Answer:
A. Transpiration
Explanation:
Plants put down roots into the soil to draw water and nutrients up into the stems and leaves. Some of this water is returned to the air by transpiration.
find a curve that passes through the point (1,-2 ) and has an arc length on the interval 2 6 given by 1 144 x^-6
Answer:
[tex]f(x) = \frac{6}{x^2} -8[/tex] or [tex]f(x) = -\frac{6}{x^2} + 4[/tex]
Step-by-step explanation:
Given
[tex](x,y) = (1,-2)[/tex] --- Point
[tex]\int\limits^6_2 {(1 + 144x^{-6})} \, dx[/tex]
The arc length of a function on interval [a,b]: [tex]\int\limits^b_a {(1 + f'(x^2))} \, dx[/tex]
By comparison:
[tex]f'(x)^2 = 144x^{-6}[/tex]
[tex]f'(x)^2 = \frac{144}{x^6}[/tex]
Take square root of both sides
[tex]f'(x) =\± \sqrt{\frac{144}{x^6}}[/tex]
[tex]f'(x) = \±\frac{12}{x^3}[/tex]
Split:
[tex]f'(x) = \frac{12}{x^3}[/tex] or [tex]f'(x) = -\frac{12}{x^3}[/tex]
To solve fo f(x), we make use of:
[tex]f(x) = \int {f'(x) } \, dx[/tex]
For: [tex]f'(x) = \frac{12}{x^3}[/tex]
[tex]f(x) = \int {\frac{12}{x^3} } \, dx[/tex]
Integrate:
[tex]f(x) = \frac{12}{2x^2} + c[/tex]
[tex]f(x) = \frac{6}{x^2} + c[/tex]
We understand that it passes through [tex](x,y) = (1,-2)[/tex].
So, we have:
[tex]-2 = \frac{6}{1^2} + c[/tex]
[tex]-2 = \frac{6}{1} + c[/tex]
[tex]-2 = 6 + c[/tex]
Make c the subject
[tex]c = -2-6[/tex]
[tex]c = -8[/tex]
[tex]f(x) = \frac{6}{x^2} + c[/tex] becomes
[tex]f(x) = \frac{6}{x^2} -8[/tex]
For: [tex]f'(x) = -\frac{12}{x^3}[/tex]
[tex]f(x) = \int {-\frac{12}{x^3} } \, dx[/tex]
Integrate:
[tex]f(x) = -\frac{12}{2x^2} + c[/tex]
[tex]f(x) = -\frac{6}{x^2} + c[/tex]
We understand that it passes through [tex](x,y) = (1,-2)[/tex].
So, we have:
[tex]-2 = -\frac{6}{1^2} + c[/tex]
[tex]-2 = -\frac{6}{1} + c[/tex]
[tex]-2 = -6 + c[/tex]
Make c the subject
[tex]c = -2+6[/tex]
[tex]c = 4[/tex]
[tex]f(x) = -\frac{6}{x^2} + c[/tex] becomes
[tex]f(x) = -\frac{6}{x^2} + 4[/tex]
You can use the formula for finding the arc length on specified interval on x axis.
The curves whose arc length on the given interval is described are
[tex]f(x) = 6x^{-2} -8[/tex]
and
[tex]f(x) = -6x^{-2} + 4[/tex]
What is the length of the arc of a function f(x) from x = a to x = b?If the function is differentiable in the given interval, then we have:
[tex]s = \int_a^b\sqrt{(1 + (f'(x))^2)}\:dx[/tex]
where s denotes the length of the arc of the given function from x = a to x = b
Using the above formula, as we're already given the arc length, thus,
[tex]\int_a^b\sqrt{(1 + (f'(x))^2)}\:dx = \int_2^6\sqrt{(1 +144x^{-6})}\:dx[/tex]
This gives us
[tex]f'(x) = \pm \sqrt{144x^{-6}} = \pm 12x^{-3}[/tex]
Integrating both sides with respect to x, we get:
[tex]f(x) = \pm \int 12x^{-3}\\\\f(x) = \pm 6x^{-2} + c[/tex]
where c is constant of integration.
