Mathematics — popular questionsPage 10

Solve $y'' + e^y = 0$

Rewrite the exponential expression as a radical expression: $-3x^{2/3}$

-3x^{2/3}

Write $(5x)^3$ as a radical expression

think of it like $\sqrt{(x)}=x^{\frac{1}{2}}$

Write $(2x^3)^{3/4}$ as a radical expression

4) $S_{4000}=\frac{4000(4000)}{2}=8\,002\,000$

3) a) $\frac{1}{3}$, $\frac{11}{3}$, $\frac{21}{3}$, $\frac{31}{3}$, ... next two $\frac{41}{3}$, $\frac{51}{3}$

4) $S_{4000}=\frac{4000(4000)}{2}

3) a) $\frac13,\frac11{3},\frac{21}{3},\frac{31}{3},\ldots$ next two $\frac{41}{3},\frac{51}{3}$

6. A sequence is defined so that $t_n = a/(n-1)d$. If $a=3, d=5$, find $t_n$ and $t_4+ t_5+ t_6+ t_7$ is $31$ and $t_4+t_5+t_6+t_7+t_8=16$. Find the value of $t_4$ (if possible).

5. The sum of the first 20 natural numbers is $190$, what is the average number in this sequence? How would the answer change if the sum of the entire consecutive integers was $990$?

4. The sum of the first $n$ natural numbers is given by the formula $\frac{n(n+1)}{2}$. Find the sum of the natural numbers between $60$ and $400$ inclusive in multiples of $5$.

3. Write the given several sequences below. Say what the next two terms would be in the sequence.

2. Suppose $13$ and counting by $8$ is possible that the numbers $85$ is in this sequence?

Prove a circle contains at least seven points in a regular hexagon point-placement problem

Solve an inequality involving powers of one quarter

How to find the interval of convergence of a power series quickly

Derive the binomial series for square root from the generalized binomial theorem

Find parameter values that make a trig inequality hold on a given interval