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son4ous [18]
3 years ago
15

Find the exact value of the trigonometric function given that sin u = -5/13 and cos v = -20/29. (Both u and v are in Quadrant II

I.) tan(u − v)
Mathematics
1 answer:
Alex3 years ago
8 0

Answer:

Tan(u–v) = –304/690

Step-by-step explanation:

Putting in mind that sin(theta) and cos(theta) are both negative in the third quadrant, we can find sin(v) and cos(u).

sin(u) = – 5/13 we have opp = 5 and hyp = 13, we make use of Pythagoras theorem to find adj.

Adj = √(13² – 5²) = √(169 – 25) = √144 = 12

cos(u) = – 12/13, therefore tan(u) = 5/12.

cos(v) = –20/29 we have adj = 20 and hyp = 29, we make use of Pythagoras theorem to find opp.

OPP = √(29² – 20²) = √(841 – 400) = √441 = 21

sin(v) = – 21/29, therefore tan(v) =21/20.

tan(u-v) = [tan(u) - tan(v)]/[1 + tan(u)xtan(v)] = [(5/12) - (21/20)]/[1 + (5/12)X(21/20)] = (–19/30)÷(1+7/16) = (–19/30)÷(23/16) =

–304/690

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In a shipment of airplane parts, 5% are known to be defective. If 21 parts are found to be defective, how many parts are in the
horrorfan [7]

We can use ratios and the cross-multiply-divide to find this.



The ratio 21:5 is avaliable via the question. We then need to compare that to the ratio x:100, the 100 being the percent and the x being the number of airplane parts.



21/5 = x/100



We can then solve for x to find the number of airplane parts. First we multiply by 100 on both sides to get 2100/5 = x. Therefore x = 420 and there are 420 airplane parts.

7 0
3 years ago
The product-3 and t is greater than 11
PSYCHO15rus [73]

Answer:

i am pretty sure its 8

Step-by-step explanation:

because a negative plus a positive = wichever one is bighger and 8 is bigger than 3 so 11 is positive. 8 +3 = 11

6 0
3 years ago
1-69.
timofeeve [1]

The question above was not written properly

Complete Question

Lacey and Haley are rewriting expressions in an equivalent, simpler form.

a. Haley simplified x³⋅ x² and got

x⁵

Lacey simplified x³ + x² and got the same result! However, their teacher told them that only one simplification is correct. Who simplified correctly and how do you know?

b. Haley simplifies 3⁵⋅ 4⁵ and gets the result 12^10, but Lacey is not sure.

Is Haley correct? Be sure to justify your answer.

Answer:

a) Haley is correct, Lacey simplified wrongly.

b) Haley is incorrect

Step-by-step explanation:

a. Haley simplified x³⋅ x² and got

x⁵

Lacey simplified x³ + x² and got the same result! However, their teacher told them that only one simplification is correct. Who simplified correctly and how do you know?

For Question a, when it comes to simplifying algebraic expression that has to do with powers, there are certain rules that should be followed.

For example

x^a × x^b = x^(a + b)

For Haley, she simplified x³⋅ x² and got

x⁵

She is correct because this follows the product rule of powers or exponents above

= x³⋅ x² = x³+² = x⁵

For Lacey she is wrong because:

x³ + x² ≠ x⁵

x³ + x² when simplified as quadratic equation = x²(x + 1)

b. Haley simplifies 3⁵⋅ 4⁵ and gets the result 12^10, but Lacey is not sure.

Is Haley correct? Be sure to justify your answer.

For question b, when we have two distinct or different numbers with the same power(exponents) the rule states that:

x^a × y^a = (x × y)^a = (xy)^a

Haley is simplified wrongly. She did not apply the rule above

Haley simplified 3⁵⋅ 4⁵ = (3 × 4) ⁵+⁵

= 12^10, this is wrong.

The correct answer according to the rule =

3⁵⋅ 4⁵ = (3 × 4) ⁵ = 12⁵

Therefore,

3⁵⋅ 4⁵ ≠ 12^10

3⁵⋅ 4⁵ = 12⁵

Haley is wrong.

3 0
3 years ago
This set of 3 numbers are measurements of a right triangle. 10,8,6<br><br>True<br>False​
arlik [135]

Answer:

True

Step-by-step explanation:

**plug it in using the Pythagorean Theorem**

6^2+8^2= 10^2

36+64=100

100=100 (true)

7 0
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Alekssandra [29.7K]

Answer:

I'm pretty sure the answer is B, I hope this helps!

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