All categories

4 years ago

Find all sets of three consecutive even integers whose sum is greater than 102 and less than 116

1 answer:

5 0

So three consecutive integers 2k,2(k+1),2(k+2)
there sum will be
2k+2(k+1)+2(k+2)
2k+2k+2+2k+4
6k+6
so setting the inequality
102<6k+6<116
subtracting 6 from all sides
96<6k<110
16<k<18.3333
since k is an integer
the only integers between 16 and 18.3
are 17 and 18
so
when k=17
2(17),2(17+1),2(17+2)
34,36,38
when k=18
2(18),2(18+1),2(18+2)
36,38,40
so to check are soultion we substitute
34+36+38=108 which is between 102 and 116
36+38+40=114 which is between 102 and 116
so our soultion is correct
the final answer will be
{{36,38,40},{38,40,42}}

You might be interested in

Help with me with this please!!!!<br><br> Find the unknown side length, x

FromTheMoon [43]

Answer: b) sq. root of 65

use pythagorean theorem to solve
a2+b2=c2
3^2+b^2=5^2
9+b^2=25
b^2=16
b=4
apply to other triangle for second leg
7^2+4^2=c^2
49+16=c^2
65=c^2
sq root of 65= c

4 0

4 years ago

The mayor of renee's town chose 160 students from her school to attend a city debate. This amount is no more than 1/4 of the stu

azamat

The answer is d.
First you have to divide 160/ 1/4. So you would do 160/1 divided by 1/4. Because of keep, change and flip. (k.c.f) you would keep 160/1, change the division sign, then flip 1/4 to 4/1. Then you multiply 160/1*4/1. Then you would get 640. Hope this helped.

7 0

3 years ago

Which term best describes the set of all points in a plane for which the sum

alina1380 [7]

The answer is gonna be Parabola for sure

5 0

3 years ago

The smallest 4 digit number which is divisible by 3?

Usimov [2.4K]

The answer to the question is 1002

4 0

3 years ago

Determine whether each of the following functions is a solution of laplace's equation uxx uyy = 0.

ratelena [41]

Both functions are the solution to the given Laplace solution.

Given Laplace's equation: $u_{x x}+u_{y y}=0$

We must determine whether a given function is the solution to a given Laplace equation.
If a function is a solution to a given Laplace's equation, it satisfies the solution.

(1) $u=e^{-x} \cos y-e^{-y} \cos x$

Differentiate with respect to x as follows:

$u_x=-e^{-x} \cos y+e^{-y} \sin x\\u_{x x}=e^{-x} \cos y+e^{-y} \cos x$

Differentiate with respect to y as follows:

$u_{x x}=e^{-x} \cos y+e^{-y} \cos x\\u_{y y}=-e^{-x} \cos y-e^{-y} \cos x$

Supplement the values in the given Laplace equation.

$e^{-x} \cos y+e^{-y} \cos x-e^{-x} \cos y-e^{-y} \cos x=0$

The given function in this case is the solution to the given Laplace equation.

(2) $u=\sin x \cosh y+\cos x \sinh y$

Differentiate with respect to x as follows:

$u_x=\cos x \cosh y-\sin x \sinh y\\u_{x x}=-\sin x \cosh y-\cos x \sinh y$

Differentiate with respect to y as follows:

$u_y=\sin x \sinh y+\cos x \cosh y\\u_{y y}=\sin x \cosh y+\cos x \sinh y$

Substitute the values to obtain:

$-\sin x \cosh y-\cos x \sinh y+\sin x \cosh y+\cos x \sinh y=0$
The given function in this case is the solution to the given Laplace equation.

Therefore, both functions are the solution to the given Laplace solution.

Know more about Laplace's equation here:

brainly.com/question/14040033

#SPJ4

The correct question is given below:
Determine whether each of the following functions is a solution of Laplace's equation uxx + uyy = 0. (Select all that apply.) u = e^(−x) cos(y) − e^(−y) cos(x) u = sin(x) cosh(y) + cos(x) sinh(y)

6 0

2 years ago