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kobusy [5.1K]
2 years ago
10

If sin theta= 2/3 and tan theta<0, what is the value of cos theta

Mathematics
2 answers:
Sergeeva-Olga [200]2 years ago
8 0
Cos
θ
=
√
5
3

or it could be cos
θ
=
√
5
−
3

Explanation:
Since sin
θ
is negative, it can be in the third or fourth quadrant
Drawing your right-angled triangle, place your
θ
in one of three corners. Your longest side will be 3 and the side opposite the
θ
will be -2. Finally, using Pythagoras theorem, your last side should be
√
5

Now, if your triangle was in the third quadrant, you would have
cos
θ
=
√
5
−
3
since cosine is negative in the third quadrant
But if your triangle was in the fourth quadrant, you would have
cos
θ
=
√
5
3
since cosine is positive in the fourth quadrant
PilotLPTM [1.2K]2 years ago
6 0

Answer: - sqrt 5 / 3

Step-by-step explanation:

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A set of magical wand prices are normally distributed with a mean of 50 dollars and a standard deviation of 4 dollars. A blackth
Anna11 [10]

Complete Question

A set of magical wand prices are normally distributed with a mean of 50 dollars and a standard deviation of 4 dollars. A blackthorn wand has a price of 45.20. What proportion of wand prices are lower than the price of the blackthorn wand? You may round your answer to four decimal places

Answer:

0.1151

Step-by-step explanation:

We solve using z score formula

z = (x-μ)/σ, where

x is the raw score = $45.20

μ is the population mean = $50

σ is the population standard deviation = $4

We are solving for x < 45.20

Hence:

z = 45.20 - 50/4

z = -1.2

Probability value from Z-Table:

P(x<45.20) = 0.11507

Approximately to 4 decimal places = 0.1151

Therefore, the proportion of wand prices that are lower than the price of the blackthorn wand is 0.1151

8 0
2 years ago
Is the number rational or irrational?
lapo4ka [179]
1. irrational: √48 = 6.92820323028

2. rational: √9 = 3

3. irrational: √39 = 6.2449979984

4. rational: √289 = 14


6 0
3 years ago
Write 4 different answers for <br><br> -1 less than or equal to r/3
STatiana [176]
-1<span> ≤  r/3                          
-1 </span><span> ≤ (r</span><span>÷3)
(r</span>÷3) <span>≥ -1
r/3 </span><span>≥ -1 </span>
3 0
2 years ago
Solve each triangle using the information provided. If necessary, round to the<br> nearest tenth.
Goryan [66]

Answer:

1) B = 66.5° c = 10.9

Step-by-step explanation:

I will do question one as an example. In general, for these questions you want to use the appropriate trigonometric ratios to solve for the variables and/or apply logic using rules regarding triangles. See attached image for all solving steps.

For side c, we can use Cosine of angle A for a ratio between 10 and c. When we write out the equation, we can solve for side c. So when we write it out, we get the equation:

cos23.5 = ¹⁰⁄c

c = ¹⁰⁄cos₂₃.₅

c = 10.9044 (make sure to round to the nearest tenth, which is one decimal place)

For angle B, since they have given two angles, you can solve for B since all angles of a triangle add up to 180 degrees.

So b = 180 - (90 + 23.5) = 180 - 113.5

b = 66.5

  • It is also possible to solve this using sine of angle B and solve it from there, but applying the theory this way is much simpler. (this is on the image if you're curious about it)

I hope this helps you with the other 3 questions.

4 0
3 years ago
What are the zeros of the quadratic function f(x) = 6x2 – 24x 1?
Valentin [98]

Answer:

1

Step-by-step explanation:

im not sure but I think it's 1

6 0
2 years ago
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