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3 years ago

Find f. f'(x)=(sqrt(x))(6+10x) f(1)=11

1 answer:

3 0

It is a matter of integrating f′:

 $f(x)=\int \sqrt{x}(6+10x)dx,
\\
\\f(x)=\int 6x^{1/2}dx+\int10x^{3/2}dx,
\\
\\f(x)=4x^{3/2}(x+1)+C.
$

Combine the constants. Then use the initial condition to find C:

$11=8+C\implies C=3$

Therefore,

$f(x)=4x^{3/2}(x+1)+3.$

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Numbers greater than -6

MakcuM [25]

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3 years ago

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The amount of calories consumed by customers at the Chinese buffet is normally distributed with mean 2885 and standard deviation

aliina [53]

Answer:

a. X~N(2,885, 651)

b. 0.086291

c. 0.00058

d. 3213.10 calories

Step-by-step explanation:

a. -A normal distribution is expressed in the form X~N(mean, standard deviation).

-Let X a random variable denoting the number of calories consumed.

-X is a is a normally distributed random variable with mean 2885 and standard deviation 651.

-This distribution is expressed as X~N(2,885, 651)

b. The probability that less than 2000 calories are consumed is calculated using the formula:

$P(X$

#substitute the given values in the formula to solve for P:

$P(X$

Hence, the probability of consuming less than 2000 calories is 0.08691

c. The proportion of customers consuming more than 5000 calories is calculated as:

$P(X>x)=P(z>\frac{\bar X-\mu}{\sigma})\\\\=P(Z>\frac{5000-2885}{651})\\\\=P(z>3.2488)\\\\=1-0.99942\\\\=0.00058$

Hence, the proportion of customers consuming over 5000 calories is 0.00058

d. The least amount of calories to get the award is calculated as:

1% is equivalent to a z value of 0.50399.

-We equate this to the formula to solve for the mean consumption:

$0.01=P(z>\frac{\bar X-\mu}{\sigma})\\\\=P(z>\frac{\bar X-2885}{651})\\\\\1\%=0.50399 \\\\\frac{\bar X-2885}{651}=0.50399 \\\\\bar X=0.50399\times 651+2885\\\\=3213.09$

Hence, the least amount of calories consumed to qualify for the award is 3213.10 calories.

8 0

4 years ago

Is 15 to 35 and 27/66 equivalent

Alex777 [14]

The two ratios are not equivalent

3 0

3 years ago

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HELP ME PLEASE! Vector's map has the scaling missing.he knows from the lake to the youth center is 8 miles. on the map, they are

Naddik [55]

Hey there!

Since 2 goes into 8, you would simplify. You would get 1 inch and 4 miles. Next, set up a ratio. The ratio is 1 inch: 4 miles. So for every inch on the map, there is 4 miles.

I hope this helps!

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4 years ago

Use the function below to find f(4). f(x)= 1/3•4^x

kenny6666 [7]

Answer:

f(4) = 85 1/3 or 85.333...

Step-by-step explanation:

To find f(4), you must substitute 4 in place of x whenever x appears:

f(x) = $\frac{1}{3}$ * $4^{x}$