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3 years ago

Examine the following graph of y=1/4x+2.

Mathematics

1 answer:

choli [55]3 years ago

3 0

Answer: 9/4

Step-by-step explanation:

The slope-intercept form is y = m x + b , where m is the slope and b is the y-intercept. y = m x + b Find the values of m and b using the form y = m x + b . m = 1/4 b = 2 The slope of the line is the value of m , and the y-intercept is the value of b . Slope: 1/4 y-intercept: 2 Any line can be graphed using two points. Select two x values, and plug them into the equation to find the corresponding y values. Choose 0 to substitute in for x to find the ordered pair. y = 2 Choose 1 to substitute in for x to find the ordered pair. Tap for fewer steps... Replace the variable x with 1 in the expression. f ( 1 ) = 1 4 + 2 Simplify the result. The y value at x = 1 is 9/4 . y = 9/4

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Evaluate the following integral using trigonometric substitution

serg [7]

Answer:

The result of the integral is:

$\arcsin{(\frac{x}{3})} + C$

Step-by-step explanation:

We are given the following integral:

$\int \frac{dx}{\sqrt{9-x^2}}$

Trigonometric substitution:

We have the term in the following format: $a^2 - x^2$ , in which a = 3.

In this case, the substitution is given by:

$x = a\sin{\theta}$

$dx = a\cos{\theta}d\theta$

In this question:

$a = 3$

$x = 3\sin{\theta}$

$dx = 3\cos{\theta}d\theta$

$\int \frac{3\cos{\theta}d\theta}{\sqrt{9-(3\sin{\theta})^2}} = \int \frac{3\cos{\theta}d\theta}{\sqrt{9 - 9\sin^{2}{\theta}}} = \int \frac{3\cos{\theta}d\theta}{\sqrt{9(1 - \sin^{\theta})}}$

We have the following trigonometric identity:

$\sin^{2}{\theta} + \cos^{2}{\theta} = 1$

$1 - \sin^{2}{\theta} = \cos^{2}{\theta}$

Replacing into the integral:

$\int \frac{3\cos{\theta}d\theta}{\sqrt{9(1 - \sin^{2}{\theta})}} = \int{\frac{3\cos{\theta}d\theta}{\sqrt{9\cos^{2}{\theta}}} = \int \frac{3\cos{\theta}d\theta}{3\cos{\theta}} = \int d\theta = \theta + C$

Coming back to x:

We have that:

$x = 3\sin{\theta}$

$\sin{\theta} = \frac{x}{3}$

Applying the arcsine(inverse sine) function to both sides, we get that:

$\theta = \arcsin{(\frac{x}{3})}$

The result of the integral is:

$\arcsin{(\frac{x}{3})} + C$

8 0

2 years ago

36 and 38<br><br>Steps and explaination please

elena55 [62]

Answer:

36. Limit = 2/3.

Step-by-step explanation:

36.

(∛ x- 1) / (√x - 1)

Rationalise the expression:-

Multiply top and bottom by (√x + 1):-

(∛x - 1)(√x + 1) / (√x - 1)(√x + 1)

= x^5/6 + ∛x - √x - 1 / (x - 1)

Applying L'hopital's rule ( differentiating top and bottom of the fraction) we have:

Limit as x ----> 1 of [5/6 x^-1/6 + 1/3 x^(-2/3) - 1/2x^-1/2] / 1

= 5/6(1) + 1/3(1) - 1/2(1) = 2/3 (answer).

8 0

2 years ago

One leg of a right triangle measures 15 m and the hypotenuse measures 17 m. What is the measure of the other leg?

wolverine [178]

15^2+x^2=17^2
225+x^2=289
289-225=64
x^2=64
x=8

6 0

3 years ago

Read 2 more answers

Write in simplest radical form: √7/8 Show all work

ratelena [41]

√7/8

= √7 / √8

= (√7 * √8) / (√8 * √8)

= (√7 * √(2^2 * 2) / 8

= 2√14 / 8

= √14 / 4

5 0

2 years ago

What is the equation in point slope form of the line that passes through the point (1, −2)and has a slope of 3? y+1=3(x−2) y−1=3

iogann1982 [59]

Answer:

Step-by-step explanation:

y + 2 = 3(x - 1) is the point slope form

3 0

2 years ago