1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Zielflug [23.3K]
2 years ago
9

First to answer gets brainliest

Mathematics
2 answers:
Lelechka [254]2 years ago
4 0

Answer:

the answer is c I believe

atroni [7]2 years ago
3 0

Answer:

Last one

Step-by-step explanation:

You might be interested in
A rectangle box with a square base and no top needs to be made using 300ft^2 of material. Find the dimensions of the box with th
Yuri [45]

The dimensions of the box are 10 ft and 5 ft

The maximum volume is 500 ft³

Step-by-step explanation:

A rectangle box with

  • A square base and no top
  • It needs to be made using 300 ft² of material
  • It has greatest volume

Surface area of a box without top (SA) = perimeter of base × height + area of the base

Volume of a box (V) = base area × height

Assume that the length of the side of the square base is x and the height of the box is y

∵ It needs to be made using 300 ft² of material

∴ The surface area of the box is 300 ft²

∵ Its base is a square of side length x ft

∴ Perimeter of the base = 4 × x = 4 x

∴ Area of the base = x²

∵ The height of the box = y ft

∵ SA = perimeter of base × height + area of the base

∵ SA = (4x)(y) + x²

∴ SA = 4xy + x²

∵ SA of the box = 300 ft²

- Equate the two expressions of SA

∴ 4xy + x² = 300

Now let us find y in terms of x

- Subtract x² from both sides

∴ 4xy = 300 - x²

- Divide each term by 4x to find y

∴ y=\frac{75}{x}-\frac{1}{4}x

∵ V = area of the base × height

∴ V = x² × y = x²y

- Substitute y by the equation of it above

∴ V=x^{2}(\frac{75}{x}-\frac{1}{4}x)

∴ V=75x-\frac{1}{4}x^{3}

∵ The volume of the box is greatest

- That means differentiate V and equate it by 0

∵ \frac{dV}{dx}=75-\frac{3}{4}x^{2}

∵ \frac{dV}{dx}=0 ⇒ greatest volume

∴ 75-\frac{3}{4}x^{2}=0

- Subtract 75 from both sides

∴ -\frac{3}{4}x^{2}=-75

- Divide both sides by -\frac{3}{4}

∴ x² = 100

- Take √ for both sides

∴ x = 10

Substitute the value of x in the equation of y

∵ y=\frac{75}{10}-\frac{1}{4}(10)

∴ y = 5

The dimensions of the box are 10 ft and 5 ft

∵ V=75x-\frac{1}{4}x^{3}

∵ x = 10

∴ V=75(10)-\frac{1}{4}(10)^{3}

∴ V=750-\frac{1}{4}(1000)

∴ V = 750 - 250

∴ V = 500 ft³

The maximum volume is 500 ft³

Learn more:

You can learn more about the volume in brainly.com/question/6443737

#LearnwithBrainly

6 0
2 years ago
What shape is produced when slicing a right rectangular pyramid perpendicular to the base?
matrenka [14]
C. triangle.
Pyramids are triangles to begin with you’re just making a smaller one
6 0
2 years ago
find the point on the terminal side of θ = negative three pi divided by four that has an x coordinate of negative 1
Mila [183]
Check the picture below, is a negative angle, thus, is going "clockwise"

\bf tan(\theta)=\cfrac{opposite}{adjacent}\qquad tan\left( -\frac{3\pi }{4} \right)=\cfrac{y}{x}\implies  tan\left( -\frac{3\pi }{4} \right)=\cfrac{y}{-1}
\\\\\\
-1\cdot  tan\left( -\frac{3\pi }{4} \right)=y\implies -1\cdot \cfrac{sin\left( -\frac{3\pi }{4} \right)}{cos\left( -\frac{3\pi }{4} \right)}=y
\\\\\\
-1\cdot \cfrac{-1}{-1}=y\implies -1

4 0
2 years ago
Starting from the origin, how is point ( – 2, – 6) plotted?
OleMash [197]
I would say b the reason is because -2 is on the x and -6 in on the y so it would be left then down.
5 0
3 years ago
Is reading a book that is 1400 pages he will read the same number of pages each day if he reads the book in 7 days how many page
Alex777 [14]
He will read 200 pages a day because 1400/7 = 200
3 0
2 years ago
Read 2 more answers
Other questions:
  • The perimeter of a certain rectangle is 16 times the width. The length is 12cm more than the width. Find the length of the recta
    8·1 answer
  • Need help with this one please show it step by step.<br> Thank you!
    7·1 answer
  • How to do I am stuck with the q
    8·1 answer
  • If a fish swims 7/8 of the depth of a 32-foot deep lake, how many feet down did the fish swim?
    7·2 answers
  • To arrive at its destination on time the bus should have maintained a speed of vv kilometers per hour throughout the journey. In
    7·1 answer
  • 5 times a number is less than 2 times that same number minus 9, what must be the value of the number?
    8·1 answer
  • How can I do 10(a)(ii) and 10(b)?n
    11·1 answer
  • Find the values of x and y for which ABCD must be a parallelogram.?
    8·2 answers
  • Simplify the following square root √ -1 =​
    7·2 answers
  • 2z-1/3- 3z+1/5=1<br> z=? <br> Have a good Earth day!
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!