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laila [671]
2 years ago
10

What is the largest of 3 consecutive integers such that the sum of the first and third is equal to three times the second.

Mathematics
1 answer:
Norma-Jean [14]2 years ago
4 0

Answer:

1

Step-by-step explanation:

What is the largest of 3 consecutive integers such that the sum of the first and third is equal to three times the second?

3 consecutive angles

= x, x + 1, x + 2

We are told in the question that:

the sum of the first and third is equal to three times the second

a + c = 3b

x + x + 2 = 3(x + 1)

2x + 2 = 3x + 3

3x - 2x = 2 - 3

x = -1

The largest of the three numbers is the third number

= x + 2

x = -1

x + 2 = -1 + 2

The third and largest number is 1

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-Dominant- [34]

Answer:

Q-12 The vertical length of the top part of elevator to ground is 0.8484 meters .

Q -14 The glide runway path is 24,752.47 feet .

Step-by-step explanation:

Q - 12

Given as :

The diagonal length of the elevator = e = 1.2 meters

The vertical length of the top part of elevator to ground = x meters

The angle made by elevator with ground = Ф = 45°

<u>Now, According to figure</u>

Sin angle = \dfrac{\textrm perpendicular}{\textrm hypotenuse}

Or, Sin Ф = \dfrac{\textrm x}{\textrm e}

Or, Sin 45° =  \dfrac{\textrm x meters}{\textrm 1.2 meters}

Or, 0.707 × 1.2 meters = x

∴ x =  0.8484 meters

So, The vertical length of the top part of elevator to ground = x = 0.8484 meters

Hence,The vertical length of the top part of elevator to ground is 0.8484 meters .  Answer

Q-14

Given as:

The altitude of decent of plane = H = 10,000 feet

The angle of descend =  Ф = 22°

Let the glide runway path = y feet

<u>Now, According to question</u>

Tan angle = \dfrac{\textrm perpendicular}{\textrm base}

Or, Tan Ф = \dfrac{\textrm H}{\textrm y}

Or, Tan 22° =  \dfrac{\textrm  10,000 feet}{\textrm y feet}

Or, 0.4040 =  \dfrac{\textrm  10,000 feet}{\textrm y feet}

Or, y =  \dfrac{\textrm  10,000 feet}{\textrm 0.4040}

∴   y = 24,752.47

So,The glide runway path = y = 24,752.47 feet

Hence, The glide runway path is 24,752.47 feet . Answer

6 0
3 years ago
There is a cookie jar in Julio's kitchen filled with 7 cookies. His mother bakes some more cookies. Now there are 14 cookies. Ho
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4 0
2 years ago
In △PQR, find the measure of ∡P. <br><br> (A)30.4°<br> (B)59.6°<br> (C)35.9°<br> (D)54.1°
Kobotan [32]

ANSWER

(D)54.1°

EXPLANATION

The measure of angle P can be calculated using the cosine ratio.

We know the adjacent side to angle P to be 33.8 and the hypotenuse of the right triangle is 57.6 units.

\cos(P)  =  \frac{adjacent}{hypotenuse}

\cos(P) =  \frac{33.8}{57.6}

Take cosine inverse,

P=  \cos ^{ - 1} (\frac{33.8}{57.6} )

P=54.07 \degree

To the nearest tenth, the measure of <P is 54.1°

7 0
3 years ago
Read 2 more answers
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