One coral reef is located 19 feet below sea level. Another is located 26 feet below sea level. What is the difference in the depths of the two reefs?


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y''+y-2=0 is the linear homogeneous DE with constant coefficients that has solution  y=c₁e⁻²ˣ+ c₂eˣ

A differential equation is an equation that contains one or more functions with its derivatives.

Given the general solution y=c₁e⁻²ˣ+ c₂eˣ

the set of fundamental solutions becomes eˣ and e⁻²ˣ

This set is corresponding to the distinct roots m= 1, -2of the corresponding auxiliary equation. Hence, the auxiliary equation so formed is

(m-1)(m-(-2))

(m-1)(m+2)

m²+2m-m-2

m²+m-2

The corresponding linear homogeneous DE with constant coefficients is

y''+y-2=0

Hence, y''+y-2=0 is the linear homogeneous DE with constant coefficients that has solution  y=c₁e⁻²ˣ+ c₂eˣ

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Answer: N = 5

Step-by-step explanation:

Answer:

The first one is B

The second one is The y intercept is 8

Step-by-step explanation:

The equation that represent each situation, in terms of x, is

The number of monthly movies watched, x, that would make the two plans have an equal monthly cost is 6 movies.

Let

Plan A:

A = 19 + 0.50x

Plan B:

B = 13 + 1.50x

Equate A and B

19 + 0.50x = 13 + 1.50x

collect like terms

19 - 13 = 1.50x - 0.50x

6 = x

Hence,

x = 6 movies

In conclusion, the number of monthly movies watched to have an equal amount is 6 movies.

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The transformation that has occurred is a vertical shift by 3 units down when the function of X = 2X is transformed to X = 2X -3

Function that have the form ax + b = 0—where a and b are constants and x is a variable—are known as linear equations. Because they plot as a single direction, these equations are referred to as "linear which is equals to The slope of this line is dictated by the value of a, and the y-intercept (where the line crosses the y-axis) is determined by the value of b. Solving a linear equation entails determining the value of x that makes the equation true. Algebraic strategies like graphing, substitution, or elimination can be used for this. In a number of disciplines, such as engineering, physics, and finance, linear equations are often utilized.

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No, because 4/5 divided by 2 is 2/5 which does not equal 1/3 :)

replace x with 0

f(x) = -x - 5

find f(0)

f(0) = 0-5

f(0) = -5

Answer: 1920

Step-by-step explanation:

Answer:

43.9823

Step-by-step explanation:

14 / 2 = 7

7 = r

2π(7)

= 43.9823

Answer: D. Qufdrant: II

                   sinΘ=12/13

Step-by-step explanation:

[tex]\displaystyle\\cos\theta=-\frac{5}{13} \ \ \ \ sin\theta > 0\\\\sin^2\theta+cos^2\theta=1\\\\sin^2\theta=1-cos^2\theta\\\\sin\theta=б\sqrt{1-cos^2\theta} \\\\sin\theta > 0, \ \ hence\\\\sin\theta=\sqrt{1-cos^2\theta} \\\\sin\theta=\sqrt{1-(-\frac{5}{13})^2 } \\\\sin\theta=\sqrt{1-\frac{25}{169} } \\\\sin\theta=\sqrt{\frac{169-25}{169} } \\\\sin\theta=\sqrt{\frac{144}{169} } \\\\sin\theta=\frac{12}{13}[/tex]

[tex]\displaystyle\\\left \{ {{cos\theta < 0} \atop {sin\theta > 0}} \right. \ \ \ \ \Rightarrow\ \ \ \ quadrant\ II[/tex]

Answer: there will be 4/7 of 7/4 groups in 1. and for 3÷7/4=1.71428571429.

Step-by-step explanation: I hope this helps.

Manita's computer installed the software 48 minutes before than Humi's computer.

A unit rate means a rate for one of something.

Given that, Manita's computer takes 3 minutes to download a program 15% and Humi's computer install it in 68 minutes 100%.

Manita's computer;-

15% in 3 min

1% in 1/5 minutes

100% in 1/5x100 = 20 minutes.

Whereas, Humi's computer took 68 minutes to install the same program.

This mean, Manita's computer was faster than Humi's.

68-20 = 48

Hence, Manita's computer installed the software 48 minutes before than Humi's computer.

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If an orchard has 468 pear trees and The number of rows exceeds the number of trees per row by 8. the number of trees that are in each row would be 18

We have to define T as the number of trees that are in a row.

