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3 years ago

Prove This :sin(A+B)+sin(A−B)=2sinA⋅cosB

Mathematics

1 answer:

MaRussiya [10]3 years ago

3 0

Answer:

We know

sin (A + B) = sin A cos B + cos A sin B

sin (A - B) = sin A cos B - cos A sin B

(A + B) + sin (A - B)

= sin A cos B + cos A sin B + sin A cos B - cos A sin B

= sin A cos B + sin A cos B

= 2 sin A cos B

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A triangle has a height that is 2 inches more than three times the base and an area of 60 in. Find the base and the height of th

const2013 [10]

Answer:

Height = 20, Base = 6

Step-by-step explanation:

The area of a triangle is $\frac{bh}{2}$

where b is the base and h is the height

$H = 3B + 2\\\frac{B(3B + 2)}{2}=60\\\\3B^2 + 2B = 120\\3B^2+2B - 120=0\\$

We can factor by grouping

$3B^2 - 18B + 20B - 120 = 0\\3B(B - 6) + 20(B-6) = 0\\GCF the (B-6)\\(B-6)(3B+20)=0\\B = 6, B = \frac{-20}{3}$

Length can only be positive, so we know that the base is 6 in

The height must be 2 + 3(6) = 20

Height = 20, Base = 6

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3 years ago

Using the least number of coins how many quarters, dimes, nickels, and pennies to make $1.74

SpyIntel [72]

Let's use our largest amount (quarter) to see how many can fit evenly into 1.74.

1.74/0.25 = 6.96
The most quarters that can fit into $1.74 is 6.

---Multiply $0.25 by 6 = $1.50

---Subtract $1.50 from $1.74 = $0.24

---We need to use the rest of the coins to fill up $0.24.

Now let's use our second largest amount (dime) to see how many can fit evenly into 0.24.

0.24/0.10 = 2.4
The most dimes that can fit into $0.24 is 2.

---Multiply $0.10 by 2 = $0.20

---Subtract $0.20 from $0.24 = $0.04

No nickels can fit into $0.04, because they are worth $0.05.

We can use our least amount (pennies) to fill in the $0.04 remaining.

Your answer is 6 quarters, 2 dimes, and 4 pennies.

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3 years ago

Which of the following expressions represents 3 less than 5 times a number 2 A) 5n - 3 B) 5 - 3n C) 3n - 5 D) 3 - 5n

vlabodo [156]

Answer:

The answer is D

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2 years ago

90 POINTS!!!!!<br> What show is this from?

Delicious77 [7]

Answer:

Trailer Park Boys I believe

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2 years ago

Read 2 more answers

You deposit $300 in a savings account. The account earns 2% simple interest per year.

Sholpan [36]

Answer:

Answer:

a. ----> $10

b. ----> $110

Step-by-step explanation:

principle ( p ) = $100

time ( t ) = 10 years

rate ( r ) = 11%

simple interest = (p × r × t)÷ 100

= ( $100 × 11 × 10 )÷ 100

= 11000 ÷ 100

= $110

interest = simple interest - principle

interest = $110 - $100

= $10

8 0

2 years ago

Prove This :sin(A+B)+sin(A−B)=2sinA⋅cosB​

Prove This :sin(A+B)+sin(A−B)=2sinA⋅cosB