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Vikki [24]
1 year ago
9

Find the surface area of the cylinder. Type an exact answer in terms of pi.

Mathematics
2 answers:
Elodia [21]1 year ago
5 0

Answer:

=150.79644...cm²

~150cm²

Step-by-step explanation:

cylinder surface area = 2 pi r h + 2 pi r²

Yakvenalex [24]1 year ago
4 0

Answer:

24π cm²

Step-by-step explanation:

Radius (r) = 3 cm

Height (h) = 5 cm

Surface area of cylinder

= 2πr (h + r)

= 2 × π × 3 (5 + 3)

= π × 3 (8)

= π × 24

= 24π cm²

______

#Rosé

Hope it helps ⚜

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What is the limit of [(x+2) /(x+1)] ^x as x approaches to infinity?
Lesechka [4]

first thing we need to do is factorise because we can't calculate infinity/infinity

and we are left with 1^infinity this is an euler function

an euler function looks like this

6 0
2 years ago
Victor earns a gross annual income of $64,570 and is buying a home for $125,340. He is making a 15% down payment and financing t
Oliga [24]
Part A:

Given that <span>Victor is buying a home for $125,340 and that he is making a 15% down payment.

The amount of down payment is given by 15% of $125,340 = 0.15 x $125,340 = $18,801.

Therefore, the amount of mortgage he needs to borrow is given by $125,340 - $18,801 = $106,539


Part B

</span>Given that he earns a gross annual income of $64,570 <span>and that the loan of $106,539 will be spread for 20 years at 3.75% interest.

$106,539 / 20 = $5,326.95

Roughly he will be paying about $5,000 every year which is way below his annual gross income. 

Therefore, he can afford the mortgage.


Part C

The monthly mortgage payment can be calculated using the present value of annuity formula given by

</span>PV=P\left( \frac{1-\left(1+\left( \frac{r}{t} \right)\right)^{-nt}}{ \frac{r}{t} } \right)
<span>
where: PV is the current value of the loan, P is the periodic (monthly) payment, r is the annual interest rate, t is the number of payment in one year and n is the number of years.

Here, PV = </span>$106,539; r = 3.75% = 0.0375; t is 12 payments in one year (since payment is to be made monthly); n = 20 years.

Thus, we have:

106,539=P\left( \frac{1-\left(1+\left( \frac{0.0375}{12} \right)\right)^{-20\times12}}{ \frac{0.0375}{12} } \right) \\  \\ =P\left( \frac{1-\left(1+0.003125\right)^{-240}}{0.003125} \right)=P\left( \frac{1-\left(1.003125\right)^{-240}}{0.003125} \right) \\  \\ =P\left( \frac{1-0.472919}{0.003125} \right)=P\left( \frac{0.527081}{0.003125} \right)=168.666P \\  \\ \Rightarrow P= \frac{106,539}{168.666} =631.66

Therefore, the monthly mortgage payment is $631.66


Part D

Since he will make a monthly payment of $631.66 for 20 years, thus he will make a total of $631.66 x 12 x 20 = $151,598.40

Therefore, his total payment for the house will be $151,598.40


Part E

Since he will make a total payment of $151,598.40 for a mortgage loan of $106,539.

Therefore, the amount of interest he will pay is given by $151,598.40 - $106,539 = $45,059.40
7 0
3 years ago
Round 34.4678 of to two decimals​
mina [271]

Answer:

34.47

Step-by-step explanation:

When you need to round it off to the second decimal, you must look at the 3rd decimal place.

In this case, it's 7. If it's a number greater than 5 or 5, you must round off to the next value and if it is less than 5 or 5.

Since it is 7 in the third decimal place, the answer would be 34.47

6 0
2 years ago
Read 2 more answers
A car dealership has found that the length of time before a major repair is required on the new cars it sells is normally distri
weqwewe [10]

Answer:

Step-by-step explanation:

Hello!

The variable of interest in this case is:

X: length of time before a major repair is required on a new car. (months)

This variable has a normal distribution with mean μ= 36 months and a standard deviation σ= 9 months.

If he wants to set a guarantee period in which only 5% of the sold cars fell, the objective is to find the value of X that has below 5% of the cars that need major repairs before the end of the guarantee period.

Check the attachment, the curve represents the distribution of the population of the time it takes before a new car needs major repairs, I've marked approximately where this value of X should be.

Symbolically:

P(X≤a)=0.05

To reach the proper value of "a" you have to work using the standard normal distribution because is a tabulated distribution and you can extrapolate it to any normal distribution.

Z= \frac{X-Mu}{Sigma}~N(0;1)

So the first step is to look in the table of the Z distribution for the value that accumulates 0.05 of probability since it is such a low probability, you have to look for the value in the left side of the table (negative values of Z). You look for 0.05 in the body of the table and then the margins for the corresponding value (see second attachment)

Z_{0.05}= -1.64

Then the value that accumulates 0.05 of probability is -1.64, now you have to reverse the standardization to reach the asked value of X

Z= (a- μ)/σ

(Z*σ)= a - μ

a=(Z*σ)+ μ

a=(-1.64*9)+36

a= 21.24 months.

The guarantee period should be 21.24 months so that only 5% of the sold cars will need major repairs before it wears of.

I hope it helps!

5 0
3 years ago
It took 2/3 of an hour to complete her science homework. It took Bethany 3/4 of the amount of time to do her math homework as he
SOVA2 [1]
We know there are 60 minutes in an hour.  To find 2/3 of an hour we divide 60/3 to find 1/3 and multiply by 2 so:
60/3 = 20
20*2 = 40 minutes (which is 2/3 of an hour) to do science

We do the same thing with the 40 minutes.  To find 1/4 of 40 minutes we divide 40 by 4 and then multiply it by 3 to get 3/4 so:

40/4 = 10
10*3 = 30 minutes

Then subtract the times 40-30 = 10 minutes

It took her 10 more minutes to complete her science homework.

Hope that helps


3 0
3 years ago
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