2})=\frac{sin(\frac{\theta}{2})}{cos(\frac{\theta}{2})}

therefore:

cos(\frac{\theta}{2})\neq0

so we need to find the angles that will make the cos function equal to zero. So we get:

cos(\frac{\theta}{2})=0

\frac{\theta}{2}=cos^{-1}(0)

\frac{\theta}{2}=\frac{\pi}{2}+\pi n

or

\theta=\pi+2\pi n

we can now start plugging values in for n:

\theta=\pi+2\pi (0)=\pi

if we plugged any value greater than 0, we would end up with an angle that is greater than 2\pi so,  that's the only angle we cannot include in our answer set, so:

\theta\neq \pi

having said this, we can now start solving the equation:

tan(\frac{\theta}{2})=sin(\theta)

we can start solving this equation by using the half angle formula, such a formula tells us the following:

tan(\frac{\theta}{2})=\frac{1-cos(\theta)}{sin(\theta)}

so we can substitute it into our equation:

\frac{1-cos(\theta)}{sin(\theta)}=sin(\theta)

we can now multiply both sides of the equation by sin(\theta)

so we get:

1-cos(\theta)=sin^{2}(\theta)

we can use the pythagorean identity to rewrite sin^{2}(\theta) in terms of cos:

sin^{2}(\theta)=1-cos^{2}(\theta)

so we get:

1-cos(\theta)=1-cos^{2}(\theta)

we can subtract a 1 from both sides of the equation so we end up with:

-cos(\theta)=-cos^{2}(\theta)

and we can now add cos^{2}(\theta)

to both sides of the equation so we get:

cos^{2}(\theta)-cos(\theta)=0

and we can solve this equation by factoring. We can factor cos(\theta) to get:

cos(\theta)(cos(\theta)-1)=0

and we can use the zero product property to solve this, so we get two equations:

Equation 1:

cos(\theta)=0

\theta=cos^{-1}(0)

\theta={\frac{\pi}{2}, \frac{3\pi}{2}}

Equation 2:

cos(\theta)-1=0

we add a 1 to both sides of the equation so we get:

cos(\theta)=1

\theta=cos^{-1}(1)

\theta=0

so we end up with three answers to this equation:

\theta={0, \frac{\pi}{2}, \frac{3\pi}{2}}

7 0
3 years ago
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