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Mathematics

1 answer:

vaieri [72.5K]2 years ago

3 0

Answer:

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Given that (5,-8) is on the graph of f(x), find the corresponding point for the function f(x+2)

galben [10]

We know that
the transformation
f(x)--------> f(x+2)
that means
A point (x,y) in graph of f(x)------> become a point (x-2, y) in graph of f(x+2)

hence
point (5,-8)-------------> become a point (5-2,-8)-----> (3,-8)

the answer is
the point (3,-8)

5 0

3 years ago

A cup of coffee contains about 100 mg of caffeine. Caffeine is metabolized and leaves the body at a continuous rate of about 12%

Mamont248 [21]

Answer:

a. $A = C_{0}(1-x)^t\\x: percentage\ of \ caffeine\ metabolized\\$

b. $\frac{dA}{dt}= -11.25 \frac{mg}{h}$

Step-by-step explanation:

First, we need tot find a general expression for the amount of caffeine remaining in the body after certain time. As the problem states that every hour x percent of caffeine leaves the body, we must substract that percentage from the initial quantity of caffeine, by each hour passing. That expression would be:

$A= C_{0}(1-x)^t\\t: time \ in \ hours\\x: percentage \ of \ caffeine\ metabolized\\$

Then, to find the amount of caffeine metabolized per hour, we need to differentiate the previous equation. Following the differentiation rules we get:

$\frac{dA}{dt} =C_{0}(1-x)^t \ln (1-x)\\\frac{dA}{dt} =100*0.88\ln(0.88)\\\frac{dA}{dt} =-11.25 \frac{mg}{h}$

The rate is negative as it represents the amount of caffeine leaving the body at certain time.

3 0

3 years ago

In a right triangle, the measure of one acute angle is 26°. What is the measure of the other acute angle?

Makovka662 [10]

The sum of the angles of a triangle ALWAYS sum up to 180 degrees. So to find the other angle, you would take 180, subtract 90, and then subtract 26, to get 64.
The measure of the 3rd angle equals 64.

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2 years ago

A person who weighs 100 pounds on Earth weighs 16.5 pounds on the Moon. If a boy weighs 60 pounds on Earth, how much does he wei

xxMikexx [17]

10 pounds you divide your weight by 6

8 0

3 years ago

What is the value of the expression when n=3 -2n(5+n-8-3n)

igor_vitrenko [27]

-2(3)(5+3-8-3(3))
=-6(5+3-8-9)
=-30-18+48+54
=54

4 0

3 years ago

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