The exact length of the curve is 7.995.
The function [tex]y=2+8x^{\frac{3}{2} }[/tex] is given.
0 ≤ x ≤ 1
Differentiating given function with respect to x.
[tex]\frac{dy}{dx}= \frac{d}{dx}2+8x^{\frac{3}{2} }[/tex]
[tex]\frac{dy}{dx}= 12x^{\frac{1}{2} }[/tex]
Length of arc, L = [tex]\int\limits^a_b {\sqrt{1+(\frac{dy}{dx} )^{2} } } \, dx[/tex]
Putting the values,
L = [tex]\int\limits^1_0 {\sqrt{1+144x } } \, dx[/tex]
Let 1 + 144x = z
144dx = dz
When we plug in "z" and "dz" values to the equation above, we get:
L = [tex]\int\limits^1_0\frac{z^{1/2} }{144} \, dx[/tex]
= [tex][\frac{z^{3/2} }{144(3/2)} ]^{1} _{0}[/tex]
= [tex]\frac{1}{216}[z^{3/2} ]^{144} _{1}[/tex]
= [tex]\frac{1}{216}[144^{3/2}-1^{3/2} ][/tex]
= [tex]\frac{1}{216}[1728-1][/tex]
= 1727/216
= 7.995
Hence, the exact length of the curve is 7.995.
Correct Question :
Find the exact length of the curve, [tex]y=2+8x^{\frac{3}{2} }[/tex], 0 ≤ x ≤ 1.
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Literal Equations:
Solve the equation for the indicated variable.
a−c=d−r, for c
Group of answer choices
c=−d+r+a
c=d−r/a
−c=d−r−a
c=d−r+a
Answer:
−c=d−r−a
Step-by-step explanation:
if we move a value to the other side of the equal sign, the value switches positive and negative signs, in this case A moved to the right, which caused it to turn negative.
a recipe for bread uses 2 cups of liquid and 6 cups of flour for 3 loaves of bread. how many cups of flour are needed for 10 loaves and how much liquid is needed if 21 cups of flour are used?
10
Step-by-step explanation:
I just did this in a lesson
A circle has a center of (5, 2) and a radius of 10. Which the fallowing points will the circle pass through ?
Answer:
centre of the circle(h,k)=(5,2)
radius(r)=10
Step-by-step explanation:
Now,
equation of the circle is giveb by (x-h)^2+(y-k)^2=r^2
or,(x-5)^2+(y-2)^2=(10)^2
or,x^2-10x+25+y^2-4y+4=100
or,x^2+y^2-10x-4y+29-100=0
or,x^2+y^2-10x-4y-71=0
Find the factor pairs for 12 1 and 12 2 and 6 3 and 4 the factors of 12 are 1,2,3,4,6,and 12
Answer:12 = 12.
x 6 = 12.
x 4 = 12.
x 3=12
Step-by-step explanation:
What’s the range?????? :(
Answer:
the range is 765
Step-by-step explanation:
to find range you must find the largest and smallest number and subtract
if it has work to show, please include it. please help
Answer:
B) 256
Step-by-step explanation:
You are doubling the amount of boxes there are each time:
Pattern 1: 1 box
Pattern 2: 2 boxes
Pattern 3: 4 boxes
Pattern 4: 8 boxes
Pattern 5: 16 boxes
Pattern 6: 32 boxes
Pattern 7: 64 boxes.
Each box takes 4 matches to create. There are 64 boxes in total by the 7th pattern. Multiply 4 with 64:
64 x 4 = 256
B) 256 matches is your answer.
~
HELP FAST I'LL MARK YOU BRAINLIEST
Which below is not always true about a Rhombus?
1. All side are equal
2. Opposite sides are equal and congruent
3. Consecutive angles are supplementary
4. Diagonals are congruent
Answer:
4
Step-by-step explanation:
In a rhombus, the diagonals are congruent. It is not always true. If the diagonals become congruent then It becomes square. Hope this helps!
Answer:
4) Diagonals are congruent is NOT always true
Step-by-step explanation:
Diagonals are only congruent if it's square, so this one is not always true.
A model rocket is launched from
the top of an observation tower
that is 75 feet high. The height
of the rocket, h(t), is
determined by the function
h(t)--16r2 + 48t +75 where t is
the number of seconds elapsed
since the rocket was launched.
