I will help you because I need points like the answers for 4 huhg
1/5^2 = 1/25
1/5^1 = 1/5
1/5^0 = 1
1/5^-1 = 5
1/5^-2 = 25
Answer:
Step-by-step explanation:
If you graph there would be two different regions. The first one would be
And the second one would be
.
If you rotate the first region around the "y" axis you get that
And if you rotate the second region around the "y" axis you get that
And the sum would be 2.51+4.188 = 6.698
If you revolve just the outer curve you get
If you rotate the first region around the x axis you get that
And if you rotate the second region around the x axis you get that
And the sum would be 1.5708+1.0472 = 2.618
The line y = x + 3 has slope 1, so we look for points on the curve where the tangent line, whose slope is dy/dx, is equal to 1.
y² = x
Take the derivative of both sides with respect to x, assuming y = y(x) :
2y dy/dx = 1
dy/dx = 1/(2y)
Solve for y when dy/dx = 1 :
1 = 1/(2y)
2y = 1
y = 1/2
When y = 1/2, we have x = y² = (1/2)² = 1/4. However, for the given line, when y = 1/2, we have x = y - 3 = 1/2 - 3 = -5/2.
This means the line y = x + 3 is not a tangent to the curve y² = x. In fact, the line never even touches y² = x :
x = y² ⇒ y = y² + 3 ⇒ y² - y + 3 = 0
has no real solution for y.
