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bija089 [108]
3 years ago
5

How do you do this question?

Mathematics
1 answer:
Nikitich [7]3 years ago
3 0

Answer:

-30√(t/a) cos(√(at)) + 30/a sin(√(at)) + C

Step-by-step explanation:

∫ 15 sin(√(at)) dt

Use substitution:

If x = √(at), then:

dx = ½ (at)^-½ (a dt)

dx = a / (2√(at)) dt

dx = a/(2x) dt

dt = (2/a) x dx

Plugging in:

∫ 15 sin x (2/a) x dx

30/a ∫ x sin x dx

Integrate by parts:

If u = x, then du = dx.

If dv = sin x dx, then v = -cos x.

∫ u dv = uv − ∫ v du

= 30/a (-x cos x − ∫ -cos x dx)

= 30/a (-x cos x + ∫ cos x dx)

= 30/a (-x cos x + sin x + C)

Substitute back:

30/a (-√(at) cos(√(at)) + sin(√(at)) + C)

-30√(t/a) cos(√(at)) + 30/a sin(√(at)) + C

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Pavlova-9 [17]

Check the picture below.

so, bearing in mind that vertical angles are equal, thus ∡AED = ∡BEC, and we know that ∡BEC = 52 = ∡AED, so those two angles added up are 104°.

now, a circle has a total of 360°, if we take away those 104° from the red angles, what's leftover is just 256°, well, the green angles there are also vertical angles and thus twins, so each one will take half of 256°.

∡BEA = 128° = ∡CED.

3 0
3 years ago
Find the equation of the line that passes through the points (-4,-2) and (-3,5) in both point-slope form and
kaheart [24]
<h2>Answer:</h2>

First, we must determine the slope, then we find the y-intercept using slope formula and slope-intercept form.

<u>For slope:</u>

<u />m = \frac{5 + 2}{-3 + 4} = \frac{7}{1} = 7<u />

Slope (m) = 7

<u>For y-intercept:</u>

<u />5 = 7(-3) + b\\\\5 = -21 + b\\\\26 = b<u />

Y-intercept (b) = 26

Using this information, we can now create the equations for this line.

y= 7x + 26\\\\y - 5 = 7(x + 3)

Formulas:

Slope formula: <em>y₂ - y₁/x₂ - x₁</em>

Slope-intercept form: <em>y = mx + b</em>

Point-slope form: <em>y - y₁ = m(x - x₁)</em>

<em></em>

*Note: (x₁, y₁), (x₂, y₂) = <em>2 points on the line</em>

6 0
3 years ago
An ant brain has approximately 300,000 brain cells. If an army ant colony consists of 75,000 members, how many brain cells do th
irina [24]

Answer:

22500000000

Step-by-step explanation:

75,000 times 300,000 equals 22500000000

4 0
3 years ago
Write a system of linear equations for the graph below.​
sp2606 [1]
<h2>Answer:</h2>

We need to determine the equation of both lines first.

  • Line 1: <em>y = -2x + 3</em>
  • Line 2: <em>y = -1/3x - 2</em>

Now that we know the equations, we can set up a system of equations for this graph where both equations are in standard form.

Line 1:

y = -2x + 3\\\\2x + y = 3

Line 2:

y = -\frac{1}{3}x - 2\\\\\frac{1}{3}x + y = -2

<em>Final answer:</em>

2x + y = 3\\\frac{1}{3}x + y = -2

5 0
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just convert it :)
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