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3 years ago

It is 2 kilometers from Jake’s house to the library. What is the distance in meters?

Mathematics

2 answers:

rusak2 [61]3 years ago

6 0

There are 1000 meters in a km. Therefore 2 km is equal to 2000 meters.

CaHeK987 [17]3 years ago

6 0

There are 1000 meters in a kilometer, so the answer is 2000 meters.

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Derive these identities using the addition or subtraction formulas for sine or cosine: sinacosb=(sin(a+b)+sin(a-b))/2

Sergeu [11.5K]

Answer:

The work is in the explanation.

Step-by-step explanation:

The sine addition identity is:

$\sin(a+b)=\sin(a)\cos(b)+\cos(a)\sin(b)$ .

The sine difference identity is:

$\sin(a-b)=\sin(a)\cos(b)-\cos(a)\sin(a)$ .

The cosine addition identity is:

$\cos(a+b)=\cos(a)\cos(b)-\sin(a)\sin(b)$ .

The cosine difference identity is:

$\cos(a-b)=\cos(a)\cos(b)+\sin(a)\sin(b)$ .

We need to find a way to put some or all of these together to get:

$\sin(a)\cos(b)=\frac{\sin(a+b)+\sin(a-b)}{2}$ .

So I do notice on the right hand side the $\sin(a+b)$ and the $\sin(a-b)$ .

Let's start there then.

There is a plus sign in between them so let's add those together:

$\sin(a+b)+\sin(a-b)$

$=[\sin(a+b)]+[\sin(a-b)]$

$=[\sin(a)\cos(b)+\cos(a)\sin(b)]+[\sin(a)\cos(b)-\cos(a)\sin(b)]$

There are two pairs of like terms. I will gather them together so you can see it more clearly:

$=[\sin(a)\cos(b)+\sin(a)\cos(b)]+[\cos(a)\sin(b)-\cos(a)\sin(b)]$

$=2\sin(a)\cos(b)+0$

$=2\sin(a)\cos(b)$

So this implies:

$\sin(a+b)+\sin(a-b)=2\sin(a)\cos(b)$

Divide both sides by 2:

$\frac{\sin(a+b)+\sin(a-b)}{2}=\sin(a)\cos(b)$

By the symmetric property we can write:

$\sin(a)\cos(b)=\frac{\sin(a+b)+\sin(a-b)}{2}$

3 0

3 years ago

What is the number written in standard notation?

expeople1 [14]

Answer:

option B

Step-by-step explanation:

To find the number which is written in the standard form, $5 \times {10}^{3}$

We expand ${10}^{3}$ and multiply by 5 to get

$= 5 \times (10 \times 10 \times 10)$

$=5\times 1000$

=5000

5 0

3 years ago

Read 2 more answers

A rectangular prism made of wood has a length of 10 centimeters, a width of 8 centimeters, and a height of 12 centimeters. A rec

lukranit [14]

Answer:

Prism volume = lbh

= 10*8*12

= 960cm^3

Note: I'm assuming the hole was cut right through it...

Hole volume = lbh

= 2*3*12

= 72cm^3

Final volume = 960 - 72 = 888cm^3

If this is not what you were looking for let me know and I will fix it right away

Step-by-step explanation:#need any questions answered within secs/mins hit me up and I got you

#brainliest

:) <3

4 0

3 years ago

Write (x+7)(x−2) as a sum

Dennis_Churaev [7]

Answer:

x^2+5x-14

Step-by-step explanation:

you multiply both equations so that you get:

x^2-2x+7x-14

and then you simplify it to:

x^2+5x-14

If you found this helpful please give it a thanks

I would also appreciate it if you give me a brainliest

8 0

2 years ago

There are 276 students.

Lynna [10]

Step-by-step explanation:

Number of males is

276 - 158 = 118

Number of males not enrolled

118 - 82 = 36

Number of females not enrolled

158 - 102 = 56

(a)

The table based on data is

Enrolled Not enrolled Total

Male 82 36 118

Female 102 56 158

Total 184 92 276

(b)

Percentage of students were males that went to magic college

enrolled male / total students = (use table above)
82/276*100% = 29.71% (rounded)

(c)

Percentage of females went to magic college

enrolled female / total female = (use table above)
102/158*100% = 64.56% (rounded)

7 0

1 year ago