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jeyben [28]
3 years ago
10

What values for theta (0 less than or equal to theta less than equal to 2pi) satisfy the equation?

Mathematics
1 answer:
Novosadov [1.4K]3 years ago
7 0
Solve this as you would an equation that does not involve trig.  Don't let the trig scare you.  If you had to solve 2x+8=0, the first thing you would do is factor out the common 2.  In our equation, we have a common cos theta.  I'm going to use beta as my angle.  When we factor out beta, here's what we have. cos \beta (2sin \beta +1)=0.  The Zero Product Property tells us that at least one of those factors has to equal zero.  So we set them both equal to zero and solve.  Let's get the equations first, then we will need our unit circle.  First equation set to equal zero is cos \beta =0.  On our unit circle, cos is the value inside the parenthesis that is in the x position within our coordinate.  Look at all those coordinates as you go around the unit circle once (once around is equivalent to 2pi).  You will find that the the cos is 0 at \frac{ \pi }{2}, \frac{3 \pi }{2}.  The next equation is 2sin\beta +1=0.  Move the 1 over by subtraction and divide by 2 to get sin \beta =- \frac{1}{2}.  Same as before, go around the unit circle one time and look to see where the coordinate in the y place is -1/2.  Sin corresponds to the y coordinate.  You will find that sin is -1/2 at \frac{7 \pi }{6}, \frac{11 \pi }{6}.  And there you go!  Trig is so much fun!!!
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What is the answer for "a boat travels 4 miles in 4 hours (with a constant speed). how far can it travel in 2 hours (with the sa
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3 years ago
Select the sets that are not functions.
Kaylis [27]

Answer:

D,E are not functions

Step-by-step explanation:

A function is a relation in which every  input has not more than one output.But the output of the inputs may be same.Here in D the input 1 has 4 different outputs as 1,2,3,4.So its not a function.Similarly in E 6 has 2 outputs as 2 and -1.For remaining sets the inputs has only one output.so they are functions.

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3 years ago
Select the two binomials that are factors of this trinomial x2+10x+16
Zigmanuir [339]

So for this trinomial, I will be factoring by grouping. Firstly, what two terms have a product of 16x^2 and a sum of 10x? That would be 8x and 2x. Replace 10x with 2x + 8x:

x^2+2x+8x+16

Next, factor x^2 + 2x and 8x + 16 separately. Make sure that they have the same quantity inside the parentheses: x(x+2)+8(x+2)

<u>Now you can rewrite this as (x+8)(x+2) , which is your final answer.</u>

5 0
3 years ago
A car rental costs $50 for the first day. Additional days cost $35 per day, unless the car is rented for 7 days or more, in whic
son4ous [18]

Answer:

\$50+\$31.5x

Step-by-step explanation:

Let

x------> the number of days

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we know that

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In this problem. the car has been rented for more than a week

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The cost of renting a car is equal to

y=\$50+\$31.5x

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3 years ago
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