MATHEMATICS MIDDLE SCHOOL

Prove the identity cos(x-y)-cos(x+y)=2sinx siny

Answers

Answer 1

Answer:

Answer:

see explanation

Step-by-step explanation:

Using the Addition/ Subtraction formulae for cosine

Consider the left side

cos(x - y) - cos(x + y)

= cosxcosy + sinxsiny - (cosxcosy - sinxsiny) ← distribute

= cosxcosy + sinxsiny - cosxcosy + sinxsiny ← collect like terms

= 2sinxsiny = right side ⇒ proven

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Is 7/8 smaller than 3/4

Answers

as decimals lets look at them:)
7/8 = 0.875
3/4 = 0.75

In this case 7/8 is actually bigger.

love, the Pineapple.
<3

7/8 is bigger. 3 quarters or 3/4 is actually 6/8.

Multiply 3/4 x 2 to get the common denominator (same number on the bottom.)

If you mulitply the bottom x2, you have to multiply the top x2 as well.

See? :)

What is the LCM of 7 and 9

Answers

The lcm of 7 and 9 is 63

Which is grater 501,107 or 89,171

Answers

greater* and 501,107

501,107 is greater by a lot.

What is 75 degrees Fahrenheit in the Celsius and kelvin scale?

Answers

To convert Fahrenheit to Celsius, remember this equation.
Subtract 32, multiply 5, divide 9.

Or vice versa,
Multiply 9, divide 5, add 32.

So, 75°F to celsius.
75 - 32 x 5 / 9 =

Ignore PEMDAS for this.

75 - 32 = 43
43 x 5 = 215
215 / 9 ≈ 23.8

To convert to Kelvin, basically do all the steps all over again, but with one more Subtract 32, multiply 5, divide 9, add 273.15.

So, 75 - 32 x 5 / 9 + 213.15

We already know we get 23.8 from the first three steps, so just add 273.15

23.80 + 273.15 ≈ 296.95

Hope this helped :)

The Smiths are sending out a batch of holiday cards. Emily signed 2/5 of the cards. Then Josh signed 1/9 of the remaining cards. Tatiana signed 20% of what Josh had left. If there were 75 cards in all, how many cards are left to be signed?

Answers

32 Cards are left to be signed.

What is probability ?

The proportion of all conceivable outcomes to the number of outcomes in an exhaustive set of equally likely outcomes that result in a certain event.
Example -Since there is a 50% chance that the outcome will be heads, we can anticipate 50 heads.

total cards are 75,

then , 2/5 of 75 = 30.

now left cards 75 -30 = 45

That leaves 45 cards

1/9 of 45 = 5 cards,

so 45 -5 = 40 ⇒ that leaves 40.

now,

Calculate 20% of 40,

40 × $(20)/(100)$ = 8