Mathematics, 10.01.2020 20:31 emmaja121003

Can someone me understand how to do these

Answers: 3

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Answers

1)

you can think of the cup's sleeve as a cylinder with say a height of 4 and a diameter of 5. Now, if the diameter is 5 inches, the radius is half that, or 2.5,

$\bf \textit{total surface area of a cylinder}\\\\
s=2\pi r(h+r)\quad 
\begin{cases}
r=2.5\\
h=4
\end{cases}\implies s=2\pi (2.5)(4+2.5)
\\\\\\
s=5\pi (6.5)\implies s=32.5\pi$

2)

same here, you can think of the tire as a cylinder, since it's a cylindrical tire, with a height of 8 and a diameter of 29, therefore a radius of 14.5,

$\bf \textit{total surface area of a cylinder}\\\\
s=2\pi r(h+r)\quad 
\begin{cases}
r=14.5\\
h=8
\end{cases}\implies s=2\pi (14.5)(8+14.5)
\\\\\\
s=29\pi (22.5)\implies s=652.5\pi$

now, that's how much spaces it covers one time only, so 5 times around is just 5 times that much.

3)

same goes for the mugs,

$\bf \textit{total surface area of a cylinder}\\\\
s=2\pi r(h+r)\quad 
\begin{cases}
r=2\\
h=3.75
\end{cases}\implies s=2\pi (2)(3.75+2)
\\\\\\
s=4\pi (5.75)\implies s=\stackrel{one~mug}{23\pi }\qquad\qquad \stackrel{4~mugs}{4\cdot 23\pi }$

4)

and the same goes for the can of peas, which is also a cylinder,

a)

$\bf \textit{total surface area of a cylinder}\\\\
s=2\pi r(h+r)\quad 
\begin{cases}
r=3.8\\
h=10
\end{cases}\implies s=2\pi (3.8)(10+3.8)
\\\\\\
s=7.6\pi (13.8)\implies s=101.08\pi$

b)

the label is only the sides, and thus only the lateral area,

$\bf \textit{\underline{lateral} surface area of a cylinder}\\\\
s=2\pi rh\quad 
\begin{cases}
r=3.8\\
h=10
\end{cases}\implies s=2\pi (3.8)(10)\implies s=76\pi$

Answer from: Quest

step-by-step explanation: so we look at the formula un = a + (n-1)d

un is the amount of seats

n is the nth term aka row number

a is the original sequence/row number

d is the difference between each term

so in this a=22 d=6 and n can remain as n because we are simply formjng a rule

lets put these in the equation

un=22+(n-1)(6)

this is your answer to part a

however

lets double check that this is correct, we'll try putting it into the second term

un=a+(n-1)d

u2=22+(2-1)(6)

u2=22+6

u2=28

as the question said the second row has 28 seats so now we know the formula we made is correct.

as for part b

un=a+(n-1)

its asking us to find a row with 100 seats.

remember un was the amount of seata so all we do is substitute this in.

un=100 a=22 d=6

un=a+(n-1)d

100=22+(n-1)(6)

so now we simplify to find n which is the row number.

100-22=22+(n-1)(6)-22

78=(n-1)(6)

78/6=(n-1)(6)/6

13=n-1

13+1=n-1+1

14=n

so now we know that in the 14th row there is 100 seats.

hope this and that you understood! its my first time using the app or anyone out on here : p its also me to revise so a bunch! ask more questions if you dont understand ☺

Answer from: Quest

graph them on a graphing calculator, press 2nd trace. select intersect. hit enter until it says answer. ti 84 works best

step-by-step explanation: