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anyanavicka [17]
2 years ago
7

Help. I need help with these questions ( see image). Please show workings.

Mathematics
1 answer:
Andrew [12]2 years ago
3 0

9514 1404 393

Answer:

  4)  6x

  5)  2x +3

Step-by-step explanation:

We can work both these problems at once by finding an applicable rule.

  \text{For $f(x)=ax^n$}\\\\\lim\limits_{h\to 0}\dfrac{f(x+h)-f(x)}{h}=\lim\limits_{h\to 0}\dfrac{a(x+h)^n-ax^n}{h}\\\\=\lim\limits_{h\to 0}\dfrac{ax^n+anx^{n-1}h+O(h^2)-ax^n}{h}=\boxed{anx^{n-1}}

where O(h²) is the series of terms involving h² and higher powers. When divided by h, each term has h as a multiplier, so the series sums to zero when h approaches zero. Of course, if n < 2, there are no O(h²) terms in the expansion, so that can be ignored.

This can be referred to as the <em>power rule</em>.

Note that for the quadratic f(x) = ax^2 +bx +c, the limit of the sum is the sum of the limits, so this applies to the terms individually:

  lim[h→0](f(x+h)-f(x))/h = 2ax +b

__

4. The gradient of 3x^2 is 3(2)x^(2-1) = 6x.

5. The gradient of x^2 +3x +1 is 2x +3.

__

If you need to "show work" for these problems individually, use the appropriate values for 'a' and 'n' in the above derivation of the power rule.

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(1/4)/(3/8)=(2/3)
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An animal shelter has 24 puppies. If the puppies are 32% of the total dog and cat population, how many dogs and cats are in the
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2 years ago
A car rental charge is $100 plus $5.00 per mile traveled. Create an equation for the situation above.
Elis [28]
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3 years ago
Two sections of a class took the same quiz. Section A had 15 students who had a mean score of 80, and Section B had 20 students
Nezavi [6.7K]

Answer: A. 85.7

Step-by-step explanation:

Given : Two sections of a class took the same quiz.

Section A had 15 students who had a mean score of 80, and Section B had 20 students who had a mean score of 90.

We know that  , \text{Mean}=\dfrac{\text{Sum of observations}}{\text{No. of observations}}

Then , for section A :

\text{Mean score }=\dfrac{\text{Sum of scores in sec A}}{\text{No. of students}}

\Rightarrow\ 80=\dfrac{\text{Sum of scores in sec A}}{15}\\\\\Rightarrow\ \text{Sum of scores in sec A}=80\times15=1200

Similarly in Section B, \text{Sum of scores in sec B}=90\times20=1800

Total scores = Sum of scores in sec A+Sum of scores in sec B

=1200+1800=3000

Total students = Students in sec A +Students in sec B

=15+20=35

Now , the mean score for all of the students on the quiz =\dfrac{\text{Total score}}{\text{Total students}}

=\dfrac{3000}{35}=85.7142857143\approx85.7

Hence, the approximate mean score for all of the students on the quiz = 85.7

Thus , the correct answer is option A. 85.7.

7 0
2 years ago
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