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boyakko [2]
4 years ago
13

Find the derivative of the algebraic function

Mathematics
1 answer:
Rama09 [41]4 years ago
7 0
f(x)=x\left(3-\dfrac{4}{x+7}\right)=3x-\dfrac{4x}{x+7}=\dfrac{3x(x+7)}{x+7}-\dfrac{4x}{x+7}=\\=\dfrac{3x^2+21x-4x}{x+7}=
\dfrac{3x^2+17x}{x+7}\\
f'(x)=\dfrac{(6x+17)(x+7)-(3x^2+17x)}{(x+7)^2}\\
f'(x)=\dfrac{6x^2+17x+42x+119-3x^2-17x}{(x+7)^2}\\
f'(x)=\dfrac{119+42x+3x^2}{(x+7)^2}\Rightarrow \text{A}
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Last Tuesday was silly hat day at Toby's school. 74 students wore a silly hat and 666 students did not. What percentage of the s
valina [46]

Answer:

10%

Step-by-step explanation:

The total population of students will be equal to the sum of both those who wore the silly hat and those who didn't hence

Total students= 74+666=740

Number of students who wore silly hat is given as 74 hence when expressed as a percentage of the total students' population we get that

percentage of the students wore a silly hat=\frac {74\times 100}{740}=10\%

Therefore, 10% of students wore a silly hat last Tuesday

4 0
3 years ago
Ali was paid $75 for mowing a neighbor's yard. This is a fourth of the money he earned all summer. Write and solve an equation t
likoan [24]

Answer:

He earned $300 all summer

Step-by-step explanation:

We are asked to write an equation and also determine the amount Ali earned all summer if he collected $75 mowing fee from a neighbor and this constitutes 1/4 of the few he had collected all summer.

Now, let the total amount of money he had all summer be $y

He collected a fourth equivalent to $75, this means 1/4 * y = 75 or y/4 = $75

Now we calculate y as y = $75 * 4 = $300

7 0
3 years ago
Please show your work; only #8!
lorasvet [3.4K]

Answer:

x = 0.16

Step-by-step explanation:

Step 3:

Solve the equation for  x  by finding  a ,  b , and  c  of the quadratic then applying the quadratic formula.

x = - \frac{11 - \sqrt{185} }{16}

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x = 0.16259190... which is about,

x = 0.16

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3 years ago
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MaRussiya [10]

Answer:

20x^50

Step-by-step explanation:

4 0
3 years ago
What is ∑n=16[4(−5)n−1] equal to?
-Dominant- [34]

Answer:

This  will be the sum of a geometric series where the first term is 4

The common ratio  is -5

And we will have 6 terms.....so....the sum is

first term   [ 1  -  common ratio^number of terms ] / [ 1 - common ratio ]  =

4  [1 - (-5)^6]  /  [ 1  - -5 ]  =

4 [ 1 - 15625 ] / 6  =

(2/3) ( -15624 )  =

-10416

Step-by-step explanation:

4 0
2 years ago
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