Answer:
a)+8x+15
b)-x-20
Step-by-step explanation:
a) (x+3)(x+5)
a)+5x+3x+15
a)+8x+15
b) (x+4)(x-5)
b) -5x+4x-20
b)-x-20
Kayaks rent for $35 per day.
1 answer:
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Answer:
The average number of pounds they bought was 30 pounds.
Step-by-step explanation:
we know that
To find out the average number of pounds, add the total number of pounds for each boy and then divide by the number of boys.
so
therefore
The average number of pounds they bought was 30 pounds.
The approximate area of the region bounded by the curves f(x) = x / √(x² + 1) and g(x) = x⁴ - x is approximately 0.806.
<h3>How to determine the approximate area of the regions bounded by the curves</h3>
In this problem we must use definite integrals to determine the area of the region bounded by the curves. Based on all the information given by the graph attached below, the area can be defined in accordance with this formula:
A = A₁ + A₂ (1)
A₁ = ∫ [g(x) - f(x)] dx, for x ∈ [- 0.786, 0] (2)
A₂ = ∫ [f(x) - g(x)] dx, for x ∈ [0, 1.151] (3)
g(x) = x⁴ - x (4)
f(x) = x / √(x² + 1) (5)
Then, we proceed to find the integrals:
∫ g(x) dx = ∫ x⁴ dx - ∫ x dx = (1 / 5) · x⁵ - (1 / 2) · x² (6)
∫ f(x) dx = ∫ [x / √(x² + 1)] dx = (1 / 2) ∫ [2 · x / √(x² + 1)] dx = (1 / 2) ∫ [du / √u] = √u = √(x² + 1) (7)
And the complete expression for the integral is:
A = A₁ + A₂ (1b)
A₁ = (1 / 5) · x⁵ - (1 / 2) · x² - √(x² + 1), for x ∈ [- 0.786, 0] (2b)
A₂ = √(x² + 1) - (1 / 5) · x⁵ + (1 / 2) · x², for x ∈ [0, 1.151] (3b)
A₁ = 0.023
A₂ = 0.783
A = 0.023 + 0.783
A = 0.806
The approximate area of the region bounded by the curves f(x) = x / √(x² + 1) and g(x) = x⁴ - x is approximately 0.806.
To learn more on definite integral: brainly.com/question/14279102
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