Then we have to define t + 8 as the number of rows that we have

This would give us the equation that is written as

t(t + 8) = 468

then we would have

t² + 8t -468 = 0

We would have to find the factors of 468 which when inputted in the equation would give us the value 468

t(t + 8) = 468

This factor would be 18

such that

18 ( 18 + 8) = 468

18 * 26 = 468

468 = 468

Hence the number of trees that are in each row would be 18

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Answer:

z = 15

Step-by-step explanation:

The sum S of the interior angles of a regular polygon is given by the formula

S = (n-2) x 180 where n is the number sides

Here n = 9

So S = (9-2) x 180 = 7 x 180 = 1,260

There are 9 interior angles and each angle is (5z + 65)

So the sum of all 9 interior angles = 9 (5z + 65)

= 45z + 585

Set these equal to each other and solve for z

45z + 585 = 1260

45z = 675

z = 675/45 = 15

The result of the definite double integral over the interval is given as follows:

[tex]\int\int_D f(x,y)dxdy = -120[/tex]

The double integral is solved in two steps, first the inner integral is solved, and then the result of the inner integral is used to calculate the outer integral.

Considering the function and the region, the complete integral in this problem is given as follows:

[tex]\int_{-4}^{2}\int_{-4}^{2} (3x + y)dxdy[/tex]

Then the inner integral in this problem is given as follows:

[tex]I = \int_{-4}^{2} (3x + y)dx[/tex]

We are integrating the variable x, then the variable y is a constant, as thus the result is given as follows:

I = 1.5x² + xy, from x = -4 to x = 2.

Then, applying the Fundamental Theorem of Calculus, the result is given as follows:

I = 1.5(2)² + 2y - 1.5(-4)² + 4y = 6y - 18.

Then the outer integral is calculated as follows:

[tex]O = \int_{-4}^{2} 6y - 18[/tex]

Then the result is given as follows:

O = y² - 18y, from y = -4 to y = 2.

O = (2)² - 18(2) - (-4)² + 18(-4)

O = -120.

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Answer:i is 20.1

Step-by-step explanation:

The linear function for the given graph is y = x + 0.1

What is a linear function?

The graph of a linear function is a straight line. The following is the form of a linear function. y = mx + b. One independent variable and one dependent variable make up a linear function. x and y are the independent and dependent variables, respectively.

The coordinates of the given graph are (0,1) and (10,2)

Then, slope (m) = (2-1)/(10-0) = 1/10 = 0.1

y-intercept (b) = 1

Then, y = 1x + 0.1

Hence, the linear function for the given graph is y = x + 0.1

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Answer:

Equipamiento para 8 jugadores

Explanation:

Porque la diferencia de dinero no es muy grande ni muy pequeña, por lo que obtienes equipamiento para más jugadores a un buen precio.

Answer: y did the chicken cross the road

Step-by-step explanation: ??????

The image of the scaled copy of the square is M'(-14,-8), N'(-8,-6), O'(-6, -12), and P'(-12, -14)

Dilation involves enlarging or reducing the side length of a shape to create another shape by a constant scale factor, where the scale factor does not equal one.

From the question, we have the following parameters that can be used in our computation:

This means that

Scaled copy = Scale factor * Vertices of MNOP

So, we have

M'N'O'P' =M(-7,-4), N(-4,-3), O(-3, -6), and P(-6, -7)* 2

Evaluate

M'N'O'P' =M'(-14,-8), N'(-8,-6), O'(-6, -12), and P'(-12, -14)

Hence, the image of the dilation is M'(-14,-8), N'(-8,-6), O'(-6, -12), and P'(-12, -14)

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Complete question

Given that Square MNOP with vertices M(-7,-4), N(-4,-3), O(-3, -6), and P(-6, -7): k = 2

Calculate the image of the scaled copy

Answer:

8(10-b)

Step-by-step explanation:

8(10-b)

open the bracket

80-8b

hope it helps.. please mark brainliest

Answer:

option number 2

Step-by-step explanation:

you can see inital and final co ordinate

Answer:

y > -2

Step-by-step explanation:

The range of a function is the set of all possible output values (y-values).

From inspection of the given graph:

Therefore, the most appropriate range from the given answer options is:

Note:  The graph appears to be the exponential function  [tex]y=2^x-2[/tex]  with a horizontal asymptote at y = -2.  This means that the curve will get closer and closer to y = -2 as x approaches negative infinity, but it will never touch it.  The function approaches infinity as x approaches infinity.  Therefore, the range for this function is y > -2

Answer:

-27

(negative number)

Step-by-step explanation:

-b/2a = -(-16)/2(1) = 16/2 = 8

                       x       +          8

                 x   x^2                8x

                 +

                 8    8x                64

So we got 64, but 64 is not 37 so we need to change that by subtracting 27 from it.

64 - 27 = 37

So the final answer (in vertex form) is:

(x+8)^2 - 27

(-27) is the number being added

Step-by-step explanation:

What you are trying to do, it solve for the zeros of the rational function. To find the domain of composite function,

[tex] \frac{x}{x - 1} [/tex]

Substitute x/(x-1) for every x you see.

