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Oduvanchick [21]
2 years ago
11

A 32 foot ladder is leaning against a building and forms a 29.37 angle with the ground how far away from the building is the bas

e of the ladder round to nearest hundredth
Mathematics
2 answers:
BARSIC [14]2 years ago
6 0

Answer:

the base of the ladder is 27.89  ft away from the building

Step-by-step explanation:

Notice that this situation can be represented with a right angle triangle. The right angle being that made between the ground and the building, the ladder (32 ft long) being the hypotenuse of the triangle, the acute angle of 29.37^o being adjacent to the unknown side we are asked about (x). So, we can use the cosine function  to solve this:

cos(\theta)=\frac{adjacent}{hypotenuse} \\cos(29.37^o)=\frac{x}{32\,\,ft}\\32 \,\,cos(29.37^o)\,\,ft=x\\x=27.887\,\,ft

which rounded to the nearest hundredth gives;

x = 27.89  ft

grigory [225]2 years ago
4 0

Answer:

27.89

Step-by-step explanation:

i took the test!!

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List the potential solutions to 2 ln x = 4 ln 2 from least to greatest.
svp [43]

We have to find the potential solutions to 2 ln x = 4 ln 2 from least to greatest.

Using the properties of ln function.

a \times ln b = ln b^{a}

Therefore, we get

ln x^{2} = ln 2^{4}

ln x^{2} = ln 16

taking antilog on both the sides, we get

x^{2} = 16

So, x = \pm 4

Therefore, the potential solutions to 2 ln x = 4 ln 2 from least to greatest is -4 and 4.

3 0
2 years ago
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Henri has $24,000 invested in stocks and bonds. The amount in stocks is $6,000 more than three times the amount in bonds. Call t
makvit [3.9K]

Answer:

The solve of that problem is that Hernry invested $18.000 in stocks and $6.000 in bonds.

Step-by-step explanation:

First, to explain you have to do a multiplication about 6 on three. Like three times more than bonds, the result is 18. Then you have to do a  subtraction on $24.000 less $18.000, and the result is $6.000, so six is the amount on bonds. And is three times less than stocks, like the questions ask.

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2 years ago
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Joining the frequent visitor program at the planetarium costs $5 per year, write an equation that can be used to determine n, th
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11n + 5 = 13n <== ur equation
7 0
2 years ago
HURRY PLEASE When 5 and 6 are multiplied by the same factor, how do the ratios compare to the ratio 5:6? The ratios are equivale
erma4kov [3.2K]

Answer:

The ratios are equivalent.

Step-by-step explanation:

If you multiply both 5 and 6, the ratio stays the same.

5:6 = 10:12 = 15:18 = 20:24 etc.

You can try this by dividing the larger number by the smaller number. You'll always get 1.2 as the "relationship", or ratio, is preserved.

24/20 = 1.2

15/18 = 1.2

10/12 = 1.2

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6 0
2 years ago
hree TAs are grading a final exam. There are a total of 60 exams to grade. (a) How many ways are there to distribute the exams a
nalin [4]

Answer:

a. 205320

b. 34220

c. 60! / (35)! (25)! + 60!/ (40)!(20)! + 60!/ (45)! (15)!

Step-by-step explanation:

a) The number of ways to dustribute exams among the TA's is:

n / (n - r)!

n= number of things to choose from

r= Choosing r number

60P3= 60! / (60 - 3)!

(60)(59)(58)(57)! / (57)!

=205320

B) The number of ways to dustribute the exams among the TA's is:

n! /(n - r)! r!

60C3= 60! /(60 - 3)! 3!

= 60!/ 57! 3!

= 60 × 59 × 58 / 3 × 2 × 1

= 34220

C) The required number of ways is:

60C25 + 60C20 + 60C15

= 60! / (35)! (25)! + 60!/ (40)!(20)! + 60!/ (45)! (15)!

6 0
2 years ago
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