Find the interest due on $1,200 at 8% for 240 days

How to find derivative of a function at a given point?

seraphim [82]

Fill in the point values in the formula for the derivative.

____

Example

y = x^2 + 3x . . . . . we want y' at (x, y) = (1, 4)

y' = 2x +3 . . . . . . . take the derivative dy/dx of the function

Fill in the value x=1 ...

y' = 2·1 +3 = 5

The value of the derivative at (x, y) = (1, 4) is 5.

4 0

3 years ago

A school wishes to enclose its rectangular playground using 480 meters of fencing.

Harlamova29_29 [7]

Answer:

Part a) $A(x)=(-x^2+240x)\ m^2$

Part b) The side length x that give the maximum area is 120 meters

Part c) The maximum area is 14,400 square meters

Step-by-step explanation:

The picture of the question in the attached figure

Part a) Find a function that gives the area A(x) of the playground (in square meters) in terms of x

we know that

The perimeter of the rectangular playground is given by

$P=2(L+W)$

we have

$P=480\ m\\L=x\ m$

substitute

$480=2(x+W)$

solve for W

$240=x+W\\W=(240-x)\ m$

Find the area of the rectangular playground

The area is given by

$A=LW$

we have

$L=x\ m\\W=(240-x)\ m$

substitute

$A=x(240-x)\\A=-x^2+240x$

Convert to function notation

$A(x)=(-x^2+240x)\ m^2$

Part b) What side length x gives the maximum area that the playground can have?

we have

$A(x)=-x^2+240x$

This function represent a vertical parabola open downward (the leading coefficient is negative)

The vertex represent a maximum

The x-coordinate of the vertex represent the length that give the maximum area that the playground can have

Convert the quadratic equation into vertex form

$A(x)=-x^2+240x$

Factor -1

$A(x)=-(x^2-240x)$

Complete the square

$A(x)=-(x^2-240x+120^2)+120^2$

$A(x)=-(x^2-240x+14,400)+14,400$

$A(x)=-(x-120)^2+14,400$

The vertex is the point (120,14,400)

therefore

The side length x that give the maximum area is 120 meters

Part c) What is the maximum area that the playground can have?

we know that

The y-coordinate of the vertex represent the maximum area

The vertex is the point (120,14,400) -----> see part b)

therefore

The maximum area is 14,400 square meters

Verify

$x=120\ m$

$W=(240-120)=120\ m$

The playground is a square

$A=120^2=14,400\ m^2$

8 0

3 years ago

Which number is rational

alekssr [168]

0.7 is the rational number

4 0

3 years ago

Read 2 more answers

How do I find the domain range and function of the graph

Allisa [31]

Answer:

D = {-3, -2, -1, 1, 4}

R = {-5, -1, 0, 2}

Step-by-step explanation:

You have correctly described the process of finding the domain and range by the way you filled in the blanks at the top of the sheet.

__

The domain is the set of x-values of the points on the graph:

D = {-3, -2, -1, 1, 4}

The range is the set of (unique) y-values of the points on the graph:

R = {-5, -1, 0, 2}

3 0

1 year ago

From a practice assignment: solve the following differential equation given initial conditions

hodyreva [135]

If $y' = e^y \sin(x)$ and $y(-\pi)=0$ , separate variables in the differential equation to get

$e^{-y} \, dy = \sin(x) \, dx$

Integrate both sides:

$\displaystyle \int e^{-y} \, dy = \int \sin(x) \, dx \implies -e^{-y} = -\cos(x) + C$

Use the initial condition to solve for $C$ :

$-e^{-0} = -\cos(-\pi) + C \implies -1 = 1 + C \implies C = -2$

Then the particular solution to the initial value problem is

$-e^{-y} = -\cos(x) - 2 \implies e^{-y} = \cos(x) + 2$

(A)

4 0

1 year ago