((-7,1). (-3,2). (0, -2). (5, -5)}What are the domain and range of the function represented by the set of ordered pairs?

Answer:

Step-by-step explanation:

Let A(t) denote the amount of salt (in ounces, oz) in the tank at time t (in minutes, min).

Salt flows in at a rate of

[tex]\dfrac{dA}{dt}_{\rm in} = \left(17 (1 + 15 \sin(t)) \dfrac{\rm oz}{\rm gal}\right) \left(8\dfrac{\rm gal}{\rm min}\right) = 136 (1 + 15 \sin(t)) \dfrac{\rm oz}{\min}[/tex]

and flows out at a rate of

[tex]\dfrac{dA}{dt}_{\rm out} = \left(\dfrac{A(t) \, \mathrm{oz}}{180 \,\mathrm{gal} + \left(8\frac{\rm gal}{\rm min} - 8\frac{\rm gal}{\rm min}\right) (t \, \mathrm{min})}\right) \left(8 \dfrac{\rm gal}{\rm min}\right) = \dfrac{A(t)}{180} \dfrac{\rm oz}{\rm min}[/tex]

so that the net rate of change in the amount of salt in the tank is given by the linear differential equation

[tex]\dfrac{dA}{dt} = \dfrac{dA}{dt}_{\rm in} - \dfrac{dA}{dt}_{\rm out} \iff \dfrac{dA}{dt} + \dfrac{A(t)}{180} = 136 (1 + 15 \sin(t))[/tex]

Multiply both sides by the integrating factor, [tex]e^{t/180}[/tex], and rewrite the left side as the derivative of a product.

[tex]e^{t/180} \dfrac{dA}{dt} + e^{t/180} \dfrac{A(t)}{180} = 136 e^{t/180} (1 + 15 \sin(t))[/tex]

[tex]\dfrac d{dt}\left[e^{t/180} A(t)\right] = 136 e^{t/180} (1 + 15 \sin(t))[/tex]

Integrate both sides with respect to t (integrate the right side by parts):

[tex]\displaystyle \int \frac d{dt}\left[e^{t/180} A(t)\right] \, dt = 136 \int e^{t/180} (1 + 15 \sin(t)) \, dt[/tex]

[tex]\displaystyle e^{t/180} A(t) = \left(24,480 - \frac{66,096,000}{32,401} \cos(t) + \frac{367,200}{32,401} \sin(t)\right) e^{t/180} + C[/tex]

Solve for A(t) :

[tex]\displaystyle A(t) = 24,480 - \frac{66,096,000}{32,401} \cos(t) + \frac{367,200}{32,401} \sin(t) + C e^{-t/180}[/tex]

The tank starts with A(0) = 15 oz of salt; use this to solve for the constant C.

[tex]\displaystyle 15 = 24,480 - \frac{66,096,000}{32,401} + C \implies C = -\dfrac{726,594,465}{32,401}[/tex]

So,

[tex]\displaystyle A(t) = 24,480 - \frac{66,096,000}{32,401} \cos(t) + \frac{367,200}{32,401} \sin(t) - \frac{726,594,465}{32,401} e^{-t/180}[/tex]

Recall the angle-sum identity for cosine:

[tex]R \cos(x-\theta) = R \cos(\theta) \cos(x) + R \sin(\theta) \sin(x)[/tex]

so that we can condense the trigonometric terms in A(t). Solve for R and θ :

[tex]R \cos(\theta) = -\dfrac{66,096,000}{32,401}[/tex]

[tex]R \sin(\theta) = \dfrac{367,200}{32,401}[/tex]

Recall the Pythagorean identity and definition of tangent,

[tex]\cos^2(x) + \sin^2(x) = 1[/tex]

[tex]\tan(x) = \dfrac{\sin(x)}{\cos(x)}[/tex]

Then

[tex]R^2 \cos^2(\theta) + R^2 \sin^2(\theta) = R^2 = \dfrac{134,835,840,000}{32,401} \implies R = \dfrac{367,200}{\sqrt{32,401}}[/tex]

and

[tex]\dfrac{R \sin(\theta)}{R \cos(\theta)} = \tan(\theta) = -\dfrac{367,200}{66,096,000} = -\dfrac1{180} \\\\ \implies \theta = -\tan^{-1}\left(\dfrac1{180}\right) = -\cot^{-1}(180)[/tex]

so we can rewrite A(t) as

[tex]\displaystyle A(t) = 24,480 + \frac{367,200}{\sqrt{32,401}} \cos\left(t + \cot^{-1}(180)\right) - \frac{726,594,465}{32,401} e^{-t/180}[/tex]

