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Tcecarenko [31]
3 years ago
11

The statement "cot theta= 12/5, sec theta = -13/5, and the terminal point determined by theta in quadrant 4"

Mathematics
1 answer:
lora16 [44]3 years ago
5 0
If cot θ = 12/5, then tan θ = 5/12.
If sec θ = -13/5, then cos θ = -5/13

For tan θ to be positive while cos θ is negative, the quadrant is 3.
The figure below shows θ graphed as a reference angle in quadrant 3.

Answer:
The statement that θ is in quadrant 4 is FALSE.

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Please find the measure of the exterior angle
makvit [3.9K]

Answer:

exterior angles:

144°and 36°

126° and 54°

90° and 90°

Step-by-step explanation:

we know that each angle in a triangle adds up to 180°.

so,

2x+3x+5x=180

10x=180

x=180/10

x=18

the interior angles are:

2x=36°

3x=54°

5x=90°

and explanation is provided to find the exterior angles above.(sorry for the bad handwriting)

6 0
3 years ago
Consider the surface z = x 2+4y 2+1. Suppose you are walking on this surface directly above a curve C in the xy-plane, where the
Bess [88]

With x(t)=\cos t and y(t)=\sin t, we have

z(t)=x(t)^2+4y(t)^2+1

z(t)=\cos^2t+4\sin^2t+1

z(t)=3\sin^2t+2

Then z(t) has critical points where

\dfrac{\mathrm dz}{\mathrm dt}=6\sin t\cos t=3\sin2t=0

\implies\sin2t=0\implies2t=n\pi\implies t=\dfrac{n\pi}2

where n is any integer.

z(t) is increasing wherever \sin2t>0, which happens for

\dfrac{2n\pi}2

\boxed{n\pi

5 0
3 years ago
PLEASE HELP ME I WILL GIVE U CREDIT ​
Ket [755]

Answer:

1. x=60

2.x=5

3.x=8

4.x=10

Step-by-step explanation:

im assuming you want to find x value for each.

8 0
3 years ago
Read 2 more answers
Andre constructs the image of line n under a dilation centered at point O that is not on line n. Becca construct a different ima
GenaCL600 [577]
<em /><u><em /></u>I think that both lines will show only 1 line because 1 line will be on top of the other. I believe this because both lines are dilated with its center at point O which does not lie on line n. Whatever dilation Andre uses may also be the dilation used by Becca since their lines centered at point O. Both lines will have the same slope and share the same coordinates.
6 0
3 years ago
Need an answer as soon as possible.
Elza [17]
Part A

Answer: The common ratio is -2

-----------------------------------

Explanation: 

To get the common ratio r, we divide any term by the previous one

One example:
r = common ratio
r = (second term)/(first term)
r = (-2)/(1)
r = -2

Another example:
r = common ratio
r = (third term)/(second term)
r = (4)/(-2)
r = -2
and we get the same common ratio every time

Side Note: each term is multiplied by -2 to get the next term

============================================================
Part B

Answer:
The rule for the sequence is 
a(n) = (-2)^(n-1)
where n starts at n = 1

-----------------------------------

Explanation:

Recall that any geometric sequence has the nth term
a(n) = a*(r)^(n-1)
where the 'a' on the right side is the first term and r is the common ratio

The first term given to use is a = 1 and the common ratio found in part A above was r = -2
So,
a(n) = a*(r)^(n-1)
a(n) = 1*(-2)^(n-1)
a(n) = (-2)^(n-1)

============================================================
Part C

Answer: The next three terms are 16, -32, 64

-----------------------------------

Explanation:

We can simply multiply each previous term by -2 to get the next term. Do this three times to generate the next three terms

-8*(-2) = 16
16*(-2) = -32
-32*(-2) = 64

showing that the next three terms are 16, -32, and 64

An alternative is to use the formula found in part B

Plug in n = 5 to find the fifth term
a(n) = (-2)^(n-1)
a(5) = (-2)^(5-1)
a(5) = (-2)^(4)
a(5) = 16 .... which matches with what we got earlier

Then plug in n = 6
a(n) = (-2)^(n-1)
a(6) = (-2)^(6-1)
a(6) = (-2)^(5)
a(6) = -32 .... which matches with what we got earlier

Then plug in n = 7
a(n) = (-2)^(n-1)
a(7) = (-2)^(7-1)
a(7) = (-2)^(6)
a(7) = 64 .... which matches with what we got earlier

while the second method takes a bit more work, its handy for when you want to find terms beyond the given sequence (eg: the 28th term)
6 0
3 years ago
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