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
OLga [1]
3 years ago
11

How much water will be needed to completely fill a rectangular vase that has a length of 4 inches, a width of 4 inches, and a he

ight of 16 inches?
Mathematics
1 answer:
antiseptic1488 [7]3 years ago
7 0
4 x 4 x 16 = 256 square inches of water
You might be interested in
What is the equation of the graph below? A graph shows a parabola that opens up with a vertex at negative three comma negative o
Tomtit [17]

Answer:

y=(x+3)^2-1\\y=x^2+6x+8

Step-by-step explanation:

Given:

Vertex of the parabola is, (h,k)=(-3,-1)

Equation of the parabola in vertex form is given as:

y=(x-h)^2+k

Plug in h=-3,k=-1. This gives,

y=(x-(-3))^2+(-1)\\y=(x+3)^2-1

Therefore, the equation of the given graph is

y=(x+3)^2-1\\y=x^2+6x+8.

5 0
3 years ago
use the general slicing method to find the volume of The solid whose base is the triangle with vertices (0 comma 0 )​, (15 comma
lyudmila [28]

Answer:

volume V of the solid

\boxed{V=\displaystyle\frac{125\pi}{12}}

Step-by-step explanation:

The situation is depicted in the picture attached

(see picture)

First, we divide the segment [0, 5] on the X-axis into n equal parts of length 5/n each

[0, 5/n], [5/n, 2(5/n)], [2(5/n), 3(5/n)],..., [(n-1)(5/n), 5]

Now, we slice our solid into n slices.  

Each slice is a quarter of cylinder 5/n thick and has a radius of  

-k(5/n) + 5  for each k = 1,2,..., n (see picture)

So the volume of each slice is  

\displaystyle\frac{\pi(-k(5/n) + 5 )^2*(5/n)}{4}

for k=1,2,..., n

We then add up the volumes of all these slices

\displaystyle\frac{\pi(-(5/n) + 5 )^2*(5/n)}{4}+\displaystyle\frac{\pi(-2(5/n) + 5 )^2*(5/n)}{4}+...+\displaystyle\frac{\pi(-n(5/n) + 5 )^2*(5/n)}{4}

Notice that the last term of the sum vanishes. After making up the expression a little, we get

\displaystyle\frac{5\pi}{4n}\left[(-(5/n)+5)^2+(-2(5/n)+5)^2+...+(-(n-1)(5/n)+5)^2\right]=\\\\\displaystyle\frac{5\pi}{4n}\displaystyle\sum_{k=1}^{n-1}(-k(5/n)+5)^2

But

\displaystyle\frac{5\pi}{4n}\displaystyle\sum_{k=1}^{n-1}(-k(5/n)+5)^2=\displaystyle\frac{5\pi}{4n}\displaystyle\sum_{k=1}^{n-1}((5/n)^2k^2-(50/n)k+25)=\\\\\displaystyle\frac{5\pi}{4n}\left((5/n)^2\displaystyle\sum_{k=1}^{n-1}k^2-(50/n)\displaystyle\sum_{k=1}^{n-1}k+25(n-1)\right)

we also know that

\displaystyle\sum_{k=1}^{n-1}k^2=\displaystyle\frac{n(n-1)(2n-1)}{6}

and

\displaystyle\sum_{k=1}^{n-1}k=\displaystyle\frac{n(n-1)}{2}

so we have, after replacing and simplifying, the sum of the slices equals

\displaystyle\frac{5\pi}{4n}\left((5/n)^2\displaystyle\sum_{k=1}^{n-1}k^2-(50/n)\displaystyle\sum_{k=1}^{n-1}k+25(n-1)\right)=\\\\=\displaystyle\frac{5\pi}{4n}\left(\displaystyle\frac{25}{n^2}.\displaystyle\frac{n(n-1)(2n-1)}{6}-\displaystyle\frac{50}{n}.\displaystyle\frac{n(n-1)}{2}+25(n-1)\right)=\\\\=\displaystyle\frac{125\pi}{24}.\displaystyle\frac{n(n-1)(2n-1)}{n^3}

Now we take the limit when n tends to infinite (the slices get thinner and thinner)

\displaystyle\frac{125\pi}{24}\displaystyle\lim_{n \rightarrow \infty}\displaystyle\frac{n(n-1)(2n-1)}{n^3}=\displaystyle\frac{125\pi}{24}\displaystyle\lim_{n \rightarrow \infty}(2-3/n+1/n^2)=\\\\=\displaystyle\frac{125\pi}{24}.2=\displaystyle\frac{125\pi}{12}

and the volume V of our solid is

\boxed{V=\displaystyle\frac{125\pi}{12}}

3 0
3 years ago
5 times the result of a number plus 7 equals 71 more than that number
lubasha [3.4K]
The answer is: 12.8
71 -7 = 64
64÷5=12.8
4 0
3 years ago
Read 2 more answers
Q2)Write an equation in slope-intercept form for the line with slope6 and y -intercept-3 .
sweet [91]
The equation is y= 6x-3
6 0
3 years ago
This is a one step equation
vichka [17]

Awnser:

I think its 7

Step-by-step explanation:

the photo is blurly can you say it and i can help u again

3 0
3 years ago
Read 2 more answers
Other questions:
  • I NEED HELP PLZZZ AN EXPERT ASAP
    10·2 answers
  • How many seconds are in 4 years?
    13·1 answer
  • What does 4/9 - 2/3 equal
    5·1 answer
  • Adult tickets to the fall play cost $8 and student tickets cost $4. The drama class sold 30 more adult tickets than student tick
    5·1 answer
  • I need help really bad I don't know how to do this
    9·2 answers
  • I attached a picture please tell me where she made a mistake i am really struggling thanks.
    10·1 answer
  • Question 6 (1 point)
    6·1 answer
  • Which of the following sets of data is bimodal?
    14·1 answer
  • In the image, pretty sure 24 is a plane. Not sure about 23.
    13·1 answer
  • 83, 15, 50, 28, 52, 96 - What is the mean? What is the mode? What is the median?
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!