The answer:
the full question is as follow:
if A+B-C=3pi, then find sinA+sinB-sinC
first, the main formula of sine and cosine are:
sinC = 2sin(C/2)cos(C/2)
sinA +sinB = 2sin[(A+B)/2]cos[(A-B)/2]
therefore:
sinA+sinB-sinC = 2sin[(A+B)/2]cos[(A-B)/2] - 2sin(C/2)cos(C/2)
sin[(A+B)/2] = cos(C/2)
2sin(C/2)cos(C/2) = cos[(A+B)/2
and
A+B-C=3 pi implies A+B =3 pi + C, so
cos[(A+B)/2] = cos [3 pi/2 + C/2]
and with the equivalence cos (3Pi/2 + X) = sinX
sinA+sinB-sinC = cos(C/2)+ sin(C/2)
Step-by-step explanation:
<u>Part 1</u>
To find out the amount of water ten big water bottles can hold, we have to find out how much water is in each water bottle. To do this, we divide the amount we are looking for by the number of items.
8 ÷ 4 = 2
Part 1 answer: Each water bottle can hold <u>2 gallons</u> of water.
<u>Part 2</u>
Now that we know the amount of water in each water bottle, we can find out how much water 10 water bottles can hold. To do so, we multiply our previous answer, 2, by the number of items (10).
2 • 10 = 20
Part 2 answer: 10 water bottles can hold <u>20 gallons</u> of water.
Our final answer: 20 gallons
I hope this helps you!
Answer:
31
Step-by-step explanation:
add all 3 sides then divide by 3
We solve the equation, ( a + a + 1 )^2 = 112 + a^2 + ( a + 1 )^2;
Then, ( 2a + 1 )^2 = 112 + a^2 + a^2 + 2a +1;
4a^2 + 4a + 1 = 113 + 2a^2 + 2a;
Finally, 2a^2 + 2a - 112 = 0;
a^2 + a - 56 = 0;
We use <span>Quadratic Formula for this Quadratic Equation;
The solutions are a1 = 7 and a2 = -8;
But a is a natural number; so, a = 7;
The natural consecutive numbers are 7 and 8.</span>
