MATHEMATICS HIGH SCHOOL

Cylinder a has a radius 2 cm and contains water to a height of 10cm cylinder b has a radius 5cm and is empty. Some of the water is poured from cylinder a to b the height is now the same

Answers

Answer 1

Answer:

Answer:

h = 1.38 cm

Step-by-step explanation:

The question is at what value is the height of both cylinders the same:

The area of the circular base on each cylinder is:

$Area=\pi r^2\nA=4\pi \ cm^2\nB=25\pi \ cm^2$

The initial volume in cylinder A is:

$V=4\pi *10\nV=40\pi\ cm^3$

We have that Va + Vb = 40π. The height of water in each cylinder as a function of volume is:

$h_A=(V_a)/(4\pi)\nh_B=(V_b)/(25\pi)$

If both heights are the same:

$(V_a)/(4\pi)=(V_b)/(25\pi)\nV_b=(25)/(4)V_a \nV_a+V_b=40\pi\nV_a+(25)/(4)V_a=40\pi\nV_a=5.5172\pi\ cm^3$

The height 'h' is:

$h=(5.5172\pi)/(4\pi)\n h=1.38\ cm$

Answer 2

Answer:

Final answer:

The question refers to the mathematics of the volume of a cylinder. It involves calculating the initial volume of water in cylinder A, and then determining the volume of water in cylinder B after it has received water from cylinder A.

Explanation:

The subject of the question is related to the mathematical concept of volume, specifically the volume of a cylinder. In this scenario, we are dealing with two cylinders and the volume of water transferred between them.

Firstly, the volume of water in cylinder A initially can be calculated using the formula for the volume of a cylinder, which is V = πr²h, where r is the radius of the base and h is the height. So, for cylinder A with radius 2 cm and height 10 cm, the volume of water initially is V = π(2)²(10) = 40π cm³.

After some water is transferred from cylinder A to cylinder B, the question states that the height of water in both cylinders is the same. It means that the volume of water in cylinder B is now equal to that of a cylinder with radius 5 cm and the same height as cylinder A after the transfer which can also be found by the formula V = πr²h.

Learn more about Volume of cylinder here:

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I sell cookies for $3 and muffins for $7. Yesterday, I made $129. I sold a total of 27 items. How many of each did I sell?

Answers

You sold 15 cookies and 12 muffins.

c - cookies
m - muffins

c + m = 27

3c + 7m = 129

I don’t know how to explain how to do efficiently but I just plugged in numbers until it worked:

3(15) + 7(12) = 129

45 + 84 = 129

Answer:

You sold 15 cookies and 12 muffins

Step-by-step explanation:

So you're given that 1 cookie is sold for $3 and 1 muffin is sold for $7

You're also given that in total you made $129, and sold 27 items

Let's make equations from that, letting c stand for amount of cookies and m for amount of muffins.

3c + 7m = 129 (equation for amount of money made)
c + m = 27 (equation for amount of items sold)

Now we can use the second equation to find m:

c + m = 27

m = 27 - c

Not we can substitute m into the first equation to find c:

3c + 7m = 129

3c + 7(27-c) = 129 [substitute m for (27-c)]

3c + 189 -7c = 129 [distribute 7 into (27-c)]

-4c + 189 = 129 [combine like terms]

-4c = -60 [subtract 189 from both sides]

c = 15 [divide both sides by -4]

Now we can substitute c into the second equation to find m:

c + m = 27

15 + m = 27

m = 12

What is -4+ 7x = y written I. Slope-intercept form,and I have to graph it

Answers

Answer:

y = 7x - 4

Step-by-step explanation:

-4 + 7x = y and y = 7x - 4 are the same thing, there ya go.

13x-7y+4x(simply the expression by combining like terms)
Please help!:) and if you can please show the steps!<3

Answers

Answer:

17−7

Step-by-step explanation:

Hope this helped good luck in your work!

13. The third term in an arithmetic sequence is 10 and the fifth term is 26. If the first term is , which is an equation for the nth term of this sequence?

Answers

n=3:
A) an = 8*3+10 = 34
B) an = 8*3 - 14 = 10 OK
C) an = 16*3+10 = 58
D) an = 16*3 - 38 = 10 OK

n=5:
B) an = 8*5-14 = 26 OK
D) an = 16*5 - 38 = 42

So the answer is B

What point on the number line is 1/4 of the way from the point -2 to the point 5