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
A rectangular park is 70 meters wide and 100 meters long.
Give the length and width of another rectangular park that has the same perimeter but a smaller area.
Answers
9514 1404 393
Answer:
60 m wide and 110 m long
Step-by-step explanation:
The more the shape deviates from a square, the smaller the area will be. The area can be reduced by making the park longer and narrower. The sum of length and width must remain the same for the perimeter to be unchanged.
Given park: 70 m × 100 m = 7000 m²
Smaller park: 60 m × 110 m = 6600 m² -- less area than 7000 m²
Which value makes the equation 3x / 6 equals 36 true
Answers
Answer:
72
Step-by-step explanation:
3x/6=36
3x=36(6)
3x=216
x=216/3
x=72
What is the slope of (-16, 7) (-1, 17) and the slope of (-11, 15)
, (-11, 6)
Answers
Answer:
2/3 and 9
Step-by-step explanation:
SLOPPY TOPY TOPPY TOPPY
Answers
Answer:
D. 51
Step-by-step explanation:
the highest number- the lowest number
54-3=51
1. h(x) = xVx + 5x-2 + 1
Polynomial function: YES or NO
Standard form:
Degree:
Type:
Leading Coefficient:
Answers
9) Choose all expressions that are equivalent to 3x + 6 (Use
Algebra tiles if needed)
a) -2x - 4 + 5x + 10
b) 3(x + 6)
c) x + 4 - 2x + 2
d) 3(x + 2)
Answers
Answer:
3(x+2)
Step-by-step explanation:
3x+6
Factor out 3.
3(x+2)
PLEASE HELP !! ILL GIVE BRAINLIEST !!
Answers
Answer:
its d
Step-by-step explanation:
trust me
Answer:
MNP and ONK
Step-by-step explanation:
Vertical angles are angles which are vertical to each other and are parallel to each other.
look at pic 10 pts will mark brainilest
Answers
Answer:
12h = 432
Step-by-step explanation:
Please help! *no links* GIVING BRAINIEST
Answers
Answer:
6. -1
7. [tex]\pi \\[/tex]
8. 2.16
9. -7
10. [tex]\sqrt{144}[/tex]
11.-7.65091254...
12. 4
Step-by-step explanation:
If f(x) = (x – 2, then find f(-3).
Answers
What kind of shape is this?
A. Pentagon
B. Quadrilateral
C. Triangle
D. Hexagon
Answers
Explanation: 5 sides
An airplane descends 2.8 miles to an elevation of 5.85 miles. Find the elevation of the plane before an airplane descends 2.2 miles to an elevation of 5.85 miles. Find the elevation of the plane before its descent.
descent.
Answers
Answer:
8.05 miles
Step-by-step explanation:
If it descended 2.2 miles to 5.85 miles then that means it was at 5.85 + 2.2 miles before its descent.
5.85 + 2.2 = 8.05
Answer:
8.05 miles
Step-by-step explanation:
5.85 + 2.2 = 8.05
5.85 + 2.8 = 8.65 (not the answer, but as an example ;b
read the information above and answer. i will give brainlest who ever answers this
Answers
Step-by-step explanation:
Your answer is x+9
Mark me brainliest
Please help me, i'm stuck on this one. thank you thank you!
A long year-end status report for work is 134 pages long. You need to print 16 copies for a meeting next week. How much is the paper going to cost for those reports? Paper is sold in reams (500 pages) for $3.53 each. Give your answer to the nearest cent, only for the paper you use (partial reams are OK)
Answers
Answer:
The total cost of the copies will be $ 15.14.
Step-by-step explanation:
Given that a long year-end status report for work is 134 pages long, and I need to print 16 copies for a meeting next week, to determine how much is the paper going to cost for those reports if paper is sold in reams (500 pages) for $ 3.53 each the following calculation must be performed:
(134 x 16) / 500 = X
2,144 / 500 = X
4.288 = X
500 = 100
144 = X
144 x 100/500 = X
14,400 / 500 = X
28.8 = X
100 = 3.53
28.8 = X
28.8 x 3.53 / 100 = X
101.664 / 100 = X
1.016 = X
1.016 + (3.53 x 4) = X
1.016 + 14.12 = X
15,136 = X
Therefore, the total cost of the copies will be $ 15.14.
10 divied by 1 half of 3
Answers
Answer: 6.66 repeated
Step-by-step explanation:
10 divided by 1.5 will give you 6.66 repeated
Answer:
1/3 divied by 10 =1/30
1/3 divided by 10= 0.333333
Step-by-step explanation:
decimal form is o.3333333
fraction form is 1/30
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original price $125 discount ? sale price $81.25
Answers
Answer:(125-81.25)/125 = 0.35 = 35%
Step-by-step explanation:
PLEASE HELP !! ILL GIVE BRAINLIEST !!
