Answer:
triangllllllllllllllllllllllllllllllllllllleeeee
Step-by-step explanation:
Answer:
Step-by-step explanation:
[Most of the work here comes from manipulating the trig to make the term (integrand) integrable.]
Recall that we can express the squared trig functions in terms of cos(2x). That is,
And so inverting these,
.
Multiply them together to obtain an equivalent expression for sin^2(x)cos^2(x) in terms of cos(2x).
Notice we have cos^2(2x) in the integrand now. We've made it worse! Let's try plugging back in to the first identity for cos^2(2x).
So then,
This is now integrable (phew),
Answer:
a) A = 36π in² ≈ 113.09 in²
b) $0.98 per slice
c) $0.09 per square inch
Step-by-step explanation:
a) area = πr²
r= diameter/2 = 12/2 = 6
A = π(6)²
A = 36π in² ≈ 113.09 in²
b) s = price per slice
s = 9.75 ÷ 10
s = $0.975 ≈ $0.98
c) price per square inch = price ÷ area
= 9.75 ÷ 113.09
= $0.086 ≈ $0.09 per square inch
Answer: n = 75; p = 30
Explanation: (a) 5p + 4n = 450 where p is for pen and n is for notebook.
(b) 10p + 3n = 525
We can use the elimination method to solve these two equations.
1. Multiply the first equation by 2 so that 10p will cancel out:
2(5p + 4n = 450)
- 10p + 3p = 525
10p + 8n = 900
- 10 p + 3n = 525
5n = 375
2. Divide by 5 to get n alone: n = 75
3. Plug 75 into the first equation: 5p + 4(75) = 450
5p + 300 = 450
4. Subtract 300 from 450: 5p = 150
5. Divide by 5 to get p alone: p = 30
We can test if this is correct by plugging our answers into the second equation:
10(30) + 3(75) = 525
300 + 225 = 525
525 = 525
This is a true statement, which means that our answers are correct.
