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}](https://tex.z-dn.net/?f=%20%5Cfrac%7B99%7D%7B2%7D%20%282x%2B98%29%3Dp%5E3%20%5C%5C%20%20%5C%5C%2099x%2B4%2C851%3Dp%5E3%5C%5C%20%5C%5C%20%5CRightarrow%20x%3D%5Cfrac%7Bp%5E3-4%2C851%7D%7B99%7D)
By substitution, we have that
![p=33](https://tex.z-dn.net/?f=p%3D33)
and
![x=314](https://tex.z-dn.net/?f=x%3D314)
.
Therefore, <span>the least possible value of the smallest of 99 consecutive positive integers whose sum is a perfect cube is 314.</span>
Answer:
(0,4) and (-2,0)
Step-by-step explanation:
y=3x²+4x+4
y = -2x +4
3x²+4x+4 = - 2x +4
3x²+6x=0
3x(x+2)=0
x=0, x= -2
x=0, y=-2x+4= -2*0 + 4 =4, (0,4)
x= - 2, y = 2x + 4= 2*(-2) +4=0, (-2,0)
Hello from MrBillDoesMath!
Answer:
f(2-k) = -2 + 5k
Discussion:
If f(x) = 8 - 5x
, then
f(2-k) = 8 - 5(2-k) =>
f(2-k) = 8 - 10 + 5k =>
f(2-k) = -2 + 5k
Regards,
MrB
Step-by-step explanation:
= -2(x - 5) + 4(9 + x)
= -2x + 10 + 36 + 4x
= (-2 + 4)x + 10 + 36
= 2x + 46
Answer:
1/2
Step-by-step explanation:
Since the Captain shoots first, the probability of a hit on the pirate ship is 1/2. In the event of a hit, the pirate will always miss (p(miss|hit)=1), so ...
... p(hit, miss) = 1/2