answer.
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
fenix001 [56]
2 years ago
12

what is the least possible value of the smallest of 99 consecutive positive integers whose sum is a perfect cube

Mathematics
1 answer:
Dmitrij [34]2 years ago
3 0
Let the least possible value of the smallest of 99 cosecutive integers be x and let the number whose cube is the sum be p, then

\frac{99}{2} (2x+98)=p^3 \\  \\ 99x+4,851=p^3\\ \\ \Rightarrow x=\frac{p^3-4,851}{99}

By substitution, we have that p=33 and x=314.

Therefore, <span>the least possible value of the smallest of 99 consecutive positive integers whose sum is a perfect cube is 314.</span>
You might be interested in
Erik and Nita are playing a game with numbers. In the game, they each think of a random number from zero to 20. If the differenc
Mademuasel [1]
Let X is the random number Erik thinks of, and Y is the random number Nita thinks of.
Both X and Y are in the range from 0 to 20.
<span>X<=20
Y<=20
If the difference between their two numbers is less than 10, then Erik wins.
The difference between the two numbers can be written X-Y, or Y-X depending on which number (X or Y) is greater. But we do not know that. In order not to get negative value, we calculate absolute value of X-Y,  written |X-Y| which will give positive value whether X is greater than Y or not.
If |X-Y|<10 Erik wins.
</span><span>If the difference between their two numbers is greater than 10, then Nita wins. 
</span><span>If |X-Y|>10 Nita Wins

</span>
6 0
2 years ago
Kiley and her parents traveled to visit her grandmother. They drove 24.3 miles from their house to the airport in hour. At the a
Tju [1.3M]
The answer is  just 24.3 miles.

The questions asked "How long was the ride from Kiley's house to the airport?"

The first sentence of the problem reads "They drove 24.3 miles from their house to the airport in an hour". The rest of the information isn't necessary to find this answer.
6 0
2 years ago
A church steeple is 30 feet tall with square cross sections. The square at the base has side 3 feet, the square at the top has s
JulijaS [17]

Answer:

Volume= 540 ft^3

Step-by-step explanation:

Since volume= length times Width times height, you do 3 times 6 times 30= 540 ft^cubed.

3 0
2 years ago
Russel wants to buy 3 identical gift cards. He wants to make sure his total cost is no more than $2 above or below $60. Which of
OverLord2011 [107]
Answer is B. took the test!
4 0
2 years ago
Which equation can be used to represent "three minus the difference of a number and one equals one-half of the difference of thr
Rina8888 [55]

Answer:

3 - (n - 1) = 1/2(3n - 4)

Step-by-step explanation:

We want to write three minus the difference of a number and one equals one-half of the difference of three times the same number and four as an equation.

Let the number be n.

The first part is: three minus the difference of a number and one:

3 - (n - 1)

The second part is: one-half of the difference of three times the same number and four:

1/2(3n - 4)

Now, let us equate the first and second parts:

3 - (n - 1) = 1/2(3n - 4)

PS: I really do not understand the options

9 0
2 years ago
Read 2 more answers
Other questions:
  • According to chebyshev's theorem, at least what percent of the observations lie within plus and minus 1.75 standard deviations o
    5·1 answer
  • Raymond works for an architecture firm. His company has a contract to design a building on a rectangular plot of land that has a
    9·2 answers
  • What is a correct first step in solving the inequality –4(3 – 5x)≥ –6x + 9? I need help ASAP!!!!!!! please help me
    13·2 answers
  • Evaluate the double integral. 9y2 da, d is the triangular region with vertices (0, 1), (1, 2), (4, 1) d
    6·1 answer
  • According to the Rational Root Theorem, the following are potential roots of f(x) = 6x4 + 5x3 – 33x2 – 12x + 20. -5/2,-2, 1, 10/
    15·2 answers
  • What is a34 of the sequence 9,6,3,
    13·2 answers
  • Below is the five-number summary for 136 hikers who recently completed the John Muir Trail (JMT). The variable is the amount of
    8·1 answer
  • A manufacturer of cordless electric shavers sampled 13 from a​ day's production and found the mean time of continuous usage with
    10·1 answer
  • Bacteria begins to grow on the water's surface in a non-operational swimming pool on September 20. The bacteria grows and covers
    7·2 answers
  • The heights of 82 roller coasters have a mean of 285.2 feet and a population standard deviation of 59.3 feet. Find the standardi
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!