Answers
I'm not sure what is meant by "partitioning the x-axis" - partition is a term more often used with computing Riemann sums. So either partitioning has a special meaning for you, or you have to approximate the area with a Riemann sum.
I'm going to assume you just want the exact area of the given region. Notice that the two curves y = 4e ˣ and y = -x + 4 intersect when x = 0 at the point (0, 4). Both curves then meet the vertical line x = 4. The exponential function is increasing while the linear one is decreasing, so 4e ˣ ≥ -x + 4.
The region is then the set of points,
R = {(x, y) | 0 ≤ x ≤ 4 and -x + 4 ≤ y ≤ 4e ˣ}
so the area is given by the integral,
[tex]\displaystyle\int_0^4 (4e^x-(-x+4))\,\mathrm dx=\int_0^4(4e^x+x-4)\,\mathrm dx=\left(4e^x+\frac{x^2}2-4x\right)\bigg|_0^4=\boxed{4e^4-12}[/tex]
Related Questions
Do u know rulers <3???
Answers
Answer:
Uhh...
Step-by-step explanation:
What? Of course I know what a ruler is. One's next to me on my desk right now. Or are you talking about a ruler of a country?
Could someone help me figure this out??
Answers
Answer:
180
Step-by-step explanation:
Find the quotient of 10x4 / 5x2.
Answers
Suppose that $2000 is invested at a rate of 3.2%, compounded quarterly. Assuming that no withdrawals are made, find the total amount after 9 years.
Do not round any intermediate computations, and round your answer to the nearest cent.
Answers
Answer:
$2664.46
Step-by-step explanation:
2000(1+(0.032)/4)^(4*9)
1+0.008 = 1.008^36 = 1.33222983678... * 2000 = 2664.45967357...
≈ $2664.46
PLEASE ANSWER THIS QUESTION FAST Please qucickllyyy
Answers
Answer: 21.4
Step-by-step explanation:
Area of a triangle = (1.7 * 2)/2=1.7 m2
Area of a rectangle = 3 * 2 = 6 m2
3 * 6 = 18 m2 2 * 1.7 = 3.4 m2
the total area is 18 + 3.4 = 21.4 m2
please help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
A) 40
B) 20
Step-by-step explanation:
By Length · Width · Height
A) (5) · (4) · (2) = 40
For part B, the length and width are the same, but the depth (height) of the water is only one foot, so we can replace the height value from the first equation with 1.
B) (5) · (4) · (1) = 20
A rectangular prism is shown.
What is the volume, in cubic inches, of this rectangular prisim
Answers
V=WxHxL
V=2x4x13=104
Answer:
Step-by-step explanation:
104 cubed , find the value of each side length x width x height
Sam is designing an open wooden box in the shape of a rectangular prism. The base of the box will be 6 feet by 8 feet. He has not yet decided what the height will be.
Answers
Answer:
10ft
Step-by-step explanation:
Let assume the volume of the box be 480ft^3
Required
height h
Volume of the box = length * width * height
Substitute
480 = 8 * 6 * h
480 = 48 * h
h = 480/48
h = 10ft
Hence the height of the box if the volume of 480ft^3 is 10ft
someone please help me answer this!!
Answers
Answer:
c = 2.2m is the answer.
Step-by-step explanation:
a = 1m
b = 2m
c = ?
According to the Pythagorean theorem,
a² + b² = c²
1² + 2² = c²
1 + 4 = c²
c² = 5
c = 2.2m
∴ the slide is 2.2m long.
PLEASE HELP !! ILL GIVE BRAINLIEST !!
Answers
Answer:
3rd one
Step-by-step explanation:
Answer:
<VWT and <UTW
<STW and <XWT
PLSSS HELP ME plssssss
Answers
Answer:
D
Step-by-step explanation:
Sign means equal to or less then. Judging off the word problem saying "at least" it means that that they have that amount of trips or more.
Answer:
B. 24 + t ≥ 48
Step-by-step explanation:
So the keyword is at least which makes it clear that 24 + t is at least 48, which would be the same as is greater than or equal to
hope this helps:)
Timothy has the following ingredients to mix together to make packages of fruit snacks: 112
1
1
2
pounds of apricots, 312
3
1
2
pounds of grapes, and 2 pounds of raspberries.
How many 14
1
4
-pound packages can he make?
Answers
Answer:
The answer I keep getting is 28 because when you add all the pounds it ends up as 7 and and you need to divide that by 1/4 which will be 7x4 be a vs he of the reciprocal so it is 28
hope this helps!!!!!!! :)
Step-by-step explanation:
Find the slope of the line.
Please Help
Answers
Darnell's Burgers cooks its burgers either well done or medium. Last night the restaurant served 15 burgers in all, 6 of which were well done. What percentage of the burgers were well done? ANSWER ASAP!
Answers
Answer:
40%
Step-by-step explanation:
6/15 as a percent is 40/100 or 40%
Hope this helps! :)
Answer:
.9%
Step-by-step explanation:
so you take a calculator and input 15 and then you subtract 6 and then you hit the % button and your answer is .9% there you go!!! oh and Darnell is been on guy's groceries games and he used to be in pearl wit his business
Leo buys a new car for $17,600. The simple interest rate is 8.4% and the amount of loan (plus simple interest) is repayable in 5 years. What is the total amount that must be repaid?
Round your answer to the nearest dollar and do not round until the final answer.
