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Dafna1 [17]
3 years ago
9

What are benefits of good study habits? Check all that apply.

Mathematics
1 answer:
Ymorist [56]3 years ago
5 0

Answer:

1, 3, 4 i hope this helps ;)

Step-by-step explanation:

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Show tan(???? − ????) = tan(????)−tan(????) / 1+tan(????) tan(????)<br> .
anyanavicka [17]

Answer:

See the proof below

Step-by-step explanation:

For this case we need to proof the following identity:

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

We need to begin with the definition of tangent:

tan (x) =\frac{sin(x)}{cos(x)}

So we can replace into our formula and we got:

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

We have the following identities useful for this case:

sin(a-b) = sin(a) cos(b) - sin(b) cos(a)

cos(a-b) = cos(a) cos(b) + sin (a) sin(b)

If we apply the identities into our equation (1) we got:

tan(x-y) = \frac{sin(x) cos(y) - sin(y) cos(x)}{sin(x) sin(y) + cos(x) cos(y)}   (2)

Now we can divide the numerator and denominato from expression (2) by \frac{1}{cos(x) cos(y)} and we got this:

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

And simplifying we got:

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

And this identity is satisfied for all:

(x-y) \neq \frac{\pi}{2} +n\pi

8 0
2 years ago
Find the volume of a square pyramid 13 m tall whose base measures 5 m on a side
goblinko [34]
a=5m;\ H=13m\\\\The\ volume\ of\ a\ square\ pyramid:V=\frac{1}{3}a^2H\\\\Subtitute\ the\ values\ of\ a\ and\ H:\\\\\boxed{V=\frac{1}{3}\cdot5^2\cdot13=\frac{1}{3}\cdot25\cdot13=\frac{325}{3}=108\frac{1}{3}\ (m^3)}
8 0
2 years ago
A recipe calls for 1 part beans to 1-1/2 parts rice. If 1-1/2 parts of beans are used how much rice should be used
Maurinko [17]
I think the answer is 2 parts rice. If you added half to the beans, do it to the rice too.
5 0
3 years ago
Read 2 more answers
Which table represents a linear function?
Serggg [28]

Answer:

1. -3

2. -5

3. -7

4. -9

7 0
3 years ago
Help please! Calculate the exact value of cos (a-b) given that sin a= 12/13 with pi/2
zloy xaker [14]

Answer:

56/65

Step-by-step explanation:

First, we know that cos(a-b) = cos(a)cos(b) + sin(a)sin(b)

We know what sin(a) and sin(b) are, and to get cos(a), we can take the equation sin²a + cos²a = 1

Thus,

(12/13)² + cos²a = 1

1 - (12/13)² = cos²a

1- 144/169 = cos²a

cos²a = 25/169

cos(a) = 5/13

Similarly,

(3/5)² + cos²b = 1

1 - (3/5)² = cos²b

1 - 9/25 = cos²b

cos²b = 16/25

cos(b) = 4/5

Our answer is

cos(a-b) = cos(a)cos(b) + sin(a)sin(b)

cos(a-b)  = (5/13)(4/5) + (12/13)(3/5)

cos(a-b)  = 20/65 + 36/65

cos(a-b)  = 56/65

4 0
2 years ago
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