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fenix001 [56]
3 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]3 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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Write a function to represent each problem situation Carmen deposits $1000into simple interest account.The rate for the account
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<h3><u>Solution:</u></h3>

Given that,

Carmen deposits $1000 into simple interest account

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To find: function the represent the balance in the account as a function of time t

Given is simple interest account

The formula for simple interest is given as:

S.I = \frac{ prt}{100}

Where, "p" is the principal and "r" is the rate of interest and "t" is the number of years

In simple interest,

total amount after "t" years = principal + simple interest

Here in this question, Carmen deposits $1000

p_0 = 1000

r = 4 \% = \frac{4}{100} = 0.04

Thus we can frame a function as:

total amount after "t" years = principal + simple interest

p(t) = p_0 + (p_0 \times r \times t )

p(t) = 1000 + (1000 \times 0.04)t\\\\p(t) = 1000 + 40t

Where, p(t) is the amount after "t" years and p_0 is the principal sum

Thus the function is obtained

7 0
3 years ago
Jane, Jasmine, and Jocelyn have record collections. Jane has 3 times as many records as Jocelyn has. Jasmine has 2 more than twi
dangina [55]
X = jane, y = jasmine, z = jocelyn

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x = 3z
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Step-by-step explanation:

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