Answers
Answer:
$24,992
Step-by-step explanation:
The equation for simple interest is I = PRT where I is the interest earned, P is the principal deposited/borrowed, R is the rate as a decimal, and T is time in years.
I = (17,600)(0.084)(5)
I = 7,392
The total amount that must be repaid is the interest + the principal:
7,392 + 17,600 = 24,992
Please let me know if you have questions
Need some help :(
What is the speed of a jet plane that flies 8100 km in 9 hours?
A. 900 km/sec
B. 900 km/hr
C. 900 meters/sec
D. 900 km/hr/hr
I will give Brainliest !!
Answers
Answer:
::::::::::::::::
B. 900 km/h
find the geometric mean of 15 and 24
Answers
Answer:
Blank 1: 360
Blank 2: 6
Blank 3: 10
Step-by-step explanation:
Concept
-Geometric mean is the average of a set of products
Given
- Geometric mean of 15 and 24
Solve
√(15×24)=√360
√360=6√10
Hope this helps!! :)
Please let me know if you have any questions
A, B, C and D form the vertices of a parallelogram.
AD = 11.1cm, AB = 15.5cm and ZBAD = 71°.
Find the area of the parallelogram. Round to 1 DP.
Answers
Answer:
Area = 162.70 square centimetre.
Step-by-step explanation:
From the given question,
AD = 11.1 cm, AB = 15.5 cm and <BAD = 71°
The area of the parallelogram can be determined by;
Area = AD x AB x Sin <BAD
= 11.1 x 15.5 x Sin 71°
= 172.05 x 0.94552
Area = 162.67672
= 162.70 [tex]cm^{2}[/tex]
Therefore, the area of the given parallelogram is 162.70 square centimetre.
find the area of the triangle by forming a parallelogram
!NO LINKS, NO FILES!
please :)
Answers
Explain: rectangle 7x5= 35
as this triangle is half of a 7x5 rectangle
35 divided by 2 = 17.5
I need help with a Delta math Assignment
Gabriella made 5% of her free throws over the season. If she shot 180 free throws, how many did she make?
Answers
Answer:
9
Step-by-step explanation:
The recipe for a fruit salad calls for 5 bananas, 3 peaches, 2 apples, 1 pear, 8 strawberries, 1 cantaloupe, and 2 oranges. What is the ratio of peaches to the total?
Answers
Answer:
3/22
Step-by-step explanation:
add all fruits together-
5+3+2+1+8+1+2
8+3+9+2
11+11
22
there are 3 peaches. Ratio- peaches/total
Ratio- 3/22
Hope this helps. Have a nice day you amazing bean child.
Answer:
3/22
Step-by-step explanation:
also hi
Question 9 (5 points)
Find the distance between a point (6,9) and a horizontal line at y= 5.
OA) 15
B) 4
OC) 11
D) 14
Answers
Workup in a photo below.
Good luck
A food truck sells burgers and hot dogs. During lunch, it sold 88 items for a total of $331. If burgers cost $4.50 and hotdogs cost $3.25, how many of each item were sold?
Answers
Number of hot dogs = d = 52
We know that b + d = 88 (they sold 88 items)
And 4.5b + 3.25d = 331 (price • number = money made)
So we will solve the first equation for b in terms of d, then substitute that in the second equation to sell for a numerical value of d.
b + d = 88
b = 88-d
4.5(88-d) + 3.25d = 331
396 - 4.5d + 3.25d = 331
-1.25d = -65 (divide both sides by -1.25)
d = 52
Now plug that into the first equation to get a numerical value for b.
b = 88 - d
b = 88 - 52
b = 36
Checking the math:
4.5(36) + 3.25(52) = 162 + 169 = 331
Please lmk if you have any questions
Please help me with this ASAP ASAP please please help
Answers
9514 1404 393
Answer:
h = 7 in
LA = 42π in²
SA = 60π in²
Step-by-step explanation:
Use the appropriate formula with the numbers you know, and solve for the number you need to know.
V = πr²h
h = V/(πr²) = (63π in³)/(π(3 in)²)
h = 7 in
__
LA = 2πrh
LA = 2π(3 in)(7 in)
LA = 42π in²
__
SA = 2πr(r +h)
SA = 2π(3 in)(3 in +7 in)
SA = 60π in²
In a class of 30 students, 12 have a brother and 25 have a sister. There are 2 students who do not have any siblings. What is the probability that a student who has a brother also has a sister?
Answers
20points!!!!
PLEASSEE HELPP
WILL GIVEE BRAINLIEST!!!!!!!!
Answers
4250cm ........... m?
Answers
Answer:42.5
Step-by-step explanation:
4250cm = 42,5m
The answer is: 42,5
Augusto wants to prove to his parents that watching TV while he does his homework will help him get better grades. He decides to ask 20 of his friends if they watch TV while they do their homework and what their grades are. He finds that his friends who have high grades also watch TV while they do their homework. He tells his parents that he has proven that watching TV while doing homework will cause his grades to improve. What mistake has Augusto made?
Answers
Answer:
Augusto was biased and only asked his friends
Step-by-step explanation:
Augusto should've asked 20 random people, since the people he hangs around the most probably have the same habits
This was not a fair collection of data
He did not use a random sample, and he tried to show cause and effect with an observational study
SOMEONE HELP PLEASE NEED ANSWER ASAP!!!
Answers
Answer:
3
Step-by-step explanation:
=12/4
the common ratio =3
4. What number comes next. Whats my rule?
34,41,. 55,63,
Whats my rule?
(2 Points)
Enter your answer