Answers
Answer:
angle jkm and angle ihf :)
Step-by-step explanation:
The choises are
4.2
4.25
4.5
4.8
Answers
Answer:
The answer would be 4.5
The Wiggins Family ate dinner at a restaurant. The total cost of the meal was $85.60. The family left a 15% tip for the waiter. How much money was the total bill? (Make sure you type your answer using $ and the decimal)
Fast please
Answers
Answer:
$98.44
Step-by-step explanation:
You already know how much the actual dinner was so all you have to do is figure out how much 15% of the $85.60 is which is $12.84 meaning that they left a tip of $12.84 for the waiter. Then you would just add the cost of the dinner with the tip to get the total amount they spent. $85.60 + $12.84 = $98.44. So the total amount the Wiggins spent is $98.44
Use the diagram to fill in the blanks
x=
m∠=
Answers
Answer:
x = 21, m∠A = 23°, the measure of angle in the right = 67°
Step-by-step explanation:
The angles of a triangle sum up to 180°.
Right angles equals to 90°.
Thus, (2x - 19)° + (3x + 4)° + 90° = 180°
=> 5x + 75 = 180
=> 5x = 105
=> x = 21
m∠A=> 2(21) -19 = 23°
the measure of angle in the right=> 3(21) + 4 = 67°
Find side length using trig
Answers
Answer:
85
Step-by-step explanation:
The cost of an online video streaming service is $9.99 per
month. Write an equation that can be used to find d, the cost
in dollars for using the service for m months.
Answers
Answer:
$9.99*m=d
Step-by-step explanation:
Answer:
d = $9.99m
Good luck!
Find the output, y, when the input, x, is 7.
y=__
Answers
Answer:
y=4
Step-by-step explanation:
Read off the graph. The corresponding y-coordinate when the x-coordinate is 7 is 4.
Answer:
4
Step-by-step explanation:
You look for the point on the teal line that has an x-coordinate of 7.
You could also go to the point (7,0), which is on the x-axis, and draw an imaginary vertical line and see which point hits it.
If using the method of completing the square to solve the quadratic equation x^+16x-5=0, which number would have to be added to "complete the square"? Find complete the Square Constant
Answers
Step-by-step explanation:
can u tell wht is the power of x?
The average annual cost of the first year of owning and caring for a cat is $1,500. A sample of 81 will be used. Based on past studies, the population standard deviation is assumed known with σ = $198. What is the margin of error for a 95% confidence interval of the mean cost of the first year of owning and caring for a cat?
Answers
Answer:
The margin of error for a 95% confidence interval of the mean cost of the first year of owning and caring for a cat is of $43.12.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
Sample of 81
This means that [tex]n = 81[/tex]
What is the margin of error for a 95% confidence interval of the mean cost of the first year of owning and caring for a cat?
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]M = 1.96\frac{198}{\sqrt{81}}[/tex]
[tex]M = 43.12[/tex]
The margin of error for a 95% confidence interval of the mean cost of the first year of owning and caring for a cat is of $43.12.
Twenty-four out of the forty pies at a bake sale are coconuts pies. What
percent of the pies are coconut?
Answers
Answer:
60%
Step-by-step explanation:
Total number of pies = 40
Number of coconut pies = 24
Percentage of coconut pies :
(Number of coconut pies / total number of pies) * 100%
(24 / 40) * 100%
0.6 * 100%
= 60%
60% of pies are coconut pies
write the sum 3+3+3+3+3+3 using sigma notation
Answers
Answer:
18
Step-by-step explanation:
The sum 3+3+3+3+3+3 can be write using sigma notation [tex]\sum_{i=1}^{6}3[/tex] .
What is sigma notation?A series can be represented in a compact form, called summation or sigma notation. The Greek capital letter, ∑ , is used to represent the sum.
According to the question
The sum 3+3+3+3+3+3
Represent the sum as sigma notation
[tex]\sum_{i=1}^{6}3[/tex] start at 1 and goes up to 6
= 3+3+3+3+3+3
Hence, the sum 3+3+3+3+3+3 can be write using sigma notation [tex]\sum_{i=1}^{6}3[/tex] .
To know more about sigma notation here:
https://brainly.com/question/16701078
#SPJ3
Carefree offers two type of care packages. The food packages sell for 20$ and the game packages sell for 32$. In one day Carefree sold 25 Care packeges. the receipt for those packages totaled 602$ How many of each type of package were sold
Answers
Answer:
Number of game package = 16.5
Number of food package = 8.5
Step-by-step explanation:
LET :
Food package = a
Game package = b
a + b = 25 - - - (1)
20a + 32b = 602 - - - (2)
a = 25 - b
Put a = 25 - b into (2)
20(25 - b) + 32b = 602
500 - 20b + 32b = 602
12b = 102
b = 102 / 12
b = 8.5
a = 25 - b
a = 25 - 8.5
a = 16.5
Number of game package = 16.5
Number of food package = 8.5
Please help will give brainliest
Answers
Answer:
-8
Step-by-step explanation:
If you input x as -2 you get 8=0 so you have to add -8 for it to be true.
Answer:
0
Step-by-step explanation:
We can substitute x for 6 and solve the equation.
Peter buried a treasure chest on a remote island and is.making a map so he can find it later. One of the key landmarks in the area is a small rectangle hut, 5m by 8m