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EleoNora [17]
2 years ago
12

A is true but f(x) is wrong need help

Mathematics
1 answer:
MrRissso [65]2 years ago
3 0

Answer:

f(x)=-18x^2

Step-by-step explanation:

Given:

1+Integral(f(t)/t^6, t=a..x)=6x^-3

Let's get rid of integral by differentiating both sides.

Using fundamental of calculus and power rule(integration):

0+f(x)/x^6=-18x^-4

Additive Identity property applied:

f(x)/x^6=-18x^-4

Multiply both sides by x^6:

f(x)=-18x^-4×x^6

Power rule (exponents) applied"

f(x)=-18x^2

Check:

1+Integral(-18t^2/t^6, t=a..x)=6x^-3

1+Integral(-18t^-4, t=a..x)=6x^-3

1+(-18t^-3/-3, t=a..x)=6x^-3

1+(6t^-3, t=a..x)=6x^-3

That looks great since those powers are the same on both side after integration.

Plug in limits:

1+(6x^-3-6a^-3)=6x^-3

We need 1-6a^-3=0 so that the equation holds true for all x.

Subtract 1 on both sides:

-6a^-3=-1

Divide both sides by-6:

a^-3=1/6

Raise both sides to -1/3 power:

a=(1/6)^(-1/3)

Negative exponent just refers to reciprocal of our base:

a=6^(1/3)

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wlad13 [49]

Answer    

Find out the what fraction of the sandcastle did they build together .

To prove

Let us assume that the fraction of the sandcastle  they build together be x .

As given

Beatrice\ built\ about\ \frac{1}{3}\ of\ a\ sandcastle.

Linda\ built\ \frac{4}{7}\ of\ the\ same\ castle.

Than the equation becomes

x = \frac{1}{3} +\frac{4}{7}

L.C .M of (3,7) = 21

solving

x = \frac{7 + 3\times4}{21}

x = \frac{19}{21}

Therefore the fraction of the sandcastle did they build together be

x = \frac{19}{21}

Hence proved



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3 years ago
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Xelga [282]
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2 years ago
How many feet are in 84 yards. (im really bad at converting) :(
Gre4nikov [31]
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There are 252 feet in 84 yards.
7 0
3 years ago
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In Covina, California, the population is 47,000. The population increases 18% every year. Determine how long it will take to rea
Alexxandr [17]

Answer: 8.5 years

Step-by-step explanation:

Hi, to answer this question we have to apply an exponential growth function:

A = P (1 + r) t  

Where:

p = original population

r = growing rate (decimal form)  =18/100 = 0.18

t= years

A = population after t years

Replacing with the values given:

192,000 = 47,000 (1+ 0.18)^t

Solving for t:

192,000/47,000 = 1.18^t

4.08 =1.18^t

ln 4.08 = ln 1.18^t

ln 4.08 =t (ln 1.18)

ln 4.08 / ln 1.18  =t

8.5 years = t

Feel free to ask for more if needed or if you did not understand something.

8 0
3 years ago
NEED HELP PLEASE!!!!
Masja [62]

Answer:

Yes

Step-by-step explanation:

\sqrt{\frac{2x}{9} }={\frac{\sqrt{2x} }\sqrt{} {9} }  =\frac{\sqrt{2x} }{3}=\frac{1}{3}\sqrt{2x}

3 0
2 years ago
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