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3 years ago

Find three consecutive positive integers such that the sum of their squares is 2354. What is the largest integer?

Mathematics

1 answer:

Ilya [14]3 years ago

4 0

Answer:

The largest integer is 29.

Step-by-step explanation:

Let the consecutive positive integers are x, x+1 and x+2.

The square of sum of squares of three consecutive positive integers is 2354 such that,

$x^2+(x+1)^2+(x+2)^2=2354\\\\x^2+x^2+2x+1+x^2+4+4x=2354\\\\3x^2+6x+5=2354\\\\3x^2+6x- 2349=0$

It is a quadratic equation whose solution is given by :

x = 27 and x = -29

First positive integer = 27

Second positive integer = 27+1 = 28

Third positive integer = 27+2 = 29

Hence, the largest integer is 29.

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navik [9.2K]

50%. students (in percent) who passed the second exam also passed the first exam.

Let's imagine that there are 100 kids in the teacher's class. We know that 40 of them passed BOTH tests, and 80 passed the second test.

Because if they weren't, they wouldn't have passed the first test and consequently wouldn't have passed both, we can be sure that the group of students who passed BOTH tests is only made up of the 80 who passed the second test.

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7 0

1 year ago

Wat the answer for this I am going crazy

Lorico [155]

0.54+12.1 =12.64
2.55+145.05=147.6
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23.04+124.1+34.06=181.2
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You’re welcome

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3 years ago

HELP 100 POINTS The population of a city is modeled with the function P=250,000e^0.013t, where t is the number of years since 2

erma4kov [3.2K]

Pretty difficult problem, but that’s why I’m here.
First we need to identify what we’re looking for, which is t. So now plug 450k into equation and solve for t.
450000 = 250000e^0.013t
Now to solve this, we need to remember this rule: if you take natural log of e you can remove x from exponent. And natural log of e is 1.
Basically ln(e^x) = xln(e) = 1*x
So knowing this first we need to isolate e
450000/250000 = e^0.013t
1.8 = e^0.013t
Now take natural log of both
Ln(1.8) = ln(e^0.013t)
Ln(1.8) = 0.013t*ln(e)
Ln(1.8) = 0.013t * 1
Now solve for t
Ln(1.8)/0.013 = t
T= 45.21435 years
Now just to check our work plug that into original equation which we get:
449999.94 which is basically 500k (just with an error caused by lack of decimals)
So our final solution will be in the 45th year after about 2 and a half months it will reach 450k people.

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2 years ago

Factor completely.

Svetach [21]

Answer:

in what do u need help?

Step-by-step explanation:

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2 years ago

Postulate: If two lines intersect, then they intersect in exactly one point. true or false

ololo11 [35]

Answer:

Step-by-step explanation:

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3 years ago