Sin(x) - cos(2x)<br><br>Question said to graph and find the answers.

A landscape architect wished to enclose a rectangular garden on one side by a brick wall costing $20/ft and on the other three s

makvit [3.9K]

Answer:

The dimensions of the garden that minimize the cost is 9.018 feet(length) and 13.528 feet(width)

Step-by-step explanation:

Let the length of garden be x

Let the breadth of garden be y

Area of Rectangular garden = $Length \times Breadth = xy$

We are given that the area of the garden is 122 square feet

So, $xy=122$ ---A

A landscape architect wished to enclose a rectangular garden on one side by a brick wall costing $20/ft

So, cost of brick along length x = 20 x

On the other three sides by a metal fence costing $10/ft.

So, Other three side s = x+2y

So, cost of brick along the other three sides= 10(x+2y)

So, Total cost = 20x+10(x+2y)=20x+10x+20y=30x+20y

Total cost = 30x+20y

Substitute the value of y from A

Total cost = $30x+20(\frac{122}{x})$

Total cost = $\frac{2440}{x}+30x$

Now take the derivative to minimize the cost

$f(x)=\frac{2440}{x}+30x$

$f'(x)=-\frac{2440}{x^2}+30$

Equate it equal to 0

$0=-\frac{2440}{x^2}+30$

$\frac{2440}{x^2}=30$

$\sqrt{\frac{2440}{30}}=x$

$9.018 =x$

Now check whether it is minimum or not

take second derivative

$f'(x)=-\frac{2440}{x^2}+30$

$f''(x)=-(-2)\frac{2440}{x^3}$

Substitute the value of x

$f''(x)=-(-2)\frac{2440}{(9.018)^3}$

$f''(x)=6.6540$

Since it is positive ,So the x is minimum

Now find y

Substitute the value of x in A

$(9.018)y=122$

$y=\frac{122}{9.018}$

$y=13.528$

Hence the dimensions of the garden that minimize the cost is 9.018 feet(length) and 13.528 feet(width)

4 0

3 years ago

Find the measurements of each angle

Lana71 [14]

GED is 43
CEB and AED is 90
GEB and FEA is 47

hope this helps!

4 0

3 years ago

Read 2 more answers

What is x at most 30

andrezito [222]

Answer:

x < 30

Step-by-step explanation:

x is every number less or equal to 30

7 0

3 years ago

(15 POINTS!) The graph shows the distance a ghost crab can run over time the D equals the distance in meters and the t equal the

Maru [420]

Answer:

B. d = 5/3t

Step-by-step explanation:

The complete question is shown in the figure attached with.

We need to find the equation of direct variation using the graph. The general equation for a direction variation is:

y = kx

In this case, the variable along x axis is time in seconds i.e. "t" and the variable along y axis is distance in meters i.e. "d". So, the equation for this case would be:

d = kt

We need to find the value of "k" to complete this equation. For this we can use any point from the graph and substitute it in the above equation. From the graph we can see that the distance covered for time = 3 seconds is 5 meters. Substituting t =3 and d = 5 in above equation, we get:

5 = 3k

k = 5/3

Using the value of k in the above equation, we get:

$d=\frac{5}{3}t$