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2 years ago

A landscape supply business charges $35 to deliver mulch. The cost of the mulch is $29.

Mathematics

1 answer:

Scorpion4ik [409]2 years ago

4 0

Answer:

$209

Step-by-step explanation:

we know that

The equation of the line in slope intercept form is equal to

$y=mx+b$

where

m is the slope

b is the y-coordinate of the y-intercept (initial value)

Let

x ----> the volume of mulch in cubic yards

y ----> the total cost in dollars

we have that

The slope of the linear equation is

$m=29\ \frac{\$}{yd^3}$

$b=\$35$ ----> flat fee to deliver mulch

The linear equation is

$y=29x+35$

For x=6 yd^3

substitute in the equation and solve for y

$y=29(6)+35$

$y=\$209$

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VikaD [51]

The correct question is:

Consider the initial value problem

2ty' = 8y, y(-1) = 1

(a) Find the value of the constant C and the exponent r such that y = Ct^r is the solution of this initial value problem.

b) Determine the largest interval of the form a < t < b on which the existence and uniqueness theorem for first order linear differential equations guarantees the existence of a unique solution.

c) What is the actual interval of existence for the solution obtained in part (a) ?

Step-by-step explanation:

Given the differential equation

2ty' = 8y

a) We need to find the value of the constant C and r, such that y = Ct^r is a solution to the differential equation together with the initial condition y(-1) = 1.

Since Ct^r is a solution to the initial value problem, it means that y = Ct^r satisfies the said problem. That is

2tdy/dt - 8y = 0

Implies

2td(Ct^r)/dt - 8(Ct^r) = 0

2tCrt^(r - 1) - 8Ct^r = 0

2Crt^r - 8Ct^r = 0

(2r - 8)Ct^r = 0

But Ct^r ≠ 0

=> 2r - 8 = 0 or r = 8/2 = 4

Now, we have r = 4, which implies that

y = Ct^4

Applying the initial condition y(-1) = 1, we put y = 1 when t = -1

1 = C(-1)^4

C = 1

So, y = t^4

b) Let y = F(x,y)................(1)

Suppose F(x, y) is continuous on some region, R = {(x, y) : x_0 − δ < x < x_0 + δ, y_0 −ę < y < y_0 + ę} containing the point (x_0, y_0). Then there exists a number δ1 (possibly smaller than δ) so that a solution y = f(x) to (1) is defined for x_0 − δ1 < x < x_0 + δ1.

Now, suppose that both F(x, y)

and ∂F/∂y are continuous functions defined on a region R. Then there exists a number δ2

(possibly smaller than δ1) so that the solution y = f(x) to (1) is

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c) Firstly, we write the differential equation 2ty' = 8y in standard form as

y' - (4/t)y = 0

0 is always continuous, but -4/t has discontinuity at t = 0

So, the solution to differential equation exists everywhere, apart from t = 0.

The interval is (-infinity, 0) n (0, infinity)

n - means intersection.

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1 year ago

A store owner wants to give a pen to each customer who visits their store. The table shows the cost for the number of pens in a

Flura [38]

Answer:

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Step-by-step explanation:

Divide the price by the quantity to receive the unit price. Here are the unit prices for each option:

1. $0.54

2. $0.43

3. $0.31

4. $0.28

5. $0.25

Basically, you want the lowest price. So, $9 for 36 is the best value because it costs $0.25 per pen.

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1 year ago

A cell tower is located 3 miles east and 4 miles north of the center of a small town. The cell tower has a coverage radius of 3

butalik [34]

Answer:

The answer is below

Step-by-step explanation:

A cell tower is located 3 miles east and 4 miles north of the center of a small town. The cell tower has a coverage radius of 3 miles.

a) Start by drawing a diagram of this situation. Your diagram might include a coordinate plane, the cell tower, and a circle representing the cell tower's coverage boundary.

a) A house is located 5 miles north of the center of the town and is to the east of the cell tower. If the house lies on the boundary of the cell tower's coverage, how far east of the center of the town is the house?

Answer:

Let the center of the town represent the origin (0,0). Also 1 unit = 1 mile. Since the cell tower is located 3 miles east and 4 miles north of the center of a small town, it is represented by A(3, 4)

The cell tower has a coverage of radius 3 miles. This can be represented by a circle with equation:

(x - a)² + (y - b)² = r². where (a,b) is the center of the circle and r is the radius. Hence:

(x - 3)² + (y - 4)² = 3²

(x - 3)² + (y - 4)² = 9

The diagram is drawn using geogebra.

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(x - 3)² = 8

(x - 3) = √8

x - 3 = ±2.83

x = 3 ± 2.83

x = 5.83 or 1.83

Since it is to the east to the cell tower, hence x = 5.83.

Therefore the house is located 5.83 miles to the east of the cell tower

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Bob spent $64 for two shirts, including tax. The difference between the costs of the shirts was $16. Write two equations that yo

djyliett [7]

x+y=64 and x-y=16 can be used to solve the system.

Step-by-step explanation:

Let,

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According to given statement;

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The difference between the costs of the shirts was $16 means subtraction;

x-y=16 Eqn 2

x+y=64 and x-y=16 can be used to solve the system.

Keywords: linear equation, addition

Learn more about linear equations at:

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