As t goes to infinity, the exponential term will converge to zero. Meanwhile the cosine term will oscillate between -1 and 1, so that A(t) will oscillate about the constant level of 24,480 oz between the extreme values of

[tex]24,480 - \dfrac{267,200}{\sqrt{32,401}} \approx 22,995.6 \,\mathrm{oz}[/tex]

and

[tex]24,480 + \dfrac{267,200}{\sqrt{32,401}} \approx 25,964.4 \,\mathrm{oz}[/tex]

which is to say, with amplitude

[tex]2 \times \dfrac{267,200}{\sqrt{32,401}} \approx \mathbf{2,968.84 \,oz}[/tex]

Step-by-step explanation:

A = (1, 3)

B = (3, 6)

C = (9, 2)

D = (7, -1)

the distance between 2 points is given by the Pythagoras equation based on the coordinate differences as legs of virtual right-angled triangles.

AD for example we get from

AD² = (7-1)² + (-1 - 3)² = 6² + (-4)² = 36 + 16 = 52

AD = sqrt(52) = sqrt(4×13) = 2×sqrt(13)

and AB we get from

AB² = (3-1)² + (6-3)² = 2² + 3² = 4 + 9 = 13

AB = sqrt(13)

the perimeter of the given rectangle is

2×sqrt(52) + 2×sqrt(13) = 2×2×sqrt(13) + 2×sqrt(13) =

= 6×sqrt(13) = 21.63330765...

and the area of the rectangle is

2×sqrt(13)×sqrt(13) = 2×13 = 26

Answer:

Larger number: 21

Smaller number: 6

Step-by-step explanation:

Step 1: Make equations.

x ... larger number

y ... smaller number

First equation: The larger of two numbers is 15 more than the smaller number.

x = y + 15

Second equation: Sum of the two numbers is 27.

x + y = 27

Step 2: Solve the system of equations.

First equation: x = y + 15

Second equation: x + y = 27

Substitute x in second equation with x from first.

x + y = 27

(y + 15) + y = 27

Solve for y.

y + 15 + y = 27

2y = 27 - 15

2y = 12

y = 6

Substitute the calculated value of y back in first equation to get x.

x = y + 15

x = 6 + 15

x = 21

Jennifer would earn more than $200. She would earn $230.02 over the period.

Simple interest is a type of interest paid only on the money invested.

Simple interest = amount invested x interest rate x time

2302 x 5 x 0.021 = $230.20

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Answer:

Answer = most college students do not use students loans.

Step-by-step explanation:

To find the percentage of students taking out student loans we take 1,000/6000 to get roughly 17%. This is a very small number of students taking out student loans.

The expression that shows how many more pieces he needs to add to the puzzle to complete it is 500 - p

The given parameters are:

Total = 500

Correct = p

The remaining piece is calculated using:

Total =Correct + Remaining

Substitute known values

p + Remaining = 500

Subtract p from both sides

Remaining = 500 - p

Hence, the expression is 500 - p

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Answer:

it is an identity that was solved

Step-by-step explanation:

cosin - the a

Answer:

The "what" is 100

Step-by-step explanation:

Rewrite this as 37.6y = 3760 and set out to determine y:

y = 3760/37.6  = 100

The "what" is 100

Answer:

Does not lie

Step-by-step explanation:

The equation of the circle is

[tex] {(x + 7)}^{2} + {(y - 4)}^{2} = 25[/tex]

If we substitute x=-11, and y=2, we get that:

[tex] {( - 11 + 7)}^{2} + {(2 - 4)}^{2} = 25 \\ {4}^{2} + {2}^{2} = 25 \\ 20 = 25[/tex]

Which is false, meaning it does not lie on the circle

Answer:

43.43 degrees

Step-by-step explanation:

This is a right triangle with the opposite LEG = 11 km and the hypotenuse = 16 km

sin (angle) = opposite/hypotenuse

                 = 11/16

arc sin (11/16) = angle = 43.43 degrees

Answer:

1

Step-by-step explanation:

let x be the number to be added to 5 and 3

expressing the ratios in fractional form

[tex]\frac{5+x}{3+x}[/tex] = [tex]\frac{3}{2}[/tex] ( cross- multiply )

3(3 + x) = 2(5 + x) ← distribute parenthesis on both sides

9 + 3x = 10 + 2x ( subtract 2x from both sides )

9 + x = 10 ( subtract 9 from both sides )

x = 1

then the number to be added to both is 1

= 17.50 or 25%

Applying it's formula, the area of the given triangle is of 30 centimeters squared, that is, 30 cm².

