1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
dmitriy555 [2]
3 years ago
14

Find 5 consecutive whole numbers if it is known that the sum of the squares of the first 3 numbers is equal to the sum of the sq

uares of the last 2 numbers.
Mathematics
1 answer:
lora16 [44]3 years ago
3 0
Let the first number of the five we are looking for equal n.

Because the numbers are consecutive, the next four can be expressed as (n+1), (n+2), (n+3) and (n+4).

Our series of 5 numbers is therefore n,(n+1),(n+2),(n+3),(n+4).

We are told the sum of the squares of the first 3 is equal to the sum of the squares of the last 2 therefore:
n² + (n+1)² + (n+2)² = (n+3)² + (n+4)²

expand all the brackets to give
n² + n² + 2n + 1 + n² + 4n + 4 = n² + 6n + 9 + n² + 8n + 16
3n²+6n+5 = 2n²+14n+25
n²-8n-20=0

factorising this gives us
(n+2)(n-10) = 0 so the solutions are n=10 and n=-2

That means that n,(n+1),(n+2),(n+3),(n+4) could be [-2, -1, 0, 1 and 2] or [10, 11, 12, 13 and 14].

Since the question asks for whole numbers, and negative numbers are not classed as whole numbers, the numbers we want must be 10, 11, 12, 13 and 14.

You can check this on a calculator by doing 10² + 11² + 12² (=365) and 13² + 14² (=365).
You might be interested in
What’s da answer<br> Need helps
natima [27]

Answer:

I think the answer is 432 cubic inches( in^3). Answer is the first option.

6 0
3 years ago
The length of the rectangular tennis court at wimbledon is 6 feet longer than twice the width. if the court's perimeter is 240 f
KATRIN_1 [288]

Length (L): 2w + 6

width (w): w

Perimeter (P) = 2L + 2w

               240 = 2(2w + 6) + 2(w)

               240 = 4w + 12 + 2w

               240 = 6w + 12

               228 = 6w

                 38 = w

Length (L): 2w + 6   = 2(38) + 6   = 76 + 6   = 82

Answer: width = 38 ft, length = 82 ft

8 0
3 years ago
Identify all solutions for a triangle with A = 38 degrees b = 10, and a= 8. Round to the nearest tenth.
rjkz [21]

Answer:

A = 38°

B = 50.32°

C = 91.68°

a = 8

b = 10

c = 12.77

Step-by-step explanation:

The first thing is to find the angle B, like this:

sin B = b * sin A / a = 10 * sin (38 °) / 8

sin B = 0.77

B = arc sin (0.77)

B = 50.32 °

For angle C, it would be:

C = 180 - 38 - 50.32

C = 91.68 °

Side c, we calculate it like this:

c = a * sin C / sin A = 8 * sin (91.68 °) / sin (38 °)

c = 12.77

5 0
3 years ago
A cylinder and a cone both have radius of 6". The height of the cone is 12". The height of the cylinder is 6". Which has the gre
Shkiper50 [21]

Answer:

cylinder has greatest volume

Step-by-step explanation:

solution

given,

radius of cylinder(r)=6cm

height of cylinder (h)=6cm

we know,

volume of cylinder=πr^2h

=22÷7×6×6×6

=4752÷7

=678.857cm^3

radius of cone(r)=6cm

height of cone(h)=12cm

we know,

volume of cone=1÷3πr^3

= 1÷3×22÷7×6×6×6

= 4752÷21

=226.2857cm^3

as a result,cylinder has greatest volume

4 0
2 years ago
Simplify: 4x + 6(3x - 2)<br> A) 10x - 12 <br> B) 18x - 12 <br> C) 22x - 12 <br> D) 30x2 - 20x
alekssr [168]
C have goood luck bye
4 0
3 years ago
Other questions:
  • Ben earns $9 per hour and $6 for each delivery he makes. He wants to make $155 in an 8-hour workday. What is the least number of
    14·2 answers
  • How do you do a probability tree? How do you start it? How do I get all my percentages to add up to 100?
    15·2 answers
  • QUIZ
    12·1 answer
  • Please help!!!! 30 pts
    12·2 answers
  • The following table shows the number of police calls that were made last year in each of the cities in Hogden county
    8·1 answer
  • There are 50 students in the fifth grade one day 20% of them were absent how many fifth graders were in class that day
    13·1 answer
  • What is 8(y-5) = 6y-18
    10·1 answer
  • https://lists.office.com/Images/2fce1dfb-919f-4938-aab8-c47f0fc9182d/759a6d77-ea1a-4b50-a9bc-86157c96a662/T14LEZ48DGIIWGRBN9LPBU
    10·1 answer
  • The amount of paper needed to cover a Vic too in the shape of a trapezoid is 198cm squared.If the height of the bud too is 18 ca
    11·1 answer
  • Sarah is reading a new book and it has 320 pages. Yesterday she read 60 in 3 hours. If she continues to read at this rate, how l
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!