4x +y = 10 graph the linear equation

A rectangular box with a square base is to be constructed from material that costs $9 per ft2 for the bottom, $5 per ft2 for the

kramer

Answer:

$18.73ft^3$

Step-by-step explanation:

Let

Side of square base=x

Height of rectangular box=y

Area of square base=Area of top= $(side)^2=x^2$

Area of one side face= $l\times b=xy$

Cost of bottom=$9 per square ft

Cost of top=$5 square ft

Cost of sides=$4 per square ft

Total cost=$204

Volume of rectangular box= $V=lbh=x^2y$

Total cost= $9(x^2)+5x^2+4(4xy)=14x^2+16xy$

$204=14x^2+16xy$

$204-14x^2=16xy$

$y=\frac{204-14x^2}{16x}=\frac{102-7x^2}{8x}$

Substitute the values of y

$V(x)=x^2\times \frac{102-7x^2}{8x}=\frac{1}{8}(102x-7x^3)$

Differentiate w.r.t x

$V'(x)=\frac{1}{8}(102-21x^2)=0$

$V'(x)=0$

$\frac{1}{8}(102-21x^2)=0$

$102-21x^2=0$

$102=21x^2$

$x^2=\frac{102}{21}=4.85$

$x=\sqrt{4.85}=2.2$

It takes positive because side length cannot be negative.

Again differentiate w.r. t x

$V''(x)=\frac{1}{8}(-42x)$

Substitute the value

$V''(2.2)=-\frac{42}{8}(2.2)=-11.55$

Hence, the volume of box is maximum at x=2.2 ft

Substitute the value of x

$y=\frac{102-7(2.2)^2}{8(2.2)}=3.87 ft$

Greatest volume of box= $x^2y=(2.2)^2\times 3.87=18.73 ft^3$

5 0

3 years ago

to get to work truman waited 11 minutes for the bus, then travled 21.78 miles on the bus at a speed of 33 miles per hour how muc

alexgriva [62]

We have 11 as our base value, meaning that we add 11 to something, so we have 11+<something>. To find that something, we want to know how long it takes to go 21.78 miles at 33 miles per hour. To get this, we want to turn miles per hour into minutes per mile and multiply that by 21.78 miles to get our answer. Therefore, we cross them out as shown in the equation to get $\frac{21.78 miles}{1} * \frac{1 hour}{33 miles} * \frac{60 minutes}{1 hour}$

6 0

3 years ago

Which payment plan is correct?

garri49 [273]

Out of what? Nothing is shown. :(

7 0

3 years ago

What is the surface area of this cube the dimensions are 5 cm 4 cm 5cm starting from lxwxh

Mashcka [7]

Given: A cuboid with the dimesion below:

$5\operatorname{cm}by4\operatorname{cm}by5\operatorname{cm}$

To Determine: The surface area of the cuboid

The formula for finding the surface area of a cuboid is given as:

$A_{\text{Cuboid Surface Area}}=2(l\times w+l\times h+w\times h)$

From the diagram, it can be seen that

$\begin{gathered} l=\text{length}=5\operatorname{cm} \\ w=\text{width}=4\operatorname{cm} \\ h=\text{height}=5\operatorname{cm} \end{gathered}$

Substitute the given into the formula as shown below:

$\begin{gathered} A_{\text{Cuboid Surface Area}}=2(l\times w+l\times h+w\times h) \\ A_{\text{Cuboid Surface Area}}=2(5cm\times4cm+5cm\times5cm+4cm\times5cm) \\ A_{\text{Cuboid Surface Area}}=2(20cm^2+25cm^2+20cm^2) \\ A_{\text{Cuboid Surface Area}}=2(65\operatorname{cm}^2) \\ A_{\text{Cuboid Surface Area}}=130\operatorname{cm}^2 \end{gathered}$

Hence, the surface area of the given cuboid is 130cm²

4 0

1 year ago

Solve for x pls help

pashok25 [27]

Answer:

x = 13

Step-by-step explanation:

In a triangle, all the angles equal 180 so

2x + 5x - 7 + 6x + 18 = 180

combine like terms

13x + 11 = 180

13x = 169

x = 13

7 0

3 years ago

4x +y = 10 graph the linear equation​

4x +y = 10 graph the linear equation