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2 years ago

The solution to an absolute value inequality is shown on the graph below.

Mathematics

1 answer:

lawyer [7]2 years ago

4 0

The solution to the absolute value inequality is (-3,-2)

<h3>How to determine the absolute inequality?</h3>

On the absolute value inequality, we have:

Interval = -3 to 2

The intervals are represented with open circles.

This means that -3 and 2 are exclusive of the values of the inequality.

So, we have:

-3 < x < 2

As an interval notation, we have:

(-3,-2)

Hence, the solution to the absolute value inequality is (-3,-2)

Read more about absolute value inequality at:

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Help me with these please

olchik [2.2K]

Step-by-step explanation:

(1) y = x e^(x²)

Take derivative with respect to x:

dy/dx = x (e^(x²) 2x) + e^(x²)

dy/dx = 2x² e^(x²) + e^(x²)

dy/dx = (2x² + 1) e^(x²)

Take derivative with respect to x again:

d²y/dx² = (2x² + 1) (e^(x²) 2x) + (4x) e^(x²)

d²y/dx² = (4x³ + 2x) e^(x²) + 4x e^(x²)

d²y/dx² = (4x³ + 6x) e^(x²)

Substitute:

d²y/dx² − 2x dy/dx − 4y

= (4x³ + 6x) e^(x²) − 2x (2x² + 1) e^(x²) − 4x e^(x²)

= 4x³ + 6x − 2x (2x² + 1) − 4x

= 4x³ + 6x − 4x³ − 2x − 4x

= 0

(2) y = sin⁻¹(√x)

sin y = √x

sin²y = x

Take derivative with respect to x:

2 sin y cos y dy/dx = 1

sin(2y) dy/dx = 1

dy/dx = csc(2y)

Take derivative with respect to x again:

d²y/dx² = -csc(2y) cot(2y) 2 dy/dx

d²y/dx² = -2 csc²(2y) cot(2y)

Substitute:

2x (1 − x) d²y/dx² + (1 − 2x) dy/dx

= 2 sin²y (1 − sin²y) (-2 csc²(2y) cot(2y)) + (1 − 2 sin²y) csc(2y)

Use power reduction formula:

= (1 − cos(2y)) (1 − ½ (1 − cos(2y))) (-2 csc²(2y) cot(2y)) + (1 − (1 − cos(2y))) csc(2y)

= (1 − cos(2y)) (1 − ½ + ½ cos(2y)) (-2 csc²(2y) cot(2y)) + cos(2y) csc(2y)

= (1 − cos(2y)) (½ + ½ cos(2y)) (-2 csc²(2y) cot(2y)) + cot(2y)

= (cos(2y) − 1) (1 + cos(2y)) csc²(2y) cot(2y) + cot(2y)

= (cos²(2y) − 1) csc²(2y) cot(2y) + cot(2y)

= -sin²(2y) csc²(2y) cot(2y) + cot(2y)

= -cot(2y) + cot(2y)

= 0

8 0

3 years ago

Find an equation of the line that (a) has the same y -intercept as the line y + 5x + 9 = 0 and (b) is parallel to the line - 3x

kap26 [50]

Equation of required line is:

$y = \frac{3}{4}x-9$

Step-by-step explanation:

First of all we will convert both equations in slope-intercept form

$y + 5x + 9 = 0$

Subtracting 5x from both sides

$y+9 = 0-5x\\y+9 = -5x$

Subtracting 9 from both sides

$y+9-9 = -5x-9\\y = -5x-9$

The y-intercept is -9.

Other equation is:

$- 3x + 4y = 3$

Adding 3x on both sides

$-3x+3x+4y = 3x+3\\4y=3x+3$

Dividing both sides by 4

$\frac{4y}{4} = \frac{3x+3}{4}\\y = \frac{3}{4}x+\frac{3}{4}$

As the required line has y-ntercept of line y + 5x + 9 = 0

So,

b = -9

And

The line is parallel to second line, so the slopes of both will be equal

$m=\frac{3}{4}$

Slope-intercept form of line is:

$y=mx+b$

Putting values of b and m

$y = \frac{3}{4}x-9$

Keywords: Equation of line, Slope-intercept form

Learn more about equation of line at:

#LearnwithBrainly

6 0

3 years ago

Tony is flying from Los Angeles to Boston. His plane ticket costs $605 and the total flight distance is 3,052 miles. What is the

Ksivusya [100]

Answer:

AROUND $0.20 per mile

Step-by-step explanation:

605/3052 is around 0.198, which rounds to 0.20.

8 0

3 years ago

A parallel the parabola has a minimum value of 0, a Y- -intercept of 4 and axis of symmetry at X =-2 . select the graph that mat

wel

I think the anwser is D

8 0

3 years ago

Read 2 more answers

Here is a base of the prism from the previous screen.

adelina 88 [10]

Answer:

you have to break it into 3 shapes tge first is 5×3=15. tge second is 4×2=8, tge 3rd is 1/2 (4)×3=6, 15+8+6=20 units

7 0

3 years ago