Since the curve passes through (1,-2), thus, putting f(x) = -2, x = 1, we get:
[tex]f(x) = \pm 6x^{-2} + c\\-2 = \pm 6 + c\\c = -2 \mp 6 = -8, or ,4[/tex]
c = -8 when we have [tex]f(x) = 6x^{-2} + c[/tex]
c = + 4 when we have [tex]f(x) = -6x^{-2} + c[/tex]
The curves whose arc length on the given interval is described are
[tex]f(x) = 6x^{-2} -8[/tex]
and
[tex]f(x) = -6x^{-2} + 4[/tex]
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please help me please i really need help please
A sign says that the price marked on all music equipment is 30℅ off the original price. you buy an electric guitar for the sale price of $315. How much money did you save
what function equation is represented by the graph
f(x) = 4^x+5
f(x) = 3^x+4
f(x) = 3^x+5
f(x) = 4^x+4
Answer:
B
Step-by-step explanation:
We know that when x=0 y=5
B and D are the only ones that meet this criteria
we know that when x=2 y= 13 or so
D no longer works
it has to be B
Can someone help please?
Answer:
25 is the correct answer
Digital Lesson
Sam does 11 jumping jacks in 8 seconds. If he does the jumping jacks at a constant rate, how many
jumping jacks can he do in 20 seconds?
Answer:
about 28
Step-by-step explanation:
The Question is in the attachment below
Answer:
Step-by-step explanation:
It is J I’m pretty sure
The following expression represents the profit made by John as he mows lawns: P = 20L
- 100
Which description correctly interprets each part of the expression?
its c because i already did that and got it right
Tickets to a movie cost $7 for adults and $5 for students . A group of friends purchased 8 tickets for $52, write a system of equations to represent this situation
What is the diameter of a sphere with a volume of 78006 in?
Answer: 53.0
Step-by-step explanation:
Then the diameter equals 53.0122774
The diameter of the sphere is 53.01 inch
What is a Sphere?
A sphere is symmetrical, round in shape. It is a three dimensional solid, that has all its surface points at equal distances from the center. It has surface area and volume based on its radius. It does not have any faces, corners or edges.
The Surface Area of a Sphere = 4πr²
The Volume of a Sphere = ( 4/3 ) πr³
where r is the radius of the sphere
Given data ,
Let the diameter of the sphere be = d
The radius of the sphere be = r
The volume of the sphere is V = 78006 inch³
The Volume of a Sphere = ( 4/3 ) πr³
Substituting the values in the equation ,we get
( 4/3 ) πr³ = 78006 inch³
Now , Multiply by ( 3 / 4 ) on both sides , we get
πr³ = ( 78006 x 3 ) / 4
= 58504.5 inch³
Divide by π on both sides , we get
r³ = 58504.5 / π
= 18622.56 inch³
Taking cube roots on both sides , we get
r = 26.506 inch
So , the radius of the sphere is r = 26.506 inch
Now , the diameter of the sphere is d = 2 x r
= 2 x 26.506
= 53.01 inch
Hence , The diameter of the sphere is 53.01 inch
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What factor is missing? 24 + 12= ____(8+4)
Answer:
3
Step-by-step explanation:
24 + 12 = ___(8+4)
36 = ___(12)
36/12 = 3
What is the value of y?
Hello Brainly pleas help
Answer:
can you take a better pick
Step-by-step explanation:
Manuel is preparing to run in a race. He has developed a training program in which he increases his running distance each day. If he continues to follow the same pattern, what distance will he run on the fifth day.
Day 1 -- 1 mile
Day 2 -- 2 miles
Day 3 -- 4 miles
Day 4 -- 7 miles
A.) 8 miles
B.) 9 miles
C.) 11 miles
D.) 14 miles
Answer:
c
Step-by-step explanation:
c)11 miles
the day and the miles on that day add together to make the miles for the next day so 4+7=11
HELP ME PLSSSSSS Kaitlyn is covering all faces of a tissue box cover shaped like a rectangular prism. The cover has dimensions of 9” x 5” x 3.75”. What is the total area in square inches that she will need to cover?
Answer:
168.75
Step-by-step explanation:
......
Answer:
168.75
Step-by-step explanation:
Arrange these in increasing order
Answer:
so least to greatest? 1/4 1/3 1/2
Answer:
1/4, 1/3, 1/2
Step-by-step explanation:
What does the enlargement look like and what are the coordinates?
Answer:
(-6, -3) (-3,-3) (-3,-6)
Step-by-step explanation:
Multiple all of the vertices by 1.5.
(-6, -3) (-3,-3) (-3,-6)
Hope I helped!
