Find the slope of the tangent line to f(x) = 2x +3 at<br> at x = 2.

URGENT!!!!!!! HELP PLEASE!!!!!!

IRISSAK [1]

Answer:

$x^\frac{2}{3}$

Step-by-step explanation:

Using the power of power rule (multiply the exponents)

$x^\frac{4}{3}$ × $^\frac{1}{3}$ $x^\frac{2}{3}$ × $^\frac{1}{3}$

$x^\frac{4}{9}$ $x^\frac{2}{9}$

When exponents are multiplied, add the answers:

x ^ ( 4/9 + 2/9 )

x ^ ( 6/9 )

x ^ ( 2/3 )

6 0

3 years ago

the area of a circle is 81 pi m^2. what is the circumference, in meters? express your answer in terms of pi.

mestny [16]

<h3>Answer: 18pi</h3>

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Explanation:

The area 81pi square meters leads to the radius 9 meters

Use the formula A = pi*r^2 to see why this is the case. You plug in A = 81pi and solve for r to get r = 9.

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Once you know the radius, you can determine the circumference C

C = 2*pi*r

C = 2*pi*9

C = 2*9*pi

C = 18pi

The circumference is the perimeter, or distance, around the circle.

8 0

3 years ago

A colony of 100 bacteria doubles in size every 60 hours what will the population be 180 hours from now

EleoNora [17]

Answer:

20 hours thank you very much

6 0

2 years ago

Point A is at (2, -8) and point C is at (-4, 7).

Dahasolnce [82]

Answer:

(-2, 2)

Step-by-step explanation:

<u>Given:</u>

Point A is at (2, -8) and point C is at (-4, 7)

<u>Difference of coordinates:</u>

Δx = 2 - (-4) = 6
Δy = - 8 - 7 = - 15

<u>The ratio of AB to AC is 2:1. So:</u>

AB = 2*AC/3 and BC = AC/3

<u>Then coordinates of point B should be 2/3 from the point A:</u>

x = 2- 6*2/3 = 2 - 4 = -2
y = - 8 - (-15)*2/3 = -8 + 10 = 2

So point B has coordinates of (-2, 2)

7 0

3 years ago

Rent and other associated housing costs, such as utilities, are an important part of the estimated costs of attendance at colleg

zhenek [66]

Answer:

96% confidence interval estimate for the mean monthly rent of all unmarried BYU students in winter 2018 is [335.89 , 356.10].

Step-by-step explanation:

We are given that a group of researchers at the BYU Off-Campus Housing department want to estimate the mean monthly rent that unmarried BYU students paid during winter 2018.

During March 2018, they randomly sampled 314 BYU students and found that on average, students paid $346 for rent with a standard deviation of $86.

So, the pivotal quantity for 95% confidence interval for the average age is given by;

P.Q. = $\frac{\bar X - \mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

where, $\bar X$ = average rent paid by 314 BYU students = $346

s = sample standard deviation = $86

n = sample of students = 314

$\mu$ = population mean monthly rent of all unmarried BYU students

So, 96% confidence interval for the population mean monthly rent, $\mu$ is ;

P(-2.082 < $t_3_1_3$ < 2.082) = 0.96

P(-2.082 < $\frac{\bar X - \mu}{\frac{s}{\sqrt{n} } }$ < 2.082) = 0.96

P( $-2.082 \times {\frac{s}{\sqrt{n} } }$ < ${\bar X - \mu}$ < $2.082 \times {\frac{s}{\sqrt{n} } }$ ) = 0.96

P( $\bar X -2.082 \times {\frac{s}{\sqrt{n} } }$ < $\mu$ < $\bar X +2.082 \times {\frac{s}{\sqrt{n} } }$ ) = 0.96

96% confidence interval for $\mu$ = [ $\bar X -2.082 \times {\frac{s}{\sqrt{n} } }$ , $\bar X +2.082 \times {\frac{s}{\sqrt{n} } }$ ]

= [ $346 -2.082 \times {\frac{86}{\sqrt{314} } }$ , $346 +2.082 \times {\frac{86}{\sqrt{314} } }$ ]

= [335.89 , 356.10]

Therefore, 96% confidence interval estimate for the mean monthly rent of all unmarried BYU students in winter 2018 is [335.89 , 356.10].

5 0

3 years ago

Find the slope of the tangent line to f(x) = 2x +3 at at x = 2.