Answer:
Step-by-step explanation:
Answer:
1)
(x + 3)(x + 4) = x^2 + 4x + 3x + 12 = x^2 + 7x + 12
Instead of multiplying 3 and 4 the student added them which gave them the answer of 7 when the correct answer is 12.
2)
a) x^2 + x - 2
b) x^2 - 7x + 10
c) 4x^2 - 1
d) x^2 + 10x + 25
Step-by-step explanation:
a. (x - 1)(x + 2)
x(x) - 1(x) + 2(x) - 1(2)
x^2 - 1x + 2x - 2
x^2 + x - 2
------------------------------------------
b. (x - 5)(x - 2)
x(x) - 5(x) - 2(x) - 5(-2)
x^2 - 5x - 2x + 10
x^2 - 7x + 10
------------------------------------------
c. (2x + 1)(2x - 1)
2x(2x) + 1(2x) - 1(2x) + 1(-1)
4x^2 + 2x - 2x - 1
4x^2 - 1
------------------------------------------
d. (x + 5)^2
(x + 5)(x + 5)
x(x) + 5(x) + 5(x) + 5(5)
x^2 + 5x + 5x + 25
x^2 + 10x + 25
The average value of a continuous function <em>f(x)</em> over an interval [<em>a</em>, <em>b</em>] is given by the integral,
Compute the integral for <em>f(x)</em> = <em>e</em> ⁻ˣ over [0, 3] :
the volume of the sphere is =4/3.pi.r^3
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
