Question

How to multiply this expression?

Answer 1

\[\huge 4\pi(4.096\times 10^{13})\]

Answer 2

@phi

Answer 3

YOu're saying you need help on it or what?

Answer 4

Yes I need help on it

Answer 5

@Nnesha Can you please help me?

Answer 6

Got about 5200
you need me to explain it or just give you the answer?

Answer 7

@calculusxy Just multiply 4*4.096. Then leave it in terms of pi and 10^13

Answer 8

the 4 * 4096 are powers of 2. Some computer types would know it is 16384
or with the decimal 16.384
multiplying by pi is harder

Answer 9

(16.384 \(\times\) \(10^{13}\))\(\pi\)

Answer 10

then make the 16.384 "smaller" to 1.6384
and compensate by making the exponent bigger by 1, from 13 to 14

Answer 11

But my teacher said for me to evaluate it even with the \(\pi\). I mean I can type it up in a calculator and then do it, but I have this thing that says \(e+\) which i have no idea about

Answer 12

are you allowed to use a calculator , but don't know what the answer means ?

Answer 13

yes.

Answer 14

I get this when I type it up in a calculator.

Answer 15

so far you have
\[ \pi(1.6384 \times 10^{14}) \\ \pi \cdot 1.6384e14 \]

Answer 16

you will get an answer of about 5.0e14

Answer 17

so how do I write it down in scientific notation?

Answer 18

here is the actual problem (look at part a) from which i am doing my work for

Answer 19

you would type in pi * 4 * 4.096 EXP 13 =

Answer 20

So my answer would be what?

Answer 21

try doing that on your calculator

Answer 22

I did type it in and then that's what i got in the screenshot with the e+14

Answer 23

yes, the "e+14" means exponent. It is short for \(10^{14}\)

Answer 24

so the problem wants for me to approximate it. what should i approximate it to?

Answer 25

you could also type in
4*pi*( 6.4 EXP 6) square (whatever button squares it)

Answer 26

the input 6.4e6 only has 1 decimal.
I would round the answer to two decimals, so 5.15e14

Answer 27

okay! so my answer would be \(5.15 \times 10^{14}\)

Answer 28

yes, and probably add m^2 (for square meters)

Answer 29

okay can you help me with the remaining two parts of the question please?

Answer 30

for part b-- i know that 70% = 0.7 (which in scientific notation would be \(7 \times 10^{-1}\). so do i do \(\large \frac{5.15 \times 10^{14}}{7 \times 10^{-1}}\)

Answer 31

ok, but you don't divide. if you wanted 70% of 100 you would do
0.7 * 100 = 70
(not divide)

and though you could change 0.7 to 7e(-1) I would not bother
I would do 0.7*5.15e14 =

Answer 32

but would i multiply \(7 \times 10^{-1}\) with \(5.15 \times 10^{14}\) then?

Answer 33

you could, but that is more work.

First, do it the way I suggested:
0.7*5.15e14 =

what do you get ?

Answer 34

3.605 x \(10^{14}\)

Answer 35

oh wow that is the answer isn't it?

Answer 36

yes. now do it the other way. You should get the same number.

Answer 37

yeah i tried and i got the same answer :)

moving on to part c

Answer 38

so for the last question, it's basically asking to find the volume of a sphere right?

Answer 39

no, something simpler.

It's a "rough" calculation, so just imagine you had a region with a bottom area of 3.6e15 m^2
and a height of 3795 m

and use Volume of a prism = area_of_base * height

Answer 40

so would i do in here
\[\large (3795)(3.605 \times 10^{14})\]

Answer 41

yes

Answer 42

okay

Answer 43

give me one more minute

Answer 44

i got
1.3680975 \(\times\) \(10^{18}\)

Answer 45

yes, with units m^3 (cubic meters)

Answer 46

okay thank you so much!!!! :)

Answer 47

you should probably round your final answer to 1.37e18 m^3