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3 years ago

Please don’t skip! Urgent! Please just give me the answers to the solution part.

Mathematics

1 answer:

svlad2 [7]3 years ago

8 0

Answer:

you have selected the correct option for the first part

in the second part, the answer is "there is no solution"

in the third part, the answer is "one solution" which is (0 , 1)

brainly it if you found this helpful

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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:

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

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

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

$\theta=\pi+2\pi n$

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

Kate decides to replace all the lights in her college apartment with energy saving light bulbs beginning this month. The packagi

tatyana61 [14]

Answer:

Kate's electric bill will be $9 for this month for bulb use only.

Step-by-step explanation:

Given:

Electricity bill lass month from bulb use = $12

Using new bulbs percent decrease in electricity = 25%

We need to find this month electric bill for bulb use.

Solution:

First we will find the reduction in bill after using new bulbs.

reduction in bill after using new bulbs can be calculated by percent decrease in electricity using new bulb multiplied by last month Electricity bill from bulb use only.

framing in equation form we get;

reduction in bill after using new bulbs = $\frac{25}{100}\times 12 =\$3$

Now we will find this month electric bill for bulb use only.

this month electric bill for bulb use only can be calculated by subtracting reduction in bill after using new bulbs from last month electric bill for bulb use only.

framing in equation form we get;

this month electric bill for bulb use only = $\$12-\$3=\$9$

Hence Kate's electric bill will be $9 for this month for bulb use only.

3 0

3 years ago

What x value solves the equation? 3x – 5 = 1 x =

USPshnik [31]

Answer:

x = 2

Step-by-step explanation:

3x - 5 = 1

Adding 5 to both sides gives us:

3x - 5 + 5 = 1 + 5

3x = 6

Dividing the equation by 3 gives us:

3x / 3 = 6 / 3

x = 2

8 0

3 years ago

Read 2 more answers

Part B

Georgia [21]

Answer:140

Step-by-step explanation: It is a really big number not the most reasonable answer for the low amount of marbles their are in the jar adding 58 and 82 gives you your answer

5 0

3 years ago

If the square below has an area of 50, what is the value of x

pishuonlain [190]

Answer:

Step-by-step explanation:

A= L²

50 = L² (do opposite operation to find L)

L = 7.07

x²= L²+ L²

x²= 7.07² + 7.07²

x² = 100 ( do opposite operation to make x the subject)

x = 10

Note: opposite operation of square is square root

4 0

3 years ago