When does the rocket land on
the ground? Round to the
nearest hundredth.
Answer:
>>> t = 3/2 - sqrt(111)/4
>>> t = 3/2 + sqrt(111)/4
Step-by-step explanation:
-16r^2 + 48t +75=0
>>> t = 3/2 - sqrt(111)/4
>>> t = 3/2 + sqrt(111)/4
In order to prove triangle similarity by AAA what does X have to equal?
Answer:
x has to be equal to 12
Step-by-step explanation:
In other to prove that the triangles are similar, the values of the angles at certain points must be equal
for example, the angle at the top vertices should be equal
So, we have it that;
6x = 3x + 36
6x-3x = 36
3x = 36
x = 36/3
x = 12
No files!!! Math work. Help.
Answer:
Number 6 would be (a) 88 degrees
Number 7 would be (c) 45 degrees
Step-by-step explanation:
What is this Geometry? I haven't done this in so long so i went to look it up online and was shocked because of how much i was overthinking it.
For number 6, since we already have the angle listed as 44 degrees, to find the arc degrees, we would multiply the 44 by two. The formula is basically mAB=2(m<C)=88.
For number 7, we already have the arc degrees, so we would have to divide by two in this case to find the angle. The formula for this would be m<X=1/2(mYZ)=45.
non proportional or proportional ?
y= 3.75x + 2
The graph of f (2) = x2 was transformed to create the graph of g(x) = f(x) – 9. Which statement about
the graphs is true?
Answer:
Step-by-step explanation:
g(x) is translation of f(x) by 9 units down.
8r= -64
what does the 8r stand for?
Answer:
r=8
Step-by-step explanation:
The number we are looking for is represented by 'r' which is multiplied by 8
A meteorologist in Seattle says there is a 75% chance of rain. A meteorologist in Tacoma says there is a 1/4 chance of rain. In which city is it more likely to rain?
A. Seattle
B. Tacoma
C. Batesville
D. Both have the same chance
hellohello, this needs to be turned in tomorrow so if you could help, i would really appreciate it. :]
Answer and Step-by-step explanation:
We are given the side lengths, so all we have to do is multiply each rectangle's lengths and widths to get their areas, then add them together,
Top rectangle Area:
4 × 7 = 28
Bottom rectangle Area:
6 × 8 = 48
Now, we add them together.
Total Area:
28 + 48 = 76
The total area of the figure is 76 [tex]units^{2}[/tex].
#teamtrees #PAW (Plant And Water)
Suppose you had to decide between an apartment that cost $800/month for a month-to-month contract, or $650 for an annual contract. The annual contract includes a 2- month early termination penalty if you leave before 12 months
Answer:
Step-by-step explanation:
Incomplete question, but if my guess is correct, you're trying to determine which is a better deal between the two. I will go with the second one. The $650/month rent.
I choose so because, $800/month totals to $9600 at the end of the year. While $650/month totals to $7800 per year. Again, with the $650/month, if you try to leave before the end of the year, say 11 months even, you pay a penalty of $1300, which still leaves you on the profit side. And the whole idea of choosing is to find which is more beneficial and cost effective.
Simplify. Your answer should only contain positive exponents (−2−2)5•44
Answer:
-21.76
Step-by-step explanation:
(-2-2)5•44
-4×5•44
-4×544 (2 decimal places)
100
-2176 (multiply -4 x544)
100
Since 100 has two zeros, -21•76 becomes the answer.
MODELING WITH MATHEMATICS The backboard of the basketball hoop forms a right triangle with the supporting rods, as shown. Use the Pythagorean Theorem to approximate
the distance between the rods where they meet the backboard. Round your answer to the nearest hundredth
Two triangles are similar. The sides of the first triangle are 8, 9 and 12. The smallest side of the second triangle is 6. Find the other two side lengths.
Answer:
second side = 6.75
third side = 9
Step-by-step explanation:
6/8 = 9/x
8x = 54
x = 6.75
8/12 = 6/y
8y = 72
y = 9
Answer:
Correct answer A. two-thirds and Correct answer D. three-halves
Step-by-step explanation
they have to be the same fraction or flipped
Which statement describes the graph of y + 2 ≥ –4(x – 3)2?
