Answer:
x=3
Step-by-step explanation:
We can use the slope formula to help complete this question
m = (y2-y1)/(x2-x1)
-1 = ( -6-0)/(x- -3)
-1 = -6/ (x+3)
Multiply each side by (x+3)
-x-3 = -6
Add 3 to each side
-x -3+3 = -6+3
-x =-3
Multiply each side by -1
x = 3
The answer that i got is 1130.97
Answer:
π/6 [37^(³/₂) − 1] ≈ 117.3187
Step-by-step explanation:
The surface area is:
S = ∫ 2π (x − 0) √(1 + (dx/dy)²) dy
0 ≤ x ≤ 3, so -4 ≤ y ≤ 5.
Find dx/dy.
y = 5 − x²
x² = 5 − y
x = √(5 − y)
dx/dy = ½ (5 − y)^(-½) (-1)
dx/dy = -½ (5 − y)^(-½)
(dx/dy)² = ¼ (5 − y)^(-1)
(dx/dy)² = 1 / (4 (5 − y))
Plug in:
S = ∫₋₄⁵ 2π x √(1 + 1 / (20 − 4y)) dy
S = ∫₋₄⁵ 2π √(5 − y) √(1 + 1 / (4 (5 − y))) dy
S = ∫₋₄⁵ 2π √((5 − y) + 1/4)) dy
S = ∫₋₄⁵ 2π √(5.25 − y) dy
If u = 5.25 − y, then du = -dy.
S = ∫ 2π √u (-du)
S = -2π ∫ √u du
S = -2π (⅔ u^(³/₂))
S = -4π/3 u^(³/₂)
Substitute back:
S = -4π/3 (5.25 − y)^(³/₂)
Evaluate between y=-4 and y=5.
S = [-4π/3 (5.25 − 5)^(³/₂)] − [-4π/3 (5.25 − -4)^(³/₂)]
S = -4π/3 (0.25)^(³/₂) + 4π/3 (9.25)^(³/₂)
S = π/6 [37^(³/₂) − 1]
S ≈ 117.3187
20% of a = 11
a = 11
a = 11
a = 55
I hope this helps! If you have any questions, feel free to ask.
Answer:
24 inches
Explanation:
Area of a triangle: 1/2 * base * h
1/2 * 32 * h = 384
16 * h = 384
h = 24
Hope this helped! :)
