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2 years ago

Your friend brings hot chocolate to school in the cylindrical thermos and drinks from her cylindrical mug shown.

Mathematics

1 answer:

Vesna [10]2 years ago

4 0

Volume=height times area of base
base=circle so area of base=pir^2
ok so solume=height times pi times r^2

1.
thermos, h=10, r=2
therefor
volume=10pi2^2=
volume=10pi4=
40pi in^3 is brought to school

2. inside is 4 inches deep
h=4, r=1.5
volume=4pi1.5^2
volume=4pi2.25
volume=9pi
answer is 9pi in^3

3. so find 80% of 9pi
80%=0.8
0.8 times 9pi=7.2pi in^3
each times is 7.2pi in^3

4. ok so this is assuming that you fill the mug to 80% (7.2pi) each time and the remainder is it less or more or equal to half of 7.2pi so

total in thermos=40pi
each pour=7.2pi
40pi-7.2pi-7.2pi-7.2pi-7.2pi-7.2pi=4pi
is 4pi more or less than 7.2pi
7.2pi/2=3.6pi
4pi>3.6pi
it is MORE

1. 40pi in^3
2. 9pi in^3
3. 7.2pi in^3
4. MORE than half

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3 years ago

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2 years ago

Read 2 more answers

PLEASE HELP ILL MARK BRAINLIEST !!!

Alexus [3.1K]

Answer:

a) the common difference is 20

b) $x_8=115 , x_{12}=195$

c) the common difference is -13

d) $a_{12}=52, a_{15}=13$

Step-by-step explanation:

a) what is the common difference of the sequence xn

Looking at the table, we get x_3=16, x_4=36 and x_5= 56

Deterring the common difference by subtracting x_4 from x_3 we get

36-16 =20

So, the common difference is 20

b) what is x_8? what is x_12

The formula used is: $x_n=x_1+(n-1)d$

We know common difference d= 20, we need to find $x_1$

Using $x_3=16$ we can find $x_1$

$x_n=x_1+(n-1)d\\x_3=x_1+(3-1)d\\15=x_1+2(20)\\15=x_1+40\\x_1=15-40\\x_1=-25$

So, We have $x_1 = -25$

Now finding $x_8$

$x_n=x_1+(n-1)d\\x_8=x_1+(8-1)d\\x_8=-25+7(20)\\x_8=-25+140\\x_8=115$

So, $\mathbf{x_8=115}$

Now finding $x_{12}$

$x_n=x_1+(n-1)d\\x_{12}=x_1+(12-1)d\\x_{12}=-25+11(20)\\x_{12}=-25+220\\x_{12}=195$

So, $\mathbf{x_{12}=195}$

c) what is the common difference of the sequence $a_m$

Looking at the table, we get a_7=104, a_8=91 and a_9= 78

Deterring the common difference by subtracting a_7 from a_8 we get

91-104 =-13

So, the common difference is -13

d) what is a_12? what is a_15?

The formula used is: $a_n=a_1+(n-1)d$

We know common difference d= -13, we need to find $a_1$

Using $a_7=104$ we can find $x_1$

$a_n=a_1+(n-1)d\\a_7=a_1+(7-1)d\\104=a_1+7(-13)\\104=a_1-91\\a_1=104+91\\a_1=195$

So, We have $a_1 = 195$

Now finding $a_{12}$ , put n=12

$a_n=a_1+(n-1)d\\a_{12}=a_1+(12-1)d\\a_{12}=195+11(-13)\\a_{12}=195-143\\a_{12}=52$

So, $\mathbf{a_{12}=52}$

Now finding $a_{15}$ , put n=15

$a_n=a_1+(n-1)d\\a_{15}=a_1+(15-1)d\\a_{15}=195+14(-13)\\a_{15}=195-182\\a_{15}=13$

So, $\mathbf{a_{15}=13}$

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2 years ago

M is the midpoint of QR<br><br> M = (-2,6)<br> Q= (8,-10)<br> R = ????

Zolol [24]

Answer:

R = (-12, 22)

Step-by-step explanation:

Unfortunately it's not a straight line, so gonna need to put in some extra work. Basically think of it like breaking it into it's horizontal and vertical components then doubling them.

From Q to M you move 10 spaces to the left, so to go from M to R you will go another 10 to the left. Similarly, you start at -10 for the y value and go up 16 to 6, and you will need to go up another 16 to get to R.

So for x, 8 -10 = -2 then -2 - 10 = -12, so R's x value is -12

y we do the same thing. Gonna do it in one step though. -10 + 16 + 16 = 22

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2 years ago

Manny can paint the office by himself in 5 hours. Dave can do the same job in 8 hours. How long will it take them to do it work

Alex Ar [27]

Answer:

3 hrs 4.6 mins

Step-by-step explanation:

1/5 + 1/8 = 1/x

x = 40/13

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1 year ago