All categories

4 years ago

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

1 answer:

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, the least possible value of the smallest of 99 consecutive positive integers whose sum is a perfect cube is 314.

You might be interested in

If a rectangle was rotated about the y-axis, like the one shown below, what would be the resulting three-dimensional shape? An i

kvasek [131]

Answer: It would be a cylinder

3 0

3 years ago

Read 2 more answers

What is this- 5(-2xy) simplfied?

sukhopar [10]

Answer:

10xy

Step-by-step explanation:

-5(-2)=10

6 0

3 years ago

Read 2 more answers

Write an equation to express the value of h+k

bonufazy [111]

When written in "vertex form":
• (h, k) is the vertex of the parabola, and x = h is the axis of symmetry.

• the h represents a horizontal shift (how far left, or right, the graph has shifted from x = 0).

• the k represents a vertical shift (how far up, or down, the graph has shifted from y = 0).

• notice that the h value is subtracted in this form, and that the k value is added.
If the equation is y = 2(x - 1)2 + 5, the value of h is 1, and k is 5.
If the equation is y = 3(x + 4)2 - 6, the value of h is -4, and k is -6.

3 0

3 years ago

How many solution does this have and how do you solve it

Vadim26 [7]

Answer:

Infinite solutions

Step-by-step explanation:

To determine the number of solutions a system has, you need its slope. If the slopes are the same, check if the equations are equivalent or not.

To find the slope, rearrange the equation to isolate "y", which makes it slope-intercept form y = mx + b.

"x" and "y" represent points on the line.

"m" represents the slope, which is how steep a line is.

"b" represents the y-intercept (where the graph hits the y-axis).

Isolate "y" in both equations:

x + 3y = 0

3y = -x Subtract 'x' from both sides

y = -x/3 Divide both sides by 3.

y = $-\frac{1}{3}x$

The slope is -1/3.

9y = -3x

y = -3x/9 Divide both sides by 9

y = $-\frac{3}{9}x$ Reduce the fraction to lowest terms

y = $-\frac{1}{3}x$

The slope is -1/3, but the two equations are the same.

Since the equations are the same, or equivalent, the two lines are always touching. The solution of a system means where two lines intersect, or meet. Therefore, there are infinite solutions.

5 0

3 years ago

The GCF of 28x^3 and 16x^2y^2

masya89 [10]

I think the greatest common factor is 4

6 0

4 years ago

Read 2 more answers