The equation of the line is
4b + a = 0

The slope of the line is
m = -1/4

With a rise of 1 and run of -4 which corresponds to a hypotenuse of
√(4² + (-1)²) = √17

Therefore, the sine of the angle is
sin θ = 1/√17<span />

8 0

3 years ago

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a school science fair has 24 projects about Earth Science in 36 projects about physical science the projects will be displayed i

Dafna1 [17]

24 =
${2}^{3} \times 3$
36 =
${2}^{2} \times {3}^{2}$
The greatest common factor of 24 and 36 is
${2}^{2} \times 3$
Thus 12 is the greatest number of projects that can be in a row.

7 0

3 years ago

Find the approximate area of the regions bounded by the curves y = x/(√x2+ 1) and y = x^4−x. (You may use the points of intersec

Finger [1]

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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6 0

2 years ago