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frutty [35]
2 years ago
5

A 12 foot ladder leans against a building. The angle of elevation from the ground to the foot of the ladder is 46°. Find, to the

nearest tenth of a foot, how far is the foot of the ladder from the building
Mathematics
1 answer:
elena55 [62]2 years ago
4 0

Answer:

8.3 ft

Step-by-step explanation:

Hypotenuse is the longest side

Opposite is the side opposite the angle

Adjacent is the remaining side

Draw the triangle out, and you'll find that the hypotenuse (length of ladder) is 12ft, and that you are looking for the adjacent side (length of the foot of the ladder to the building). Rule out the opposite side (side of building) as it is not needed. The appropriate trigonometric formula is then the cos(angle) = \frac{adjacent}{hypotenuse}, rearranged to find the adjacent side is adjacent = cos(angle)*hypotenuse  

substitute the values in and you get cos(46) x 12 = 8.335900446

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3 years ago
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bixtya [17]

Answer:  \bold{(1)\ \dfrac{19,683}{64}\qquad (2)\ 16}

<u>Step-by-step explanation:</u>

(1)           (12, 18, 27, ...)

The common ratio is:

r=\dfrac{a_{n+1}}{a_n}\quad r =\dfrac{18}{12}=\boxed{\dfrac{3}{2}}\quad \rightarrow \quad r=\dfrac{27}{18}=\boxed{\dfrac{3}{2}}

The equation is:

a_n=a_o(r)^{n-1}\\\\Given:a_o=12,\  r=\dfrac{3}{2}\\\\\\Equation:\\a_n =12\bigg(\dfrac{3}{2}\bigg)^{n-1}\\\\\\\\9th\ term:\\a_9=12\bigg(\dfrac{3}{2}\bigg)^{9-1}\\\\\\a_9=12\bigg(\dfrac{3}{2}\bigg)^{8}\\\\\\.\quad =\large\boxed{\dfrac{19643}{64}}

(2)\qquad \bigg(\dfrac{1}{16},\dfrac{1}{8},\dfrac{1}{4},\dfrac{1}{2}\bigg)\\\\\\\text{The common ratio is}:\\\\r=\dfrac{a_{n+1}}{a_n}\quad  r=\dfrac{\frac{1}{8}}{\frac{1}{16}}=\boxed{2}\quad \rightarrow \quad r=\dfrac{\frac{1}{4}}{\frac{1}{8}}=\boxed{2}

The equation is:

a_n=a_o(r)^{n-1}\\\\Given:a_o=\dfrac{1}{16},\  r=2\\\\\\Equation:\\a_n =\dfrac{1}{16}(2)^{n-1}\\\\\\\\9th\ term:\\a_9=\dfrac{1}{16}(2)^{9-1}\\\\\\a_9=\dfrac{1}{16}(2)^{8}\\\\\\.\quad =\large\boxed{16}

3 0
3 years ago
A code consists of two digit numbers chosen from 00-99 (i.E 00, 01, 02…..99) followed by two different letters of the alphabet.
Ede4ka [16]

Answer: 1/67600

Step-by-step explanation:

probability that the code is 43MZ:

Probability = (Total Required outcome / total possible outcomes)

Possible outcomes (digit) = (00,.............. ..., 99)

2.) possible outcomes (alphabet) = (A, B,............... .., Z)

P(43MZ) = P(43) × P(M) × P(Z)

P(43) = 1/100

P(M) = 1/26

P(Z) = 1/26

THEREFORE ;

P(43MZ) = (1/100) × (1/26) × (1/26) = 1/67600

4 0
3 years ago
What is the value of the expression?
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Vsevolod [243]
There are 25 species of trees, each with a known abundances. The question is how many possible ways to randomly select one tree there are.
We should calculate the number of combinations. Combinations, because we select item/s from a collection. In this case, when we select only one item, the combination is also a permutation. From set of n objects we select r. In our case: n=25, r=1. 
The equation is: n!/r!(n-r)!= 25!/1!*24!=25*24!/24!=25
There are 25 different outcomes (events).
3 0
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