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STatiana [176]
3 years ago
15

The point (5/13, y) in the fourth quadrant corresponds to angle theta on the unit circle. Find sec theta and cot theta

Mathematics
1 answer:
VikaD [51]3 years ago
8 0
Cos (theta) =\frac{5}{13} sec (theta) = \frac{1}{cos(theta)} =  \frac{1}{ \frac{5}{13} }= \frac{13}{5} sin(theta)=\sqrt{1- cos^{2}(theta) } =  \sqrt{1 -  \frac{25}{169} } = \sqrt{ \frac{144}{169} }=- \frac{12}{13} cot(theta)=\frac{cos(theta)}{sin(theta}= \frac{ \frac{5}{13} }{ \frac{-12}{13} }= \frac{-5}{12}
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Sarah cuts a piece of rope that is 4.5 feet long.
icang [17]

Answer:

4.5 feet = 1.5 yards

Step-by-step explanation:

1 yard equals 3 feet

Then:

1 ----- 3

x -----4.5

x = 4.5/3 = 1.5 yards

Hope this helps

3 0
2 years ago
in 2012, the population of a city was 63,000. by 2017, the population was reduced to approximately 54,100. identify any equation
Akimi4 [234]

Answer:

<em></em>f(x) = 63000(0.97)^x<em></em>

<em></em>

Step-by-step explanation:

Given

f(0) = 63000 ---x = 0, in 2012

f(5) = 54100 -- x = 5, in 2017

Required

Select all possible equations

Because there is a reduction in the population, as time increases; the rate must be less than 1.

An exponential function is represented as:

f(x) = ab^x

Where

b = rate

rate > 1 in options (a) and (b) i.e. 1.03

This implies that (a) and (b) cannot be true

For option (c), we have:

f(x) = 63000(0.97)^x

Set x = 0

f(0) = 63000(0.97)^0 = 63000*1=63000\\

Set x = 5

f(5) = 63000(0.97)^5 = 63000*0.8587=54098.1 \approx 54100

<em>This is true because the calculated values of f(0) and f(5) correspond to the given values</em>

For option (d), we have:

f(x) = 52477(0.97)^x

Set x = 0

f(0) = 52477(0.97)^0 - 52477* 1 = 52477

<em>This is false because the calculated value of f(0) does not correspond to the given value</em>

For option (e), we have:

f(x) = 63000(0.97)^\frac{1}{5x}

Set x = 0

f(0) = 63000(0.97)^\frac{1}{5*0} = 63000(0.97)^\frac{1}{0} =undefined

<em>This is false because the f(x) is not undefined at x = 0</em>

For option (f), we have:

f(x) = 52477(0.97)^{5x

Set x = 0

f(0) = 52477(0.97)^{5*0} = 52477(0.97)^0 =52477*1= 52477

<em>This is false because the calculated value of f(0) does not correspond to the given value</em>

<em>From the computations above, only (c) </em>f(x) = 63000(0.97)^x<em> is true</em>

4 0
3 years ago
Compute the norm of v when v = (-8,7,4)​
dexar [7]

Answer:

the norm of V = =11.357816691601..

Step-by-step explanation:

\left\vert \overrightarrow{V} \right\vert  =\sqrt{\left( -8\right)^{2}  +\left( 7\right)^{2}  +\left( 4\right)^{2}  }

      =\sqrt{64+49+16}

      =\sqrt{129}

      =11.357816691601...

4 0
2 years ago
How do I solve for x ?X +8=-15
DanielleElmas [232]
Subtract 8 from both sides
So you end up with x = -23
7 0
3 years ago
Read 2 more answers
Reid at of the pumpkin pie. Vince ate 3 of the same pie. How much of the pie was left after Reid and Vince ate their pieces?
-Dominant- [34]
Whats the question? It doesn't make since
8 0
3 years ago
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