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2 years ago

(2x³)⁴= ? What is the right answer, with full explanation please:

2 answers:

7 0

So you multiply the 4th power

2 times 4 is 8
4 times 3 is 12
Then you plug it In 8x^12

So your answer is D

Hope this helps *smiles*

Lostsunrise [7]2 years ago

6 0

Answer:

B. $= 16 {x}^{12}$

Step-by-step explanation:

$(2 {x}^{3} {)}^{4}$

➡️ ${2}^{4} \times ( {x}^{3} {)}^{4}$

➡️ $2 \times 2 \times 2 \times 2$ $= 16$

➡️ $16 \times ( {x}^{3} {)}^{4}$

➡️ $( {x}^{3} {)}^{4}$

➡️ ${x}^{3 \times 4} = {x}^{12}$

➡️ B. $= 16 {x}^{12}$ ✅

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Suppose that $p$ and $q$ are positive numbers for which \[\log_9 p = \log_{12} q = \log_{16} (p + q).\] what is the value of $q/

SVEN [57.7K]

Given $p,q>0$ and $\log_9p=\log_{12}q=\log_{16}(p+q)=x$ (say).

Then,

$p=9^x\\ q=12^x\\ p+q=16^x$

From the above 3 equations,

$\frac{q}{p} =(\frac{12}{9} )^x\\ \frac{q}{p} =(\frac{4}{3} )^x\\ \frac{p+q}{p} =(\frac{16}{9} )^x\\ \frac{p+q}{p} =(\frac{4}{3} )^{2x}\\$

From the equations, we get

$\frac{p+q}{p}=(\frac{q}{p})^2\\ 1+\frac{q}{p}=(\frac{q}{p})^2\\ (\frac{q}{p})^2-\frac{q}{p}-1=0\\ \frac{q}{p}=\frac{1 \pm \sqrt{5}}{2}$

Since $p,q>0$ , the negative value is rejected.

$\frac{q}{p}=\frac{1 + \sqrt{5}}{2}$

3 0

3 years ago

First find f′ and then find f. f′′(x)=3x^3+6x^2−x+2, f′(1)=9, f(1)=−7. f′(x)= f(x)=

Vadim26 [7]

I haven't learned antiderivitives yet but I can try to logic it

First find f′ and then find f. f′′(x)=3x^3+6x^2−x+2, f′(1)=9, f(1)=−7.

we reverse chain rule

3x^3, we know that it was a 4th degree thing, and the coefient is 3, so
4*what=3?, answer is 3/4
3/4x^4

6x^2
we know it was x^3, and the coefient is now 6 so
3*what=6? what=2
2x^3

-1x, the power was 2 and coefient is now -1, so
2 times what=-1?, -1/2
-1/2x^2

2, that is from 2x

so

3/4x^4+2x^3-1/2x^2+2x=f'(x)
test x=1
(3/4)(1)+2(1)-(1/2)(1)+2(1)=
3/4+2-2/4+2=
4 and 1/4 we need to get it to 9
4 and 1/4 +what=9
answer is 4 and 3/4
so we add that to the end since it will become 0 from derivitive


f'(x)=3/4x^4+2x^3-1/2x^2+2x+4 and 3/4

now reverse drivitive again

3/4x^4
exponent is 5 and coefient is 3/4
5 times what=3/4? answer is 3/20
3/20x^5

2x^3
exponent should be 4 and coefient is 2
4 times what=2? answer is 1/2
1/2x^4

-1/2x^2
exponent should be 3 and coefient is -1/2
3 times what=-1/2? answer is -1/6
-1/6x^3

2x
exponent should be 2 and coefient is 2
2 times what=2? answer is 1
1x^2

4 and 3/4 turns to (4 and 3/4)x


f(x)=3/20x^5+1/2x^4-1/6x^3+x^2+(4 and 3/4)x
try evaluating it for x=1
f(1)=(3/20)+(10/20)-(10/50)+1+(19/4)
f(1)=6 and 7/30
what do we add to get -7
-13 and 7/30

f(x)=3/20x^5+1/2x^4-1/6x^3+x^2+(4 and 3/4)x-13 and 7/30



ANSWER
f'(x)=3/4x^4+2x^3-1/2x^2+2x+19/4
f(x)=3/20x^5+1/2x^4-1/6x^3+x^2+19/4x-187/30

4 0

2 years ago

I have another one :( what is 3x - 8- 4

iVinArrow [24]

Answer:

3x-12 is the simplififed answer

Step-by-step explanation:

the equation is almost already simplified. when you combine -8 and -4, which are like terms, you get 3x-12. because there are no more lie temrs in the equation, it can not be simplififed any further.

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2 years ago

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Find the greatest common factor of the following monomials pq^2 and pq^5

diamong [38]

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2 years ago