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fenix001 [56]
4 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]4 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>
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Explain how to subtract 247 from 538?
alexandr402 [8]
1. 538 - 247 = ?

2. 8 - 7 = 1

3. You can't subtract 3 and 4, so you have to take  number from 5 (turning it into a 4) and then you add a 1 right next to 3 (which makes it 13;13 - 4 = 9

4. 4 - 2 = 2

538 - 247 = 291

So the answer is 291.
7 0
4 years ago
Find the difference of 1-3/8
Vilka [71]
1-3=-2 so -2/8 is -1/4 so negative one fourth
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3 years ago
Explain the steps necessary to convert a quadratic function in standard form to vertex form
SIZIF [17.4K]

Answer:

See below.

Step-by-step explanation:

Here's an example to illustrate the method:

f(x) = 3x^2 - 6x + 10

First divide the first 2 terms by the coefficient of x^2 , which is 3:

= 3(x^2 - 2x) + 10

Now  divide the -2 ( in -2x) by 2 and write the x^2 - 2x in the form

(x - b/2)^2 - b/2)^2  (where b = 2) , which will be equal to x^2 - 2x in a different form.

= 3[ (x - 1)^2 - 1^2 ] + 10 (Note: we have to subtract the 1^2 because (x - 1)^2 = x^2 - 2x  + 1^2  and we have to make it equal to x^2 - 2x)

= 3 [(x - 1)^2 -1 ] + 10

= 3(x - 1)^2 - 3 + 10

= <u>3(x - 1)^2 + 7 </u><------- Vertex form.

In general form the vertex form of:

ax^2 + bx + c  = a [(x - b/2a)^2 - (b/2a)^2] + c .

This is not easy to commit to memory so I suggest the best way to do these conversions is to remember the general method.

3 0
3 years ago
Read 2 more answers
A principal of ​$5000 is invested in an account paying an annual rate of 7​%. Find the amount in the account after 5 years if th
Alekssandra [29.7K]

Answer:

$7,012.76

Step-by-step explanation:

First, convert R as a percent to r as a decimal

r = R/100

r = 7/100

r = 0.07 rate per year,

Then solve the equation for A

A = P(1 + r/n)nt

A = 5,000.00(1 + 0.07/1)(1)(5)

A = 5,000.00(1 + 0.07)(5)

A = $7,012.76

Summary:

The total amount accrued, principal plus interest, with compound interest on a principal of $5,000.00 at a rate of 7% per year compounded 1 times per year over 5 years is $7,012.76.

8 0
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Ainat [17]

Answer:

600 units of for snack-size, 1800 units for family-size

Step-by-step explanation:

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