The exact length of the curve is (4/3)(21^(3/4) - 1) units
To find the length of the curve given by x = 3t^2, y = 4t^3, where 0 ≤ t ≤ 5, we need to use the formula:
L = ∫[a,b]sqrt(dx/dt)^2 + (dy/dt)^2 dt
where a and b are the values of t that correspond to the endpoints of the curve.
First, let's find dx/dt and dy/dt:
dx/dt = 6t
dy/dt = 12t^2
Then, we can compute the integrand:
sqrt(dx/dt)^2 + (dy/dt)^2 = sqrt((6t)^2 + (12t^2)^2) = sqrt(36t^2 + 144t^4)
So, the length of the curve is:
L = ∫[0,5]sqrt(36t^2 + 144t^4) dt
We can simplify this integral by factoring out 6t^2 from the square root:
L = ∫[0,5]6t^2sqrt(1 + 4t^2) dt
To evaluate this integral, we can use the substitution u = 1 + 4t^2, du/dt = 8t, dt = du/8t:
L = ∫[1,21]3/4sqrt(u) du
Now, we can use the power rule of integration to evaluate the integral:
L = (4/3)(u^(3/4))/3/4|[1,21]
L = (4/3)(21^(3/4) - 1^(3/4))
L = (4/3)(21^(3/4) - 1)
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.
What number is 75 percent of 64? Please help!
Answer:
The answer is 48.
2. The length of Manny's pool is 7 times as the width increased by 4. What is the area, in
feet, of Manny's pool?
Answer:
L=7w+4
Step-by-step explanation:
we do not know a width to give an exact answer in numbers
Please helpASP hurry please and ty
need to know the middle part
[tex]\Large\boxed{\tt Answer:~3x=2x+10;~x=10}[/tex]
[tex]\tt Step-by-step~explanation:[/tex]
Since it shows us that both ends of the segment in the middle bisects the sides of the triangle in the middle, we know that the segment in the middle is half of the hypotenuse (4x + 20).
[tex]\tt a)~ 3x =\frac{1}{2} (4x+20)[/tex]
Let's solve the right side of the equation by distributing[tex]\tt 0.5 (4x+20)\\4x*0.5=2x\\20*0.5=10\\\\b)~2x+10;~3x=2x+10[/tex]
Now, we can solve for x by moving the variable x to one side of the equation and everything else on the other side.
[tex]\tt 3x-(2x)=2x-(2x)+10\\\\c)~x=10[/tex]
What is (-3)^-9 times (-3)^5
Answer:
1/80 or 0.01234568
Step-by-step explanation:
Exponentiation: (-3) ^ (-9) = -5.08052634253E-5 = -1/
19683
Exponentiation: (-3) ^ 5 = -243
= -1/
19683
* (-243) = -1 · (-243)/
19683 · 1
= 243/
19683
= 1 · 243/
81 · 243
= 1/
81
help me please this is very important to me for rbainlist and explain
Answer:
Step-by-step explanation:
The probability of getting one even and one odd is the sum of probability of getting even and of getting odd and even. Since there are 3 even or odd on each die out of six numbers you have
P(EO)(3/6)(3/6)=1/4 and P(OE)=(3/6)(3/6)=1/4 so 1/4+1/4= 1/2
or you can find the probability of getting two odds or two evens and subtract that from 1
P(EE)=(3/6)(3/6)=1/4, P(OO)=(3/6)(3/6)=1/4
P(EO)=1-1/4-1/4=1/2
Find the product of 2x4(3x2 + 4x + 1).
6X6 + 8x5 + 2x4
6x3 + 3x4+1
5X6 + 6x5 + 3x4
5x8 + 6x4 + 1
Answer:
A: 6X6 + 8x5 + 2x4
Step-by-step explanation:
what is the ratio then what is the value of the ration?
Answer:
For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six (that is, 8∶6, which is equivalent to the ratio 4∶3).
if m1=2x° and m3=3x° what is m1
Answer:
36
Step-by-step explanation:
Using the angle addition postulate
angle 1+angle 2+angle 3=180
Angle 2 is 90 degrees,
Angle 1 is 2x degrees
Angle 3 is 3x degrees
Plug this into equation
[tex]2x + 90 + 3x = 180[/tex]
[tex]5x + 90 = 180[/tex]
[tex]5x = 90[/tex]
[tex]x = 18[/tex]
Plug 18 into 2x
[tex]2(18) = 36[/tex]
Solve the equation graphically :-
4x-3y = 0
2x + 3y -18 = 0
Solve 77/8 - 3
3 > 8.
Answer:
77/8-3= 53/8
3>8 is false
Step-by-step explanation:
A bag has some purple marbles and
some green marbles in it. This can be
modeled with the following equation.
T = p + g.
Solve the equation for the number of
purple marbles, p.
Enter the variable that belongs in the green box.
p = [?] - [ ]
Answer:
p= T-g
Step-by-step explanation:
Answer:
p=t-g
Step-by-step explanation:
Write an solve the inequality. A gym charges a one time sign-up fee of $10.25 and then $5 each time you go. A student can pay up to $135.25. How many times can the student go to the gym?
Answer:
25 visits
Step-by-step explanation:
Given data
One time fee= $10.25
let the number of times visited be x
and the total cost for x visits be y
Hence
y=10.25+5x------------1
for y=135.25
let us find x
135.25= 10.25+5x
135.25-10.25= 5x
125=5x
x= 125/5
[tex]x\geq 25 visits[/tex]
What are the coordinates of the endpoints of segment M'N'? M'(-6, 9) and N'(4, 9) M'(-6, 9) and N'(3, 9) M'(-2, 3) and N'(7, 9) M'(-2, 3) and N'(1, 3)
Answer:
The answer is B. M'(-6,9) and N'(3,9)
Step-by-step explanation:
To find the coordinates of the endpoints of segment M'N' you'll have to use the rule through which it was dilated.
