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4 years ago

Hello, Can someone please explain on how to do this? thank you!

Mathematics

2 answers:

Marrrta [24]4 years ago

7 0

Steps:

1) determine the domain

2) determine the extreme limits of the function

3) determine critical points (where the derivative is zero)

4) determine the intercepts with the axis

5) do a table

6) put the data on a system of coordinates

7) graph: join the points with the best smooth curve

Solution:

1) domain

The logarithmic function is defined for positive real numbers, then you need to state x - 3 > 0

=> x > 3 <-------- domain

2) extreme limits of the function

Limit log (x - 3) when x → ∞ = ∞

Limit log (x - 3) when x → 3+ = - ∞ => the line x = 3 is a vertical asymptote

3) critical points

dy / dx = 0 => 1 / x - 3 which is never true, so there are not critical points (not relative maxima or minima)

4) determine the intercepts with the axis

x-intercept: y = 0 => log (x - 3) = 0 => x - 3 = 1 => x = 4

y-intercept: The function never intercepts the y-axis because x cannot not be 0.

5) do a table

x y = log (x - 3)

limit x → 3+ - ∞

3.000000001 log (3.000000001 -3) = -9

3.0001 log (3.0001 - 3) = - 4

3.1 log (3.1 - 3) = - 1

4 log (4 - 3) = 0

13 log (13 - 3) = 1

103 log (103 - 3) = 10

lim x → ∞ ∞

Now, with all that information you can graph the function: put the data on the coordinate system and join the points with a smooth curve.

Mazyrski [523]4 years ago

7 0

We are given a log function.

y= log(x-3).

Note: A log never takes 0 or negative values.

We have x-3 there.

The value of x-3 should be greater than 0.

Let us solve it for x.

x-3>0.

Adding 3 on both sides, we get

x-3+3 >0+3.

x>3.

So, we got domain of the given function x>3. So, we can take any value greater than 3 for x.

Let us make a table of different values of x and y for the given function

______________________________________

x y=log(x-3)

______________________________________

4 y=log(4-3) = log(1) = 0

5 y=log(5-3) = log(2) = 0.3010

6 y=log(6-3) = log(3) = 0.4771

7 y=log(7-3) = log(4) = 0.6021

10 y=log(10-3)= log(7) = 0.8450

______________________________________

Ploting points on the graph.

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3 years ago

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3 years ago

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F(x) =x2+2x-3 g(x)=3x-14

Leviafan [203]

The solution to the composite function f(g(x)) is 9x² - 78x + 165.

<h3>What is composite function?</h3>

A composite function is generally a function that is written inside another function.

Function composition is an operation that takes two functions f and g, and produces a function h = g ∘ f such that h(x) = g.

From the given composite function, the solution is determined as follows;

to solve for f(g(x)), we use the following methods.

f(x) = x² + 2x - 3, g(x) = 3x - 14

f(g(x)) = (3x - 14)² + 2(3x - 14) - 3

= 9x² - 84x + 196 + 6x - 28 - 3

= 9x² - 78x + 165

Thus, the solution to the composite function f(g(x)) is 9x² - 78x + 165.

Learn more about composite function here: brainly.com/question/10687170

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The complete question is below:

F(x) =x2+2x-3 g(x)=3x-14, find f(g(x))

8 0

1 year ago

The amount of syrup that people put on their pancakes is normally distributed with mean 63 mL and standard deviation 13 mL. Supp

andreyandreev [35.5K]

Answer:

(a) X ~ N( $\mu=63, \sigma^{2} = 13^{2}$ ).

$\bar X$ ~ N( $\mu=63,s^{2} = (\frac{13}{\sqrt{43} } )^{2}$ ).

(b) If a single randomly selected individual is observed, the probability that this person consumes is between 61.4 mL and 62.8 mL is 0.0398.

(c) For the group of 43 pancake eaters, the probability that the average amount of syrup is between 61.4 mL and 62.8 mL is 0.2512.

