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Evgesh-ka [11]
3 years ago
6

Sinx = 1/2, cosy = sqrt2/2, and angle x and angle y are both in the first quadrant.

Mathematics
1 answer:
Leviafan [203]3 years ago
7 0

Answer:

Option D. 3.73​

Step-by-step explanation:

we know that

tan(x+y)=\frac{tan(x)+tan(y)}{1-tan(x)tan(y)}

and

sin^{2}(\alpha)+cos^{2}(\alpha)=1

step 1

Find cos(X)

we have

sin(x)=\frac{1}{2}

we know that

sin^{2}(x)+cos^{2}(x)=1

substitute

(\frac{1}{2})^{2}+cos^{2}(x)=1

cos^{2}(x)=1-\frac{1}{4}

cos^{2}(x)=\frac{3}{4}

cos(x)=\frac{\sqrt{3}}{2}

step 2

Find tan(x)

tan(x)=sin(x)/cos(x)

substitute

tan(x)=1/\sqrt{3}

step 3

Find sin(y)

we have

cos(y)=\frac{\sqrt{2}}{2}

we know that

sin^{2}(y)+cos^{2}(y)=1

substitute

sin^{2}(y)+(\frac{\sqrt{2}}{2})^{2}=1

sin^{2}(y)=1-\frac{2}{4}

sin^{2}(y)=\frac{2}{4}

sin(y)=\frac{\sqrt{2}}{2}

step 4

Find tan(y)

tan(y)=sin(y)/cos(y)

substitute

tan(y)=1

step 5      

Find tan(x+y)

tan(x+y)=\frac{tan(x)+tan(y)}{1-tan(x)tan(y)}

substitute

tan(x+y)=[1/\sqrt{3}+1}]/[{1-1/\sqrt{3}}]=3.73

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Angelina_Jolie [31]

Answer:

n + 5

Step-by-step explanation:

"Sum" is the result of an addition.

The sum of n and 5 means the addition of n and 5.

Answer: n + 5

8 0
2 years ago
I answered the question 3x-y=5 but is there a different way to answer this?
Svet_ta [14]

Step-by-step explanation:

Hi,

I agree with what you did. You could also add y on both sides and get 3x = y + 5 and then divided by three to get...

x = 5 + y /3

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But that's just complicated, it works, but it's complicated. What you did is correct and what I gave you is the value of x, but I'm 100 percent sure yours is correct.

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3 0
3 years ago
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Which sequence could be described by the explicit definition: t_n=2^n+1t n = 2 n + 1
yuradex [85]

Answer:

2. 27

3. Option C. 3, 5, 9, 17, 33, ...

Step-by-step explanation:

2. The sequence is defined by the explicit function t_{n} = 2^{n}  - n

Therefore, the 5th term i.e. t_{5} of the sequence.

t_{5} = 2^{5}  - 5 = 32 - 5 = 27 (Answer)

3. The explicit definition is t_{n} = 2^{n}  + 1

Hence, t_{1} = 2^{1}  + 1 = 3

t_{2} = 2^{2}  + 1 = 5

t_{3} = 2^{3}  + 1 = 9

t_{4} = 2^{4}  + 1 = 17

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4 0
3 years ago
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Base = 5 ft Height= 3.5 ft what is the area
Advocard [28]

Answer:

the area is 17.5 ft if the shape is a square/rectangle

the area is 8.75 ft if the shape is a triangle

Step-by-step explanation:

6 0
3 years ago
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HELP ME PLEASE I REALLY NEED THE HELP​
dedylja [7]

Answer:

Answer = 126 square inches

Step-by-step explanation:

Square area formula is Area = s^2    (replace the s with the side length)

Square area -->  Area = 4^2       Area = 16in

Parallelogram area formula is Area = h * b (replace h with height length and replace b with base length)

Parallelogram area --> Area = 3.5 * 10     Area = 35

Rectangle area formula is Area = w * h    (replace width and height)

Rectangle area --> Area = 12.5 * 6    Area = 75

Then add them all up  75 + 35 + 16 = 126 square inches

3 0
3 years ago
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