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lisabon 2012 [21]
3 years ago
12

F(x)=4/x g(x)=4/x Find f(g(x))

Mathematics
1 answer:
qaws [65]3 years ago
4 0
The answer of the question is x.
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Mark cycles from home to school at a speed of 16 kilometers per hour. He cycles back on the
katrin [286]

Answer:

Write a time equation, time = dist/speed

:

go time + return time = total time

d%2F16 + d%2F15 = 7.75 hrs

multiply equation by the least common multiple 240, cncel the denominators:

 

15d + 16d = 240(7.75)

31d = 1860

d = 1860/31

d = 60 km one way

total dist = 120 km

:

Check this, find the actual time each way

60/16 = 3.75 hrs

60/15 = 4 hrs

-----------------

total time 7.75 hrs

Step-by-step explanation:

7 0
2 years ago
F is a twice differentiable function that is defined for all reals. The value of f "(x) is given for several values of x in the
nadezda [96]

The correct answer is actually the last one.

The second derivative f''(x) gives us information about the concavity of a function: if f''(x) then the function is concave downwards in that point, whereas if f''(x)>0 then the function is concave upwards in that point.

This already shows why the first option is wrong - if the function was concave downwards for all x, then the second derivate would have been negative for all x, which isn't the case, because we have, for example, f''(8)=5

Also, the second derivative gives no information about specific points of the function. Suppose, in fact, that f(x) passes through the origin, so f(0)=0. Now translate the function upwards, for example. we have that f(x)+k doesn't pass through the origin, but the second derivative is always f''(x). So, the second option is wrong as well.

Now, about the last two. The answer you chose would be correct if the exercise was about the first derivative f'(x). In fact, the first derivative gives information about the increasing or decreasing behaviour of the function - positive and negative derivative, respectively. So, if the first derivative is negative before a certain point and positive after that point. It means that the function is decreasing before that point, and increasing after. So, that point is a relative minimum.

But in this exercise we're dealing with second derivative, so we don't have information about the increasing/decreasing behaviour. Instead, we know that the second derivative is negative before zero - which means that the function is concave downwards before zero - and positive after zero - which means that the function is concave upwards after zero.

A point where the function changes its concavity is called a point of inflection, which is the correct answer.

7 0
3 years ago
Jack bought 50 lbs of clay for his art projects. He used 13.2 lbs to make a sculpture, and 0.72 lbs for each mug. How many mugs
KIM [24]

Given :

Jack bought 50 lbs of clay for his art projects. He used 13.2 lbs to make a sculpture, and 0.72 lbs for each mug.

To Find :

How many mugs did Jack make if he had 28.88 lbs of clay left over.

Solution :

Clay required to make 1 mug, r = 0.72 lbs.

Amount of clay left after making sculpture is, T = 28.88 lbs.

Now, number of clay mug Jack can make is :

n = \dfrac{28.88}{0.72}\\\\n= 40.11

Since, number of mug cannot be in decimal, so we take the floor value.

Therefore, number of mug that can be prepared is 40 .

3 0
3 years ago
Anyone know this pls help
svet-max [94.6K]
9x+3y=12\\
3x+y=4\\
y=-3x+4
7 0
3 years ago
Calvin wants to buy a car alarm that has a full price of $325, plus a 12% sales tax. Which is the better offer, a 35%-off sale o
tester [92]
First calculate the total price of the car alarm
P = 325 + 0.12(325)
P = $ 364 is the total prize of the car alarm

then calculate the discounted price
35%-off sale
P = 364( 1 - 0.35)
P = 364(0.65)
P = $ 236.6

$ 100 coupon
P = 364 - 100
P = $ 264
so it is better to have the 35%-off sale
so the answer is A
4 0
3 years ago
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