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3 years ago

I need help with a question.

Mathematics

1 answer:

Over [174]3 years ago

7 0

The answer is x =-2

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Derivative using direct definition of derivative 2-x/2+x

Daniel [21]

Let f(x) = (2 - x)/(2 + x). By definition of the derivative,

$\displaystyle f'(x)=\lim_{h\to0}\frac{f(x+h)-f(x)}h$

$\displaystyle f'(x)=\lim_{h\to0}\frac{\frac{2-(x+h)}{2+(x+h)}-\frac{2-x}{2+x}}h$

$\displaystyle f'(x)=\lim_{h\to0}\frac{\frac{(2-x-h)(2+x)-(2-x)(2+x+h)}{(2+x+h)(2+x)}}h$

$\displaystyle f'(x)=\lim_{h\to0}\frac{-4h}{h(2+x+h)(2+x)}$

$\displaystyle f'(x)=-4\lim_{h\to0}\frac1{(2+x+h)(2+x)}=\boxed{-\frac4{(2+x)^2}}$

3 0

3 years ago

A standardized exam's scores are normally distributed. In a recent year, the mean test score was 1491 and the standard deviati

Alinara [238K]

Answer:

$z(1910)=1.3429\\\\z(1230)=-0.9006\\\\z(2190)=2.2404\\\\z(1380)=-0.3558$

Step-by-step explanation:

-Given the population mean is $\mu=1491$ and the standard deviation is $\sigma=312$ , we calculate the z-scores using the formula:

$z=\frac{\bar x-\mu}{\sigma}$

#The z-score for 1910 can be calculated as:

$z(1910)=\frac{x-\mu}{\sigma}\\\\=\frac{1910-1491}{312}\\\\=\frac{419}{312}\\\\=1.3429$

#The z-score for 1230can be calculated as:

$z(1230)=\frac{x-\mu}{\sigma}\\\\=\frac{1230-1491}{312}\\\\=\frac{-281}{312}\\\\=-0.9006$

#The z-score for 2190 is calculated as follows:

$z(2190)=\frac{x-\mu}{\sigma}\\\\=\frac{2190-1491}{312}\\\\=\frac{699}{312}\\\\=2.2404$

#The z-score for 1380 is calculated as:

$z(1380)=\frac{x-\mu}{\sigma}\\\\=\frac{1380-1491}{312}\\\\=\frac{-111}{312}\\\\=-0.3558$

7 0

3 years ago

If you take away 5 from 2 times y, you get 15

dexar [7]

Answer:

y = 10

Step-by-step explanation:

2y - 5 = 15

make y the subject of the formula

2y = 15 + 5

2y = 20

y = 20/2

y = 10

3 0

3 years ago

Lance rides his bike at a constant speed of 32 mph. Write an equation to represent the total distance, d, he can ride in h hours

wolverine [178]

Answer:

d = 32h

Step-by-step explanation:

5 0

3 years ago

Simplify 6days to 4weeks to it lowest term in ratio

FromTheMoon [43]

4 weeks = 28 days,
ratio = 6:28,

simplified ratio = 3:14

8 0

3 years ago