All categories

2 years ago

The sum of three consecutive even integers is 642. What are the integers? (Show your work too please)

Mathematics

2 answers:

Oliga [24]2 years ago

3 0

Answer:

212,214,216

Step-by-step explanation:

n+n+2+n+4=642

add the n's and 2 and 4

3n+6=642

subtract 6 from both sides

636 divided by 3

you get 212 then add 2 twice.

Dennis_Churaev [7]2 years ago

3 0

Answer:

212, 214, 216

Step-by-step explanation:

Basically you can divide 642 by 3 to find the average number of the 3. get You get 214, so that means 214 + 214 + 214 = 642

We need consecutive EVEN integers though, so you can take the one even BEFORE and then one even AFTER 214

This means 212 and 216 are used as they are 2 before and 2 after, so when added they still total 642.

You might be interested in

Find the shortest distance, d, from the point (5, 0, −6) to the plane x + y + z = 6.

DENIUS [597]

Answer:

$\frac{7}{\sqrt{3}}$

Step-by-step explanation:

The shortest distance d, of a point (a, b, c) from a plane mx + ny + tz = r is given by:

$d = |\frac{(ma + nb + tc - r)}{\sqrt{m^2 + n^2 + t^2}} |$ --------------------(i)

From the question,

the point is (5, 0, -6)

the plane is x + y + z = 6

Therefore,

a = 5

b = 0

c = -6

m = 1

n = 1

t = 1

r = 6

Substitute these values into equation (i) as follows;

$d = |\frac{((1*5) + (1*0) + (1 * (-6)) - 6)}{\sqrt{1^2 + 1^2 + 1^2}} |$

$d = |\frac{((5) + (0) + (-6) - 6)}{\sqrt{1 + 1 + 1}} |$

$d = |\frac{(-7)}{\sqrt{3}} |$

$d = \frac{7}{\sqrt{3}}$

Therefore, the shortest distance from the point to the plane is $d = \frac{7}{\sqrt{3}}$

5 0

3 years ago

For fun question

ZanzabumX [31]

Consider the function $f(x)=x^{1/3}$ , which has derivative $f'(x)=\dfrac13x^{-2/3}$ .

The linear approximation of $f(x)$ for some value $x$ within a neighborhood of $x=c$ is given by

$f(x)\approx f'(c)(x-c)+f(c)$

Let $c=64$ . Then $(63.97)^{1/3}$ can be estimated to be

$f(63.97)\approxf'(64)(63.97-64)+f(64)$
$\sqrt[3]{63.97}\approx4-\dfrac{0.03}{48}=3.999375$

Since $f'(x)>0$ for $x>0$ , it follows that $f(x)$ must be strictly increasing over that part of its domain, which means the linear approximation lies strictly above the function $f(x)$ . This means the estimated value is an overestimation.

Indeed, the actual value is closer to the number 3.999374902...

4 0

3 years ago

Find the equation of the line through (2,4) and (3,-1)

Natasha2012 [34]

y=23x+143 hope this helps

3 0

2 years ago

Read 2 more answers

You usually buy a 16.5-ounce bottle of shampoo. There is a new bottle that says it gives you 30% more free.

Katarina [22]

Answer:

$\frac{x-16.5}{16.5}=0.30$