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3 years ago

5

PLEASE HELP 100 POINTS!!! The function f(x)=12sin(x−π4) is used to describe a water wave. The value x is the time in seconds, an

d f(x) is the position of the wave in feet above or below the normal water level. https://imgur.com/rnfVqIR

1 answer:

Digiron [165]3 years ago

6 0

|0, pi | i’m pretty sure is the answer

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Using a graphing utility, find the exact solutions of the system. Round to the nearest hundredth and choose a solution to the sy

Margaret [11]

Answer:

Part 1) The exact solutions are

$(\frac{-1+\sqrt{21}} {2},4+\sqrt{21})$ and $(\frac{-1-\sqrt{21}} {2},4-\sqrt{21})$

Part 2) (1.79, 8.58)

Step-by-step explanation:

we have

$y=x^{2} +3x$ ----> equation A

$y=2x+5$ ----> equation B

we know that

When solving the system of equations by graphing, the solution of the system is the intersection points both graphs

<em>Find the exact solutions of the system</em>

equate equation A and equation B

$x^{2} +3x=2x+5\\x^{2} +3x-2x-5=0\\x^{2} +x-5=0$

The formula to solve a quadratic equation of the form

$ax^{2} +bx+c=0$

is equal to

$x=\frac{-b\pm\sqrt{b^{2}-4ac}} {2a}$

in this problem we have

$x^{2} +x-5=0$

so

$a=1\\b=1\\c=-5$

substitute in the formula

$x=\frac{-1\pm\sqrt{1^{2}-4(1)(-5)}} {2(1)}$

$x=\frac{-1\pm\sqrt{21}} {2}$

so

The solutions are

$x_1=\frac{-1+\sqrt{21}} {2}$

$x_2=\frac{-1-\sqrt{21}} {2}$

<em>Find the values of y</em>

<em>First solution</em>

For $x_1=\frac{-1+\sqrt{21}} {2}$

$y=2(\frac{-1+\sqrt{21}} {2})+5$

$y=-1+\sqrt{21}+5\\\\y=4+\sqrt{21}$

The first solution is the point $(\frac{-1+\sqrt{21}} {2},4+\sqrt{21})$

<em>Second solution</em>

For $x_2=\frac{-1-\sqrt{21}} {2}$

$y=2(\frac{-1-\sqrt{21}} {2})+5$

$y=-1-\sqrt{21}+5\\\\y=4-\sqrt{21}$

The second solution is the point $(\frac{-1-\sqrt{21}} {2},4-\sqrt{21})$

Round to the nearest hundredth

<em>First solution </em>

$(\frac{-1+\sqrt{21}} {2},4+\sqrt{21})$ -----> $(1.79,8.58)$

$(\frac{-1-\sqrt{21}} {2},4-\sqrt{21})$ -----> $(-2.79,-0.58)$

see the attached figure to better understand the problem

6 0

3 years ago

1. A fish is 12 meters below the surface of the ocean. What is its elevation? meters 2. A sea bird is 28 meters above the surfac

Vlad1618 [11]

Answer:

- 12 meters

28 meters

40 meters

Step-by-step explanation:

Given that:

A fish is 12 meters below the surface of the ocean. What is its elevation?

Position of fish = 12 meters below the surface = - 12 ;

Sea level = 0

Elevation = sea level + position

Elevation = 0 + (- 12)

= - 12 meters

2. A sea bird is 28 meters above the surface of the ocean. What is its elevation?

Position of bird = 28 meters below the surface = (28) ;

Sea level = 0

Elevation = sea level + position

Elevation = 0 + 28

= 28 meters

3. If the bird is directly above the fish, how far apart are they?

If bird is directly above the fish;

Distance between bird and fish :

Elevation of bird - elevation of fish

28 - (-12)

28 + 12

= 40 Meters

3 0

3 years ago

HELP ME SOMEBODY PLSS

OverLord2011 [107]

Answer:

-6/8

Step-by-step explanation:

The rate of change is the same as the slope (I don't know if you have learned that term yet), but basically its the change in y's over the change in x's. to find this out, all you have to do is count from the point on the graph that is the farthest right (in this case, (6,1)), up to the y coordinate of the point farthest to the left (-2, 7) which is 6, and then count the number of spaces between the x coordinates, which is 8. put the rise (up and down count) over the run (horizontal count) in a fraction form, which gives you 6/8, and then notice how the line is pointing towards the bottom RIGHT hand corner making the line negative, so you need to make the rate of change negative, giving you the final answer of -6/8.

4 0

3 years ago

A rectangular box has faces with areas of 12,15, and 20 square units. What is the volume of the box?

miv72 [106K]

First find the side lengths of the box by factoring each area:

12: 1, 2, 3, 4, 6, 12
15: 1, 3, 5, 15
20: 1, 2, 4, 5, 10, 20

Find 3 numbers that both have 2 sides have in common and can multiply to make the areas of the faces:

12: 3 * 4
15: 3 * 5
20: 4 * 5

Sides: 3, 4, and 5

Then multiply to get the volume:

3 * 4 * 5 = 60 units^2

6 0

3 years ago

What is the slope-intercept equation of the line below?

marissa [1.9K]

The correct answer is B. y=-3x+4

3 0

3 years ago