Answer:
slope= - 5/4
Step-by-step explanation:
<span>since sin and cos = each other at pi/4; take your integrals from 0 to pi/4
</span><span>[S] cos(t) dt - [S] sin(t) dt ;[0,pi/4]
</span>
<span>to revolve it around the x axis;
we do a sum of areas
[S] 2pi [f(x)]^2 dx
</span>
<span>take the cos first and subtract out the sin next; like cutting a hole out of a donuts.
</span><span>pi [S] cos(x)^2 dx - [S] sin(x)^2 dx ; [0,pi/4]
</span>
<span>cos(2t) = 2cos^2 - 1
cos^2 = (1+cos(2t))/2
</span>
<span>1/sqrt(2) - (-1/sqrt(2) +1)
1/sqrt(2) + 1/sqrt(2) -1
(2sqrt(2) - sqrt(2))/sqrt(2) = sqrt(2)/sqrt(2) = 1</span>
Answer:
Step-by-step explanation:
K(0 , 4)
Midpoint M (3 , 3)
Let Point L(x₂ , y₂)
Compare x and y coordinates
Cross multiply,
x₂ = 3*2 ; 4 + y₂ = 3*2
x₂ = 6 ; 4+ y₂ = 6
y₂ = 6- 4
y₂ = 2
L(6 , 2)
Answer:yes
Step-by-step explanation:
For this problem, we are asked to convert from one unit to another unit so we need conversion factors to be able to do this. We need to convert from gallon to cubic inches then from cubic inches to liter. We do as follows:
14 gallon ( 231 in^3 / 1 gallon ) ( 2.54 cm / 1 in )^3 ( 1 L / 103 cm^3) = 514.52 L
