Function f(x) = ax^{2}+bx+c, where a, b, and c are some constants. Define functions g and h as follows:g(x) = f(x+ 1)−f(x)
h(x) = g(x+ 1)−g(x)
Find algebraic form of h(x)
Can anyone explain how to make it step by step?

Answers

Answer 1

Answer: g(x) = f(x+1) - f(x)
=[ a(x+1)^2+b(x+1)+c ] - [ax^2+bx+c]
=[ a(x^2+2x+1) +bx + b + c ] - [ax^2 + bx + c]
=[ ax^2 + 2ax + a + bx + b + c ] - [ax^2 + bx + c]
= ax^2 + 2ax + a + bx + b + c - ax^2 - bx - c
= 2ax + a + b
Therefore g(x) = 2ax + a + b
h(x) = g(x+1) - g(x)
=2a (x+1) + a + b - [2ax+a+b]
=2ax + 1 + a +b - 2ax - a - b
Therefore h(x) = 1

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18A person typically breathes about 8.64 x 10^3 liters of air per day. The life expectancy of
a person in the United States at birth is about 29,200 days. Estimate the total amount of
air a person born in the United States breathes over a lifetime.

Answers

Answer:

2.53×10^8 liters

Step-by-step explanation:

(8.65×10^3 L/da)(0.292×10^5 da) ≈ 2.53×10^8 L

Final answer:

The total amount of air a person born in the United States breathes over a lifetime is estimated to be 2.52 x 10^8 liters. This is calculated by multiplying the daily air intake (8.64 x 10^3 liters) with the average life expectancy in days (29,200 days).

Explanation:

To estimate the total amount of air a person born in the United States breathes over a lifetime, we can simply multiply the amount of air breathed daily by the expected length of life in days. Here's how it works:

The given daily air intake is 8.64 x 10^3 liters.
The average life expectancy is 29,200 days.
We multiply these two values together to get the total lifetime air intake.

So, 8.64 x 10^3 liters/day x 29,200 days = 2.52 x 10^8 liters.

Therefore, a person born in the United States breathes an estimated 2.52 x 10^8 liters of air over a lifetime.

Learn more about Lifetime Air Intake here:

brainly.com/question/34703968

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Roy is planning a trip to Iceland. His plane ticket will cost kr 60,170 (60,170 Icelandic krónur), his lodging will cost kr 47,249, he needs kr 39,877 for food, and his Icelandic friend has suggested that he bring at least kr 41,054 for sightseeing and spending money. However, Roy has only kr 160,500 saved up. How much more will he need before he can go on his trip?a. kr 23,350
b. kr 26,673
c. kr 27,850
d. kr 28,741

Answers

Answer: c. kr 27,850

Step-by-step explanation:

Given: The cost of plane ticket = kr 60,170

The cost of lodging = kr 47,249

The cost of food = kr 39,877

The amount suggested by friend for sightseeing and spending money = kr 41,054

Total cost for trip = $60,170+47,249+39,877+41,054$

$=kr\ 188,350$

Saved money by Roy = kr 160,500

The amount needed before he can go on his trip= $188,350- 160,500$

$=kr\ 27,850$

Hence, he need kr 27,850 before he can go on his trip.

c. kr 27,850had a test

A recipe for modeling clay requires 1/3 cup of salt. how many recipes of salt can carla make with 7 3/4 cups of salt

Answers

Answer:

- The error is: $((31)/(4))((1)/(3))$

- The correct solution is: $(93)/(4)=23^{(1)/(4)}$ (Carla can make approximately 23 recipes with the clay).

Step-by-step explanation:

1. Carla must divide $(31)/(4)$ ÷ $(1)/(3)$ as following:

- Take the reciprocal of $(1)/(3)$ .

- Multiply the numerators and the denominators.

Then:

$((31)/(4))((1)/(3))=((31)(3))/((4)(1))=(93)/(4)$

2. As a mixed number:

$(93)/(4)=23^{(1)/(4)}$

3. Therefore, Carla can make approximately 23 recipes with the clay.

The radius of a circle is 5 miles. What is the circumference?

Answers

Answer:

31.4

Step-by-step explanation:

Circumference = 2 x Radius x π. π = Pi = 3.14, thus, the math to calculate the circumference of a circle with a radius of 5 is: 2 x 5 x 3.14 = 31.4. And the answer to the circumference of a circle with a radius of 5 is approximately: ≈ 31.4.

-https://numbermaniacs.com/circumference/radius/what-is-the-circumference-of-a-circle-with-a-radius-of-5.html#:~:text=Circumference%20%3D%202%20x%20Radius%20x%20%CF%80.%20%CF%80,radius%20of%205%20is%20approximately%3A%20%E2%89%88%2031.4.%20

4 is what percent of 20

Answers

20%
Finding percentage u have to
Divide 4/20= 0.2 then multiply by 100 to get percentage which is 20%

cone A has a height of 3 meters and radius of 2 meters. Cone B has the same radius, but height og 6 meters, calculate the volume of each cone. Which conclusion is correct ? The volume of cone A is twice the volume of cone B, the volume of cone Bis ywice the volume of cone A , The volume of cone B is 4 time the volume of cone A or The volume of cone B is 3 times the volume of cone A?