The area of a triangle of base b and height h is given by half the multiplication of these measures, that is:

A = 0.5bh.

In this problem, we have that b = 12 cm, h = 5 cm, hence:

A = 0.5 x 12 cm x 5 cm = 30 cm².

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Answer:

Quadrant 4

Answer is D........

Answer:

29

Step-by-step explanation:

it is 29 because mode is most occuring digit or number so 29 is the mode

Answer:

area of a triangle =1/2 x b x h

which is half base x hieght

The slope of the graph is 745 and the y-intercept of the graph is 500

The points are given as:

(2, 1990) (5, 4225) (9, 7205)

The slope is calculated using:

m = (y2 - y1)/(x2 - x1)

So, we have:

m = (4225 - 1990)/(5 - 2)

Evaluate

m = 745

This means that the amount earned per day is 745

Hence, the slope of the graph is 745

In (a), we have

m = 745

To calculate the y-intercept, we use the following points

(x1 , y1) = (0,y)

Recall that:

m = (y2 - y1)/(x2 - x1)

So, we have:

745 = (4225 - y)/(5 - 0)

Evaluate the difference

745 = (4225 - y)/(5)

Multiply both sides by 5

3725 = 4225 - y

Solve for y

y = 500

This means that the initial amount earned is 745

Hence, the y-intercept of the graph is 500

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Answer: 25

Step-by-step explanation:

[tex]\frac{23+27}{2}=\boxed{25}[/tex]

Answer:

x=0 y=0

x=1 y=5

x=2 y=8

x=3 y=9

x=4 y=8

x=5 y=5

x=6 y=0

Step-by-step explanation:

Answer:

Step-by-step explanation:

2(6²)-3(6)+2=y

(2x36)-18+2=y

72-18+2=y

y=52 BODMAS

It may also be 56 tho im not sure if thats right

Put x in Equation

Answer:

1. Triangle 2. Pentagon 3. Hexagon 4. Parallelogram

Step-by-step explanation:

Using translation concepts, it is found that graph 3 represents the function [tex]f(x) = \sqrt{x} + 1[/tex].

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

In this problem, the function is:

[tex]f(x) = \sqrt{x} + 1[/tex]

Which is a shift up of one unit of [tex]\sqrt{x}[/tex]. The square root function has y-intercept at (0,0), hence the translated function will have y-intercept at (0,1). Additionally, [tex]\sqrt{4} = 2[/tex], since f(4) = 3, which means that graph 3 is represents the function.

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Answer:

9/8 cans of paint

Step-by-step explanation:

if the furniture maker used the same amount of paint for each chair ,

we have to divide 9/4 by two to get the answer

(9/4)/(2/1) = (9*1)/(4*2) = 9/8

=> 9/8

hope this helps :)

Answer:

9/8 is the answer.

The range of salary is (a) the range of salaries is from $38,500 to $39,800.

The given parameters are:

Average salary = 39,800

Vary = Less than $1300

Let the salary be x.

So, we have:

x = 39,800

When the salary varies, the equation becomes

x = 39800 - 1300

Evaluate

x = 38500

This means that the salary is from 38500 to 39800

Hence, the range of salary is (a) the range of salaries is from $38,500 to $39,800.

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Answer:.2

Step-by-step explanation:.4/(.4+.3+.6+.7)

The true statement about the functions is:

"f(x) and g(x) have the same domain but different ranges."

Here we have the functions:

[tex]f(x) = -(7)^x[/tex]

[tex]g(x) = 7^x[/tex]

Two exponential functions. Notice that you can use any input in these functions, so both of these have the same domain, which is the set of all real numbers.

But the ranges are different. The exponential part can't change the sign of the base, so f(x) has the range (-∞, 0), and for g(x) the range is (0, ∞).

Then the correct option is:

"f(x) and g(x) have the same domain but different ranges."

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Answer:

its b on edge 2022 they have the same domain but different ranges

Step-by-step explanation:

I got it right :D good luck.

Answer:

6/11*5/10 = 3/11

Step-by-step explanation:

first we can get 6/11 which is the probability.

then we minus both sides by 1 to get 5/10

then we times them