M(-4,6) after the rule it will be (-4*1.5, 6*1.5) = M'(-6,9)
N(2,6) after the rule it will be (2*1.5, 6*15) = N'(3,9)
The answer is B. M'(-6,9) and N'(3,9)
Hope this helps :)
The required endpoint of the segment M'N' is given as M'(-6,9) and N'(3,9) respectively. Option B is correct.
What is coordinate?Coordinate, is represented as the values on the x-axis and y-axis of the graph. while the coordinate x is called abscissa and the coordinate of the y is called ordinate.
Here,
The equation for the dilation is given as,
= {1.5x, 1.45y}
Now,
Put coordinates of M and N in the above equation,
Coordinate of M' = (-4×1.5, 6×1.5) = M'(-6,9)
Similarly, the coordinate of N',
Coordinate of N' = (2×1.5, 6×1.5) = N'(3,9)
Thus, the required endpoint of the segment M'N' is given as M'(-6,9) and N'(3,9) respectively. Option B is correct.
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Help please and tysm
6 x (5 + 4) - 3 - (2+1)
A 18
B) 30
C) 48
D) 54
Answer:
54
Step-by-step explanation:
guys please tell me the all questions brifley it's very important for me
Answer:
3.a) 8 b) -28 c) √21 d) 2
4.a) 27 b) 25 c) √3 + √24 d) -4
Step-by-step explanation:
3. a) 3+5=7 4. a) 7(3)-3(-2)
b) 4(-4-1)+2(-4) 21+6
4(-5)-8 27
-20-8 b) 5*(3(3)+2(-2))
-28 5*(9-4)
c) √2(3)^2+3 5*(5)
√2(9)+3 25
√18+3 c) √3 + √2(3)(-2)^2
√21 √3 + √2(3)(4)
d) (-4+3)(8/-4) √3 + √24
(-1)(8/-4) d) (4/-2) + (3/3)
2 Find the LCM of 2 and 3
3(4/-2) + 2(3/3)
-6 + 2
-4
Hope this helps.
What's the circumference of a circle with a radius of 5 inches
Answer:
10π
Step-by-step explanation:
Please let me know if you want me to write an explanation for my answer :)
jake has a recipe that uses 4 cups of flour. He has a bag with 48 cups of flour. He wants to know how many recipes he can make using the bag of
flour. He finds the answer using this number sentence:
48 4=
Which number sentence shows another way to solve this problem?
A x 4 = 48
B. 48 x = 4
C 0 : 4 = 48
D. 4: 48 = 0
Answer:
D
Step-by-step explanation:
It is just like 4/48.
Answer: b
Step-by-step explanation: b because you can multiply which 48 times 4
decide whether the triangle is a right triangle.
Answer:
no it is not a right angle triangle
Can somebody help me solve for x?
Answer:
x = 18
Step-by-step explanation:
80 / 48 = 30 / x
80x = 1440
x = 18
Please help due today
Solve the missing angle measurement
Determine if the triangles are congruent by HL, SAS, SSS, AAS, or
ASA
Somebody help please!!!
i need help it's due today will give 30 points and brainliest
Answer:
t=5
a=-13
q=-9
z=-6
r=-2
u=9
y=-45
w=-13
s=11
p=-1
Step-by-step explanation:
Answer:
1.t=5
2.a=(-13)
3.-9=q
4.-6=z
5.r=(-2)
6.u=9
7.y=(-45)
8.w=(-13)
9.s=11
10.p=(-1)
hope this helps have a blessed day=)
HELP HELP HELP We can think of 8 ÷ 2 as the answer to the question “How many groups of 2 are in 8?” What is the answer to the question? *
Solve for x and y.
8
5
Х
15
У
12
Answer:
1.84553470835e+37
Step-by-step explanation:
What is this number in standard form? (3×100)+(1×1/10)+(4×1/1,000) Enter your answer in the box. please help fast . im panicking . btw it has to be decimal form
Answer:
300.104
Step-by-step explanation:
I posted a photo what the difference between expanded and standard form.
Hope this helped
HELP ME PLEASE !! Mao changes the incline angle on his treadmill from 0° to 5°. If the walking surface of the treadmill is 5
feet long, how many inches did Mao raise the end of the treadmill from the floor to the nearest tenth of an inch?
Answer:
5.2 inches
Step-by-step explanation:
We can use trigonometry for this. We know that sin = opposite/hypotenuse so opposite = hypotenuse sin. If we want the answer in inches we set the hypotenuse to inches 5 ft = 60 inches. We just use 60 sin 5 degrees to get to our answer.
Mr. Mika paid a total of $150 to rent a room at a hotel for two nights. The table shows information about four other
guests who rented rooms at the hotel.
Hotel Bills
Number of Nights
Room Was Rented
Total Amount
Paid
Guest
1
6
$450
II
3
$225
III
8
$600
IV
5
$360
Which guest did NOT pay the same nightly rate that Mr. Mika did?
Answer:
Well, one night at the hotel equals $75.
Step-by-step explanation:
All you have to do is mulitlpy the nights by $75.
The last one is wrong it should be
5 nights = $375.
Hope this helps! Bye
Which expression represents the factor form of the equation above ?
Answer:
(x+4)(x+25)
Step-by-step explanation:
x*x=x^2
x*20=20x
4*x=4x
4*25=100
x^2+20x+4x+100
put the commons together and you will get
x^2+29x+100