3 years ago

3x^2(x^3-1)+2x^3(2x^2+2) Whats the simplified answer?

Mathematics

1 answer:

ahrayia [7]3 years ago

4 0

Answer:

$\large\boxed{7x^5+4x^3-3x^2}$

Step-by-step explanation:

$3x^2(x^3-1)+2x^3(2x^2+2)\qquad\text{use the distributive property:}\ a(b+c)=ab+ac\\\\=(3x^2)(x^3)+(3x^2)(-1)+(2x^3)(2x^2)+(2x^3)(2)\qquad\text{use}\ a^na^m=a^{n+m}\\\\=3x^{2+3}-3x^2+4x^{3+2}+4x^3\\\\=3x^5-3x^2+4x^5+4x^3\qquad\text{combine like terms}\\\\=(3x^5+4x^5)-3x^2+4x^3\\\\=7x^5+4x^3-3x^2$

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Caroline puts $400 into a savings account that earns 6% annually. Write a function that represents this situation, where t is th

DaniilM [7]

Answer: 19 years

Step-by-step explanation:

Given

Amount invested $\$400$

Rate of interest $R=6\%$

after 1-year amount becomes

$A=400\left (1+6\%\right)\\A=400\left (1+0.06\right)\\A=400\times 1.06\\A=\$424$

After n years it is

$A=400\left (1.06\right)^n$

Sum accumulated is $\$1200$

$\Rightarrow 1200=400\left(1.06\right)^n\\\Rightarrow 3=\left(1.06\right)^n\\\text{Taking log both sides}\\\Rightarrow n=\dfrac{\ln 3}{\ln 1.06}\\\\\Rightarrow n=18.85\approx 19\ \text{years}$