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3 years ago

If x < 0, y > 0, and x + y = z, which statement about z is true?

Mathematics

1 answer:

vivado [14]3 years ago

7 0

Answer:

Z is greater than zero because it equals 1 or more.

Step-by-step explanation:

X/Y/Z=1+

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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

PLEASE HELP MEEEEEEE I WILL GIVE BRAINLIEST!!!

Marina CMI [18]

The y-intercept is 60
the slope is 30
the equation of the line is y=30x+60
the ordered pair (4,120) represents and increase of 30 minutes per hour

7 0

3 years ago

Read 2 more answers

Working with your cousin, you can finish a table in 4 hours. working alone, your cousin can finish the job in 5 hours. how long

Allushta [10]

I think the answer is A but i could be wrong

4 0

2 years ago

A function is shown.<br><br> f(x)=−3⋅4x<br> What is the value of x when f(x) = −48?

galben [10]

Answer:

576

Step-by-step explanation:

Whenever you are solving these types of problems, you just put the value given in place of x. For this equation you would have done f(48)=-3·4(48)

6 0

3 years ago

2. f(x) = √x-5<br> What is the domain and range

Dafna1 [17]

Answer:

solution - x is less then or equal to 5

Step-by-step explanation:

the domain of a function is the set of input or argument values for which the function is real and defined.

3 0

3 years ago