(d) Yes, for part (d), the assumption that the distribution is normally distributed necessary.

Step-by-step explanation:

We are given that the amount of syrup that people put on their pancakes is normally distributed with mean 63 mL and a standard deviation of 13 mL.

Suppose that 43 randomly selected people are observed pouring syrup on their pancakes.

(a) Let X = amount of syrup that people put on their pancakes

The z-score probability distribution for the normal distribution is given by;

Z = $\frac{X-\mu}{\sigma}$ ~ N(0,1)

where, $\mu$ = mean amount of syrup = 63 mL

$\sigma$ = standard deviation = 13 mL

So, the distribution of X ~ N( $\mu=63, \sigma^{2} = 13^{2}$ ).

Let $\bar X$ = sample mean amount of syrup that people put on their pancakes

The z-score probability distribution for the sample mean is given by;

Z = $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\mu$ = mean amount of syrup = 63 mL

$\sigma$ = standard deviation = 13 mL

n = sample of people = 43

So, the distribution of $\bar X$ ~ N( $\mu=63,s^{2} = (\frac{13}{\sqrt{43} } )^{2}$ ).

(b) If a single randomly selected individual is observed, the probability that this person consumes is between 61.4 mL and 62.8 mL is given by = P(61.4 mL < X < 62.8 mL)

P(61.4 mL < X < 62.8 mL) = P(X < 62.8 mL) - P(X $\leq$ 61.4 mL)

P(X < 62.8 mL) = P( $\frac{X-\mu}{\sigma}$ < $\frac{62.8-63}{13}$ ) = P(Z < -0.02) = 1 - P(Z $\leq$ 0.02)

= 1 - 0.50798 = 0.49202

P(X $\leq$ 61.4 mL) = P( $\frac{X-\mu}{\sigma}$ $\leq$ $\frac{61.4-63}{13}$ ) = P(Z $\leq$ -0.12) = 1 - P(Z < 0.12)

= 1 - 0.54776 = 0.45224

Therefore, P(61.4 mL < X < 62.8 mL) = 0.49202 - 0.45224 = 0.0398.

(c) For the group of 43 pancake eaters, the probability that the average amount of syrup is between 61.4 mL and 62.8 mL is given by = P(61.4 mL < $\bar X$ < 62.8 mL)

P(61.4 mL < $\bar X$ < 62.8 mL) = P( $\bar X$ < 62.8 mL) - P( $\bar X$ $\leq$ 61.4 mL)

P( $\bar X$ < 62.8 mL) = P( $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ < $\frac{62.8-63}{\frac{13}{\sqrt{43} } }$ ) = P(Z < -0.10) = 1 - P(Z $\leq$ 0.10)

= 1 - 0.53983 = 0.46017

P( $\bar X$ $\leq$ 61.4 mL) = P( $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ $\leq$ $\frac{61.4-63}{\frac{13}{\sqrt{43} } }$ ) = P(Z $\leq$ -0.81) = 1 - P(Z < 0.81)

= 1 - 0.79103 = 0.20897

Therefore, P(61.4 mL < X < 62.8 mL) = 0.46017 - 0.20897 = 0.2512.

(d) Yes, for part (d), the assumption that the distribution is normally distributed necessary.

4 0

3 years ago

What is the equation of the line that passes through the points (1,5) and (0,3)?

Pavlova-9 [17]

Answer:

y=2x+3

Step-by-step explanation:

first use the y2-y1/x2-x1 then use y=mx+b after

plug in 3 for y2 and 5 for y1

then plug in 0 for x2 and 1 for x1

$\frac{3-5}{0-1}$ = $\frac{-2}{-1} =2$ and 2 is ur slope

___________________

now use y=mx+b

i usually use the first point but u can u anyone u want

plug in 1 for x

plug in 5 for y

and plug in 2 for m

5=2(1)+b

5=2+b

subtract 2 on both sides

5-2=3

3=b and b is ur y-intercept

y=2x+3

hope this helps

4 0

3 years ago