[tex] \frac{ \frac{x}{x - 1} }{ \frac{x}{x - 1} - 1} = \frac{x(x \\ - 1)}{1} = x(x - 1)[/tex]

We know that the function domain can not be 1, this functions works for all reals, so our domain is

All reals except 1.

The motion of the arrow, described by the kinematic equation for the height, h(t) = 60·t - 0.8·t² are as follows;

(a) The velocity after 1 second is 58.4 m/s

(b)  The arrow hits the moon after 75 seconds

(c) The velocity of the arrow when it hits the moon is 60 m/s

(d) The arrow reaches the maximum height  in37.5 seconds.

A kinematic equation is an equation that describes the motion of an object moving under constant acceleration.

The kinematic (equation) function for the height of the arrow is; h(t) = 60·t - 0.8·t²

The initial velocity of the arrow = 60 m/s

(a) The velocity of the arrow = The rate of change of the height, therefore;

v = h'(t) = 60 - 2 × 0.8·t = 60 - 1.6·t

The velocity after 1 second = h'(1) = 60 - 1.6 × 1 = 58.4

The velocity of the arrow after 1 second is 58.4 m/s

(b) When the arrow hits the moon, we get;

h(t) = 0, therefore;

h(t) = 60·t - 0.8·t² = 0

( 60 - 0.8·t)·t = 0

t =  0  or 60 - 0.8·t = 0

t = 60/0.8 = 75

The time the arrow hit the moon is 75 seconds after being shot

(c) The velocity of the arrow when it hits the moon is  found using the equation;

h'(37.5) = 1.6 × 37.5 = 60

The velocity when it hits the moon, the velocity is 60 m/s

(d) The motion of the arrow is symmetrical, therefore, the time it takes the arrow to reach the the maximal height is the time it takes the arrow to reach back to the moon surface, which indicates;

The time it takes the arrow to reach maximum height is half the time it takes the arrow to hit the moon after being shot = 75/2 seconds = 37.5 seconds

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The given function in slope-intercept should be used to complete the table of values as follows;

x                     y

9                    4

6                    2

0                    -2

-3                   -4

A function that relates the distance (d) traveled to the time (t) is d = 120t.

A graph of the function is shown in the image attached below and it is a linear function.

Mathematically, the slope-intercept form of a line can be calculated by using this equation:

y = mx + c

Where:

Next, we would use the given function in slope-intercept to complete the table of values as follows;

When y = 9, the value of x is given by:

y = 3x/2 + 3

9 = 3x/2 + 3

3x/2 = 9 - 3

3x/2 = 6

3x = 12

x = 12/3

x = 4.

When y = 6, the value of x is given by:

y = 3x/2 + 3

6 = 3x/2 + 3

3x/2 = 6 - 3

3x/2 = 3

3x = 6

x = 6/3

x = 2.

When y = 0, the value of x is given by:

y = 3x/2 + 3

0 = 3x/2 + 3

3x/2 = -3

3x = -6

x = -6/3

x = -2.

When y = -3, the value of x is given by:

y = 3x/2 + 3

-3 = 3x/2 + 3

3x/2 = -3 - 3

3x/2 = -6

3x = -12

x = -12/3

x = -4.

Mathematically, a constant of proportionality (speed) for this train's journey (distance) can be represented with the following mathematical expression:

d = kt

Where:

Next, we would determine the constant of proportionality (k) as follows:

Constant of proportionality (k) = d/t

Constant of proportionality (k) = 360/3

Constant of proportionality (k) = 120

Therefore, the required function that relates the distance (d) and time (t) is given by;

d = kt

d = 120t

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Answer:

[tex]\dfrac{x}{3}+\dfrac{3}{y}[/tex]

Step-by-step explanation:

Given fraction:

[tex]\dfrac{xy+9}{3y}[/tex]

[tex]\textsf{Apply the fraction rule} \quad \dfrac{a+b}{c}=\dfrac{a}{c}+\dfrac{b}{c}:[/tex]

[tex]\implies \dfrac{xy}{3y}+\dfrac{9}{3y}[/tex]

Rewrite 9 as 3 · 3:

[tex]\implies \dfrac{xy}{3y}+\dfrac{3 \cdot 3}{3y}[/tex]

Cancel the common factor y in the first fraction and the common factor 3 in the second fraction:

[tex]\implies \dfrac{x\diagup\!\!\!\!y}{3\diagup\!\!\!\!y}+\dfrac{\diagup\!\!\!\!3 \cdot 3}{\diagup\!\!\!\!3y}[/tex]

[tex]\implies \dfrac{x}{3}+\dfrac{3}{y}[/tex]

Answer:

this is what I got and hope this helps sorry if it's wrong

Answer:

148cm

Step-by-step explanation: