The value of the line integral is:
[tex](1/27) (49^{(3/2)} - 13^{(3/2)})[/tex]
≈ 36.724
To evaluate the line integral:
[tex]\int C x^2/y^{(4/3)} ds[/tex]
C is the curve given by x = t² and y = t^3, and ds is the element of arc length along the curve.
We can parameterize the curve as:
r(t) = (t², t³), 1 ≤ t ≤ ∛2
Then the tangent vector to the curve is:
r'(t) = (2t, 3t²)
The length of the tangent vector is:
|r'(t)| = √(4t² + 9t⁴ = t√(4 + 9t²)
So, the element of arc length ds is:
ds = |r'(t)| dt = t√(4 + 9t²) dt
The integral becomes:
[tex]\int C x^2/y^{(4/3)} ds[/tex]
=[tex]\int(1 to 3\sqrt 2) (t^4)/(t^{(8/3)}) (t\sqrt{(4 + 9t^2)}) dt[/tex]
= [tex]\int (1 to 3\sqrt 2) t^{(2/3)}\sqrt (4 + 9t^2) dt[/tex]
To evaluate this integral, we can make the substitution u = 4 + 9t²:
u = 4 + 9t²
du/dt = 18t
dt = du/(18t)
The limits of integration become:
u(1) = 13
u(∛2) = 49
The integral becomes:
[tex]\int C x^2/y^{(4/3)} ds[/tex]
= [tex](1/18) \int (13 to 49) u^{(1/2)} du[/tex]
=[tex](1/27) (49^{(3/2)} - 13^{(3/2)})[/tex]
So, the value of the line integral is:
[tex](1/27) (49^{(3/2)} - 13^{(3/2)})[/tex]
≈ 36.724
For similar questions on line integral
https://brainly.com/question/28381095
#SPJ11
Suppose f(x) = 3x^2 - 2x... Find f(-4)
I GIVE BRAINIEST
Can someone help me with questions 4,5, and 6? pls show all work pls.
Answer:
4. 3,4
5. 0,4
6. -8, -1
Hope that helps!
Step-by-step explanation:
A five feet tall man casts a shadow rhat is 4 1/3 feet long. A telephone pole casts a shadow that is 25.5 feet long. How tall is the telephone pole in inches
Answer:
22.1 inches
Step-by-step explanation:
The shadow is formed at a specific factor of the original image hence if a 5 feet tall man casts a shadow rhat is 4 1/3 feet long then a telephone pole casts a shadow that is 25.5 feet long must have a length
5 / 4 1/3 = x / 25.5
where x is the length of the pole
5 / 13/3 = x/ 25.5
15/13 = x/25.5
cross multiply
15 * x = 13 * 25.5
Divide both sides by 15
x = 13 * 25.5 / 15
x = 22.1 inches
The telephone pole in inches is 22.1 long
Can somebody pls help me with problems 16 and 17? I’m in a rush...thx
S+f=24 s=3f
I need this now
Answer:
f=6 and s=18
Step-by-step explanation:
Let's solve your system by substitution.
s+f=24;s=3f
Rewrite equations:
s=3f;f+s=24
Step: Solves=3ffor s:
s=3f
Step: Substitute3fforsinf+s=24:
f+s=24
f+3f=24
4f=24(Simplify both sides of the equation)
4f
4
=
24
4
(Divide both sides by 4)
f=6
Step: Substitute6forfins=3f:
s=3f
s=(3)(6)
s=18(Simplify both sides of the equation)
Answer:
f=6 and s=18
What is another way of writing the following expression?
4 + 5 + 2
Answer:
2+4+5 or 5+4+2 it functions in all the ways Simce it is sum XD
A family of four bought 6 bags of peanuts to share equally. If
each bag contained 36 peanuts, how many did each family
member receive?
Answer:
54
Step-by-step explanation: 36 * 6 = 216
216 divided by 4 = 54
Jean needs 2 gallons of olive oil to make a recipe. If the olive oil 8:00 a quart how much money will she need to buy the olive oil
Answer:
$64
Step-by-step explanation:
Given that :
Required amount of olive oil = 2 gallons
Cost per quartz = $8
Recall:
1 quartz = 0.25 gallons
Amount of quartz in 2 gallons :
2 / 0.25 = 8 quartz
Cost of olive oil needed :
8 quartz * $8
= $64
How do I expand this
Step-by-step explanation:
We have
[tex](sc^2x-1)^2[/tex]
Which is the same as
[tex](sc^2x-1)(sc^2x-1)[/tex]
To expand this polynomial, we can use the FOIL method. Meaning that we multiply the Fronts, Outsides, Insides, and Lasts together and then add each of these products.
The two fronts are [tex]sc^2x[/tex] and [tex]sc^2x[/tex],
[tex](sc^2x )(sc^2x )=s^2c^4x^2[/tex]
The two Outsides are [tex]sc^2x[/tex] and [tex]-1[/tex],
[tex](sc^2x )(-1)=-sc^2x[/tex]
The two Insides are [tex]-1[/tex] and [tex]sc^2x[/tex],
[tex](-1)(sc^2x )=-sc^2x[/tex]
The two lasts are [tex]-1[/tex] and [tex]-1[/tex],
[tex](-1)(-1)=1[/tex]
Now we just need to add these together to get
[tex]s^2c^4x^2-sc^2x-sc^2x+1\\\\s^2c^4x^2-2sc^2x+1[/tex]
Answer:
[tex]cot^{4} x[/tex]
Step-by-step explanation:
If Maria makes $40 each day at her job, and she gets paid $20 for a training course
Answer:
Where is the rest of the question?
Step-by-step explanation:
40x +20
Elena is ordering dried chili peppers and corn husks for her cooking class. Chili peppers cost $16.95 per pound and corn husks cost $6.49 per pound.
Elena spends less than $50 on d pounds of dried chili peppers and h pounds of corn husks.
Can Elena purchase 1.5 pounds of dried chili peppers and 3 pounds of corn husks and spend less than $50? Explain your reasoning.
Yes, Elena purchase 1.5 pounds of dried chili peppers and 3 pounds of corn husks and spend less than $50.
What is the reference as the equation?In its most basic form, an equation is an assertion that demonstrates that two formulas are equal. 63x + 5 = 14, for example, is an equation wherein 63x + 5 and 14 are two representations separated by a 'equal' sign.For the given question;
Let the pounds of dried chili peppers be 'd'.Let pounds of corn husks be 'h'.Chili peppers cost $16.95 per pound Corn husks cost $6.49 per pound.The equation becomes;
16.95 d + 6.49 h
16.95 (1.5) + 6.49 (3)
25.425 + 19.47
44.895 < $50
Thus, Elena purchase 1.5 pounds of dried chili peppers and 3 pounds of corn husks and spend less than $50.
To know more about the equation, here
https://brainly.com/question/2972832
#SPJ2
Sam is saving for a guitar. He already has $50 saved and intends to save $30 each week. Sam found a guitar that costs $410. After how many weeks will Sam have saved enough money to buy the guitar?
Answer:
12 weeks
Step-by-step explanation:
30 x 12 = 360
which equals 12 weeks in this case and 360 + 50 equals 410 the 50 came from the 50 he already had
I hope this helps!!
What is the value of Z?
Answer:
21
Step-by-step explanation:
Answer:
The first option is the answer
hola cual es la raiz cuadrada de √639+(393)
Answer:
393 + 39√6
Step-by-step explanation:
√639 + (393)
Simplify
393 + 39√6 (Answer)
Microsoft Rewards
Earn Gift Cards using Microsoft Rewards by searching daily and completing daily tasks.
Subtract -2x^2-6x+10−2x^2+9.
Answer:
−4x^2−6x+19
Step-by-step explanation:
this should be right
Sam wants to make a sketch of the white house with a scale factor of 2 inches to 15 feet. She knows that the white house is about 85 feet wide and 152 feet long. What will the width and height of her model be?
Answer: The width of the model = 11.33 inches and the height of the model = 20.27 inches.
Step-by-step explanation:
Given: Scale factor: 2 inches in model = 15 feet in actual.
White house is about 85 feet wide and 152 feet long.
Width of model = [tex]\dfrac2{15}\times85=\dfrac{34}{3}=11.33\text{ inches}[/tex]
Height of model = [tex]\dfrac{2}{15}\times152\approx20.27\text{ inches}[/tex]
Hence, the width of the model = 11.33 inches and the height of the model = 20.27 inches.
what is the factored form of -1/2(32x - 40) - (20x - 4)?
Answer:
12(-3x + 2)
Step-by-step explanation:
-1/2 ( 32x - 40) - (20x - 4) = -16x + 20 - 20x + 4 = -36x + 24 = 6(-6x + 4) = 12(-3x + 2)
Find the elapsed time.
from 2:08 A.M. to 11:03 A.M.
3 h 5 min
8 h 55 min
8 h 45 min
9 h 5 min
!!!!!!Plss Help Me!!!!!!!
Write the problem as an equation:
5n <65
Solve for n by dividing both sides by 5:
n <13
Because the inequality does not contain an equal sign, n (13) is not included in the answer so there would be an open circle on the number 13
The correct answer would be A.
Which situation is best described by this number line?
Answer:
B? I think itts B
Step-by-step explanation:
A car traveling at an average rate of 60 miles per hour will drive 270 miles in 4.5 hours.
A. True
O
B. False
A car traveling at an average rate of 60 miles per hour will drive 270 miles in 4.5 hours is true.
What is Speed?Speed is the time rate at which an object is moving along a path,
Given that car traveling at an average rate of 60 miles per hour will drive 270 miles in 4.5 hours.
We have to check whether the statement is true or false.
To check, we can use the formula:
distance = rate x time
Substituting the given values, we get:
distance = 60 x 4.5 = 270 miles
Therefore, the statement is true.
Hence, A car traveling at an average rate of 60 miles per hour will drive 270 miles in 4.5 hours is true.
To learn more on Speed click:
https://brainly.com/question/28224010
#SPJ2
what are two numbers that share a product of -24 and a sum of 5
[tex] - 3 \: and \: 8[/tex]
//
[tex] - 3 + 8 = 5[/tex]
[tex] - 3 \times 8 = - 24[/tex]
Urgent please hell..
A child wants to fill up a box with snow he can only carry the box if it weighs under 30 pounds the dimensions of the box are 30in by 24 inches by 24 inches each cubic inch of snow weighs .004 pounds if the child fills the box entirely with snow will he be able to carry the box?
Answer:
As a rule of thumb, snow weighs approximately 20 pounds per cubic foot, or 1.25 pounds per inch of depth. Depending on moisture content, snow can weigh from 1 pound per cubic foot to over 21 pounds per cubic foot. NOTE: Any ice build-up on the roof would need to be added to this formula.
Step-by-step explanation:
A flying squirrel lives in a nest that is 9 meters high in a tree. To reach a fallen acorn that is 4 meters from the base of the tree, how far will the flying squirrel have to glide? If necessary, round to the nearest tenth.
Answer:
Flying squirrel have to glide is for 9.8 meters approximately.
Step-by-step explanation:
Here we can use Pythagoras theorem.
Height is 9 , base is 4.
We need to find the hypotenuse measure.
So, let's use Pythagoras theorem [tex]a^{2} +b^{2}= c^{2}[/tex]
Plug in a as 9 and b 4.
[tex]9^{2} +4^{2}=c^{2}[/tex]
Simplify the left side of the equation
[tex]81+16=c^{2}[/tex]
[tex]97=c^{2}[/tex]
Take square root on both sides.
c=9.8 meters.
Type the correct answer in the box.
V12 V5
The value of V10 V6 is closest to the whole number
Answer:
the nearest whole number is one i took the test
Step-by-step explanation:
This is for one person (you know who you are) lol
Answer:
Nope...
Step-by-step explanation:
Check out my profile for [tex]incredible \lim_{n \to \infty} a_n[/tex] answers!
Answer:
Step-by-step explanation:
Solve the following system of equations graphically on the set of axes below.
y= 2x-2
y= -x+7
Answer:
x=y + 2
2
y=2(x - 1)
Step-by-step explanation:
y=2 x -2
swap sides so that all variable terms are on the left hand side
2x - 2 =y
add 2 to both sides
2x = + 2
Divide both sides by 2.
2 x = y + 2
2. 2
Dividing by 2 undoes the multiplication by 2.
x = y + 2
2
Divide y +2 by 2.
x = y + 1
2
A CIRCLE HAS A CIRCUMFENCE 43.96 YD FIND THE RADUIS OF THE CIRCLE explain
Answer:
≈ 7
Step-by-step explanation:
A 12-inch diameter pizza has 22 calories per square inch.
About how many calories are in the entire pizza?
Use 3.14 for pi.
Select from the drop-down menu to correctly complete the statement.
There are about
Choose...
calories in the pizza. optains : 264, 414, 2487, 9948
Answer:
2486.88
Step-by-step explanation:
Find the area of the pizza. A=πr²
the radius is half the diameter so here it's 6.
A= π6²
6²=36
36 × 3.14= 113.04
the pizza is 113.04 in². multiply that by 22.
Answer:
2487
Step-by-step explanation:
This is correct for k12 people