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3 years ago

If sum of 3 consecutive integers is 51, what is the largest integer

Mathematics

2 answers:

Ilia_Sergeevich [38]3 years ago

5 0

Answer:

Step-by-step explanation:

16+17+18 = 51

(by doing 51/3 you get 17, the middle one).

ki77a [65]3 years ago

3 0

Answer:

Largest number = 18

Step-by-step explanation:

Let the consecutive integers be (x-1),x,(x+1)

x - 1 + x + x + 1 = 51

3x = 51

x = 51/3

x = 17

x-1 = 17-1 = 16

x+1 = 17+1 = 18

The numbers are :16,17,18

Largest number = 18

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2 years ago

What are the factors of 345

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1,3,5,345 are factors of 345

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2 years ago

Use an algebraic equation to find the measures of the two angles described below. Begin by letting x represent the degree measur

Romashka [77]

Answer:

Step-by-step explanation:

For two angles x and y to be supplementary, the sum of the angles must be 180°

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8 0

3 years ago

R 3. The mean of 4 numbers is 8. Three of the numbers add up to 22. What is the last number?

statuscvo [17]

<h2>Solution : </h2>

let the last number be x

we know,

$\boxed{mean = \frac{sum \: \: of \: \: all \: \: observations}{number \: \: of \: \: observations} }$

So,

$\hookrightarrow \: 8 = \dfrac{22 + x}{4}$

$\hookrightarrow \: 8 \times 4 = 22 + x$

$\hookrightarrow \: 32 = 22 + x$

$\hookrightarrow \: x = 32 - 22$

$\hookrightarrow \: x = 10$

therefore, the last number is 10.

7 0

2 years ago

Help me with trigonometry

poizon [28]

Answer:

See below

Step-by-step explanation:

It has something to do with the Weierstrass substitution, where we have

$\int\, f(\sin(x), \cos(x))dx = \int\, \dfrac{2}{1+t^2}f\left(\dfrac{2t}{1+t^2}, \dfrac{1-t^2}{1+t^2} \right)dt$

First, consider the double angle formula for tangent:

$\tan(2x)= \dfrac{2\tan(x)}{1-\tan^2(x)}$

Therefore,

$\tan\left(2 \cdot\dfrac{x}{2}\right)= \dfrac{2\tan(x/2)}{1-\tan^2(x/2)} = \tan(x)=\dfrac{2t}{1-t^2}$

Once the double angle identity for sine is

$\sin(2x)= \dfrac{2\tan(x)}{1+\tan^2(x)}$

we know $\sin(x)=\dfrac{2t}{1+t^2}$ , but sure, we can derive this formula considering the double angle identity

$\sin(x)= 2\sin\left(\dfrac{x}{2}\right)\cos\left(\dfrac{x}{2}\right)$

Recall

$\sin \arctan t = \dfrac{t}{\sqrt{1 + t^2}} \text{ and } \cos \arctan t = \dfrac{1}{\sqrt{1 + t^2}}$

Thus,

$\sin(x)= 2 \left(\dfrac{t}{\sqrt{1 + t^2}}\right) \left(\dfrac{1}{\sqrt{1 + t^2}}\right) = \dfrac{2t}{1 + t^2}$

Similarly for cosine, consider the double angle identity

Thus,

$\cos(x)= \left(\dfrac{1}{\sqrt{1 + t^2}}\right)^2- \left(\dfrac{t}{\sqrt{1 + t^2}}\right)^2 = \dfrac{1}{t^2+1}-\dfrac{t^2}{t^2+1} =\dfrac{1-t^2}{1+t^2}$

Hence, we showed $\sin(x) \text { and } \cos(x)$

======================================================

$5\cos(x) =12\sin(x) +3, x \in [0, 2\pi ]$

Solving

$5\,\overbrace{\frac{1-t^2}{1+t^2}}^{\cos(x)} = 12\,\overbrace{\frac{2t}{1+t^2}}^{\sin(x)}+3$

$\implies \dfrac{5-5t^2}{1+t^2}= \dfrac{24t}{1+t^2}+3 \implies \dfrac{5-5t^2 -24t}{1+t^2}= 3$

$\implies 5-5t^2-24t=3\left(1+t^2\right) \implies -8t^2-24t+2=0$

$t = \dfrac{-(-24)\pm \sqrt{(-24)^2-4(-8)\cdot 2}}{2(-8)} = \dfrac{24\pm 8\sqrt{10}}{-16} = \dfrac{3\pm \sqrt{10}}{-2}$

$t=-\dfrac{3+\sqrt{10}}{2}\\t=\dfrac{\sqrt{10}-3}{2}$

Just note that

$\tan\left(\dfrac{x}{2}\right) = \dfrac{3\pm 8\sqrt{10}}{-2}$

and $\tan\left(\dfrac{x}{2}\right)$ is not defined for $x=k\pi , k\in\mathbb{Z}$

6 0

2 years ago