[enlargment will still be a triangle]
Question 7
Write the integer that is equivalent to |10|
Answer:
10
Step-by-step explanation:
A rectangle and 2 congruent quarter circles were used to make the figure shown. Which measurement is closest to the area of the figure in square centimeters?
Answer:
109.3
Step-by-step explanation:
The area of the figure in square centimeters is 89.6 cm².
What is Area?Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape. The area of a plane figure is the area that its perimeter encloses. The quantity of unit squares that cover a closed figure's surface is its area.
Given:
We have the figure consist of rectangle and 2 quadrants.
Then to calculate area of figure
= Area of 2 quadrant + area of rectangle
So, Area of 2 quadrant = 2 x πr²/4 = πr²/2
= 3.14 x 5² /2
= 19.625 cm²
and, area of rectangle= l x w= 7 x 10 = 70 cm²
Thus, area of figure
= Area of 2 quadrant + area of rectangle
= 19.625 + 70
= 89.625 cm²
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6+(9-1)2 divided by 4x (1/2)
Answers:
Here you go, hope this helps
Step-by-step explanation:
6+2x
i need help with this .
Answer: electricity can be used to create magnetism
Step-by-step explanation:
Solve for X.
Х
3 ft.
6 ft.
9 ft.
Lluvia got $100 from her grandparents for her birthday. She has a weekly after school babysitting job. She earns $40 per week from her babysitting job.
A. If she does not spend any of her money, write an algebraic expression that shows how much money she has after w weeks.
B. How much money will she have after 10 weeks.
C. Alex thinks the expression 10 (40w + 10) is represents the. total amount of money Lluvia will have after w weeks. Explain whether or not Alex is correct.
Answer:
A. Y= 40w+100
B. $500
C. That would make her $400 per week plus the 100 dollars from her grandparents
Step-by-step explanation:
When all the kids who tried out for the Little league were divided into teams of 16 players, there were exactly 8 teams. How many kids tried out?
Answer:
128
Step-by-step explanation:
16 x 8 = 128
Answer:
128
Step-by-step explanation:
you multiply 16 and 8 because each team has 16 and there are 8 teams so, 16×8=128
A scientist wants to predict the number of nitrates in the river. Which sample is better for making this prediction?
Sample A: A random sample of 5 gallons of water from one location in the river
Sample B: A random sample of 5 gallons of water from five different locations in the river
Answer:
Sample B: A random sample of 5 gallons of water from five different locations in the river
Step-by-step explanation:
List the factors in the expression 4r + 5s +8.
PLZ HELP MEEEEE!!!!!
Given g(x)
=
3x + 6
2
and g(x) = 15, solve for x.
Answer:
=x?15
Step-by-step explanation:
Answer:
hhhhh
Step-by-step explanation:
I owe $8500 on my credit card. The card has a promotional interest rate of 0% for 24 months. To repay the debt, I'm going to pay a fixed amount toward the balance every month. After 12 months, my remaining debt will be $6460. Which of the following equations correctly relates the remaining debt (D) to the number of months (t) I've been making payments? (Select all that apply.)
Question 4 options:
D=6460+170t
D=170t−6460
170t+D=8500
D=−170t+8500
D+6460=8500t
Answer:
170t+D=8500
D=170t−6460
Step-by-step explanation:
Mathematical models are used to explain real life situations.
We can see from the question that the total debt is $8500 while there is interest rate of 0% for 24 months. We are also told that after 12 months, the remaining debt was $6460.
Now, the equations that correctly model the situation are;
170t+D=8500D=170t−6460Learn more about mathematical models:https://brainly.com/question/731147
Solve for x and y. Please help, I will mark as brainliest and give many points
Answer:
x=13 y=25
Step-by-step explanation:
Answer:
x = 30°, y = 45°, w = 14√2, v = 7√2Step-by-step explanation:
ΔABC has AB = 2BC, hypotenuse is twice the leg
⇒ x = 30°ΔBCD is isosceles right triangle
⇒ y = 45°ΔMPN is isosceles right triangle (∠M = 45°)
⇒ w = MN = √2PN = 14√2ΔMKP is isosceles right triangle (∠M = 45°)
v= KP = MK = 1/2MN = 1/2(14√2) = 7√2do this for brainliest! :)
Answer:
Question 13 is 27/2 (decimal form, 13.5, Mixed fraction 13 1/2)
Question 14 = 4
Step-by-step explanation:
hope this helped you:)