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igomit [66]
2 years ago
13

An escalator lifts people to the second floor of a building, 21 ft above the first floor. the escalator rises at a 30 degree ang

le. to the nearest foot, how far dies a person travel from the bottom to the top of the escalator?
Mathematics
1 answer:
Ira Lisetskai [31]2 years ago
7 0
We use the trigonometric function for this case. An escalator is an inclined path. We form a right triangle since we have given the value of the height. The height from the first floor to second floor is called the adjacent while the travelled distance of the people is called the hypothenuse. We use cosine function because we are given in terms of adjacent and hypothenuse. The ratio of cosine function is
cos x = a/h
where x is the angle
Solving for h,
h = a/(cos x) = 21/(cos 30) = 24.25 ft
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What is 32:42 simplified as a fraction
Andre45 [30]
The answer is 16/21 because it is equivalent to 32/42
8 0
2 years ago
I need help, someone help me
Bezzdna [24]

The sum of the angles of a triangle must add up to 180 degrees.

180 = 35 + 70 + x

180 = 105 + x

180 - 105 = x

75 = x

Option B is your answer.

3 0
3 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
Sanjay has £356.54 in his bank account. He spends £595.99 on a new mountain bike. What is his new bank balance?
Vaselesa [24]

your answer would be -239.45.

356.54

-595.99

-------------

-239.45

3 0
3 years ago
Add the following using the common denominator method. Show all of your work. <br><br> 2/3 + 2/9
Alekssandra [29.7K]

Answer:

8/9

Step-by-step explanation:

First we need to get both of the fractions to the same denominator.

1. 2/3 + 2/9 = 6/9 + 2/9

Next, we simply just add the fractions.

2. 6/9 + 2/9 = 8/9

8 0
3 years ago
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