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3 years ago

Let f(x)=4-x^2,find ( f(x+h)-f(x) ) / h and simplify

Mathematics

1 answer:

Alja [10]3 years ago

7 0

If $f(x)=4-x^2$ , then

$f(x+h)=4-(x+h)^2=4-(x^2+2xh+h^2)=4-x^2-2xh-h^2$

$\dfrac{f(x+h)-f(x)}h=\dfrac{(4-x^2-2xh-h^2)-(4-x^2)}h=-\dfrac{2xh+h^2}h$

Then for $h\neq0$ , we can cancel common terms:

$\dfrac{f(x+h)-f(x)}h=-2x+h$

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Write the equation of the line that passes through the given points in slope intercept form

shepuryov [24]

Answer:

y=3x

Step-by-step explanation:

To put this in slope intercept form, let’s first find the slope

To find slope, use the equation Y2-Y1/X2-X1

When we do this, we get 0-6/0-2

This simplifies out into -6/-2 which is 3

So our slope is 3. Our equation becomes y=3x+b

Now, we find our b

We don’t have to do any solving for this, since we have the point 0,0 listed for us, it goes through the origin and that is our y-intercept or b

So our final equation is y=3x

Hope this helps and have a good day!

5 0

1 year ago

Read 2 more answers

The 2010 General Social Survey reported a sample where about 48% of US residents thought marijuana should be made legal. If we w

Sati [7]

Answer:

The sample size is $n = 600$

Step-by-step explanation:

From the question we are told that

The sample proportion is $\r p = 0.48$

The margin of error is $MOE = 0.04$

Given that the confidence level is 95% the level of significance is mathematically represented as

$\alpha = 100 - 95$

$\alpha = 5 \%$

$\alpha = 0.05$

Next we obtain the critical value of $\frac{\alpha }{2}$ from the normal distribution table , the values is

$Z_{\frac{\alpha }{2} } = 1.96$

The reason we are obtaining critical value of $\frac{\alpha }{2}$ instead of $\alpha$ is because

$\alpha$ represents the area under the normal curve where the confidence level interval ( $1-\alpha$ ) did not cover which include both the left and right tail while

$\frac{\alpha }{2}$ is just the area of one tail which what we required to calculate the margin of error

Generally the margin of error is mathematically represented as

$MOE = Z_{\frac{\alpha }{2} } * \sqrt{ \frac{\r p(1- \r p )}{n} }$

substituting values

$0.04= 1.96* \sqrt{ \frac{0.48(1- 0.48 )}{n} }$

$0.02041 = \sqrt{ \frac{0.48(52 )}{n} }$

$0.02041 = \sqrt{ \frac{ 0.2496}{n} }$

$0.02041^2 = \frac{ 0.2496}{n}$

$0.0004166 = \frac{ 0.2496}{n}$

=> $n = 600$

5 0

3 years ago

Joan and Ernie are earning money for summer camp. Joan receives a $7 weekly allowance plus $6 for each hour she helps her father

AysviL [449]

Answer:

6x+7

Step-by-step explanation:

3 0

2 years ago

Please help me with this I would give you 50 points.

mr Goodwill [35]

Answers for #5

- s/10

- 8*b

- h+7

- 3*r-8

Question 6

62 miles/hour x 4 hours = 248 miles traveled

6 0

1 year ago

Read 2 more answers

Anthony has 15 coins, all of which are quarters and dimes. In all, they're worth $3.60. How many of each kind of coin does Antho

Usimov [2.4K]

Answer:

1 Dime

14 Quarters

Step-by-step explanation:

d + q = 15

0.10d + 0.25q = 3.60

d = 15 - q

0.10d + 0.25q = 3.60

0.10(15 - q) + 0.25q = 3.60

1.5 - 0.10q + 0.25q = 3.60

0.15q = 3.60 - 1.5

0.15q = 2.1

0.15q/0.15 = 2.1/0.15

q = 14

d = 15 - q

d = 15 - 14

d = 1

8 0

3 years ago