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butalik [34]
3 years ago
13

Find the average rate of change of f(x) = 2x-1 from x=0 to x=1

Mathematics
1 answer:
charle [14.2K]3 years ago
6 0

Answer:

2

Step-by-step explanation:

Av. rate of change = [(f(x2) -f(x1)]/[x2 -x1]

x2=1, x1=0

f(x) = 2x-1

f(x2)= 2*1-1=1

f(x1)=2*0 - 1= -1

Av. rate of change = [(1 - (-1)]/[1-0] = 2

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a_sh-v [17]

Answer:

photomath bro

8 0
3 years ago
An oil tank has to be drained for maintenance. The tank is shaped like a cylinder that is 4 ft long with a diameter of 2.2 ft. S
gavmur [86]

Answer:

8\:\mathrm{minutes}

Step-by-step explanation:

The volume of a cylinder is given as:

r^2\cdot\pi\cdot h

Since the diameter is 2.2, the radius is \frac{2.2}{2}=1.1.

Therefore, the volume of this cylinder is:

1.1^2\cdot 3.14\cdot 4=15.1976\:\mathrm{ft^3}, using \pi=3.14 as requested in the problem.

Since the tank is emptied at a constant rate of 1.5\:\mathrm{ft^3\:per\:minute}, it will take

\frac{15.1976}{1.5}=7.5988=\fbox{$8\:\mathrm{minutes}$} to empty the tank.

8 0
3 years ago
QUESTION
Lorico [155]
1. For this item we just refer to the prompt to know the conjectures of Ernest and Denise. According to Ernest, they should swim 1 kilometer on the first week then add 0.25km every week while Denise believes that they should swim 1 kilometer on the first week then add 0.5km every week.

2. Yes, these distances make an arithmetic sequence. It's because an arithmetic sequence is defined as a group of increasing or decreasing numbers where the difference between any two consecutive numbers is constant. This just means that every number has the same interval. In the case of their schedule, this is true.

3. For this item we just follow the descriptions of Ernest's and Denise's schedule in item number 1. For Ernest, we just keep adding 0.25 from 1 kilometer until we added it thrice. For Denise, we also keep adding a number thrice but this time it's 0.5 instead of 0.25.

Ernest's Schedule: 1, 1.25, 1.5, 1.75
Denise's Schedule: 1, 1.5, 2, 2.5

4. Here we are asked to determine a formula that will describe the schedules of Ernest and Denise. In the given formula a_{n}= a_{n-1}+d, a_{n} refers to the next term in the sequence, a_{n-1} refers to the previous term, while d refers to the common difference. In the recursive formula all we need is to insert the value of d to the equations.

Ernest: a_{n}= a_{n-1}+0.25
Denise: a_{n}= a_{n-1}+0.5

5. For this item we basically do the same thing but this time we are given another formula. Our formula is in the form a_{n}= a_{1}+(n-1)d where a_{n} is still the nth term of the sequence, a_{1} is the very first time, n is the number of terms, and d is the common difference. 

Ernest: a_{n}= 1.0+0.25(n-1)
Denise: a_{n}= 1.0+0.5(n-1)

6. In this item we will just basically substitute numbers to one of the equations that we've set up in item #5. For this we need Ernest's explicit formula first. To know how far they will be swimming on week 10, the number of elements (n) must be 10.

a_{10}= 1.0+0.25(10-1)
a_{10}= 1.0+0.25(9)
a_{10}= 1.0+2.25
a_{10}= 3.25

7. Here, we just do the same thing as item #6 but this time we will consider Denise's explicit formula. Since we are also asked how far the students will be swimming on week 10, the number of elements would also be 10 and this would also be our value for n.

a_{10}= 1.0+0.5(10-1)
a_{10}= 1.0+0.5(9)
a_{10}= 1.0+4.5
a_{10}= 5.5

8. The answer for this question is obvious. You would just need to look at the 10th element in Ernest's and Denise's sequences and tell whose schedule had more than or equal to 5 as an answer. Following Ernest's schedule, you will just get 3.5 kilometers on the 10th week so it's definitely a no. Denise's schedule, on the other hand, would get you to 5.5 kilometers on week 10 so her training schedule should be followed.
7 0
3 years ago
Pedro raced 96 km from Perry to Medford and then slowly made his way back. If the round trip took 8 hours, what was Pedro's aver
suter [353]

Answer:

12 km/h

Step-by-step explanation:

Because they are asking for Pedro's average speed, you can divide the distance by the amount of time taken to travel. So in this case, Pedro's speed is equal to 96km/8h, which when divided simplifies to 12km/h. A little tip is to look at the units the answer is asking for (like in this problem it asks what was Pedro's average speed in km per hour). Km per hour is km/h, which will give you a hint on what units you will need to divide by. Hope this helps!

5 0
3 years ago
Which statement about the function f(x)=|x+3| is true?
Stels [109]

The given function f(x) = |x + 3| has both an absolute maximum and an absolute minimum.

What do you mean by absolute maximum and minimum ?

A function has largest possible value at an absolute maximum point, whereas its lowest possible value can be found at an absolute minimum point.

It is given that function is f(x) = |x + 3|.

We know that to check if function is absolute minimum or absolute maximum by putting the value of modulus either equal to zero or equal to or less than zero and simplify.

So , if we put |x + 3| = 0 , then :

± x + 3 = 0

±x = -3

So , we can have two values of x which are either -3 or 3.

The value 3 will be absolute maximum and -3 will be absolute minimum.

Therefore , the given function f(x) = |x + 3| has both an absolute maximum and an absolute minimum.

Learn more about absolute maximum and minimum here :

brainly.com/question/17438358

#SPJ1

5 0
11 months ago
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