A- a parabola opening up, with shading above the vertex
B- a parabola opening up, with shading below the vertex
C- a parabola opening down, with shading above the vertex
D- a parabola opening down, with shading below the vertex
Its C
Answer:
c
Step-by-step explanation:
c
The graph of y + 2 ≥ –4(x – 3)² is a a parabola opening down, with shading above the vertex
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The graph of y + 2 ≥ –4(x – 3)² is a a parabola opening down, with shading above the vertex
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jeremy bought 5 pencils for w dollars. each pen cost 35¢ more than a pencil
A survey of 100 high school students provided this
frequency table on how students get to school:
Drive to Take the
Grade
Walk
School bus
Sophomore 2
25
3
Junior
13
20
2
25
5
5
Senior
What is the probability that a randomly selected student
is a junior who takes the bus?
?
P(Junior' n Take the bus)
Answer:
The answer is 1/5
Step-by-step explanation:
Trust me.
The probability that a randomly selected student is a junior who takes the bus is [tex]\frac{1}{5}[/tex] .
What is probability?Probability or chance is how likely something is to happen. If something has a low probability, it is unlikely to happen. If something has a high probability, it is likely to happen.
[tex]probability=\frac{number\ of\ favourable\ cases }{total\ number\ of cases}[/tex]
Given,
Total number of students = 100
Number of students who are juniors and take bus = 20
[tex]probability=\frac{number\ of\ favourable\ cases }{total\ number\ of cases}[/tex]
Probability of junior students who take bus = [tex]\frac{20}{100}[/tex]
Probability of junior students who take bus = [tex]\frac{1}{5}[/tex]
Hence, The probability that a randomly selected student is a junior who takes the bus is [tex]\frac{1}{5}[/tex] .
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Please help ASAP.
Solve the quadratic equation by factoring.
9x^2+24x+20=4
A. x=-3/4
B. x=-4/3
C. x=4
D. x=4/3
Answer:
the answer is B x= -4/3
Step-by-step explanation:
9x^2+24x+20=4
9x^2+24x+20-4=0
9x^2+24x+16=0
(3x+4)^2=0
3x+4=0
3x=-4
x= -4/3
mallory and five of her friends bought a box of 36 cookies. together they ate 2/3 of the cookies
Answer:
24 cookies got eaten 12 weren't eaten
Step-by-step explanation:
36 divided by 3 = 12
12 x 2 = 24 ( since they ate 2/3)
36-24=12 (12 weren't eaten)
Write an expression to describe the sequence below. Use n to represent the position of a term in the sequence, where n = 1 for the first term.
10, 11, 12, 13
Answer:
[tex]9 + n[/tex]
Step-by-step explanation:
Well it's an arythmetic sequence, so it will look like:
[tex]a + d\cdot n[/tex]
Note that the first element is:
[tex]a + d\cdot 1[/tex]
and the second element is:
[tex]a + d \cdot 2[/tex]
So the difference between the two gives us d!
[tex]d = 11 - 10 = 1[/tex]
Now let's find the [tex]a[/tex]:
[tex]a + d\cdot 1 = 10\\a + 1 \cdot 1 = 10\\a + 1 = 10\\a = 9[/tex]
solve for x
3x - (8-x) = 47
7th grade math help me pleaseee
Part A. n+6=15>>>n=9
Part B.n+6=15 >>> n+6-6=15-6
n=9
A TV has a listed price of $616.99 before tax. If the sales tax rate is 9.75%, find the total cost of the TV with sales tax included. Round your answer to the nearest cent, as necessary.
Answer:
The sales tax is determined by computing a percent of the purchase price. To find the sales tax multiply the purchase price by the sales tax rate. Remember to convert the sales tax rate from a percent to a decimal number. Once the sales tax is calculated, it is added to the purchase price.
Solve for the roots in simplest form using the quadratic formula:
4x^2+5=−12x
what is the equation of a line parallel to the following line that passes through the points given. y=-4x+6 (2,-1)
Answer:
Short Answer Type:
y = -4x + 6
Therefore slope = (-4)
Given:
Point = (2,-1)
Slope = -4
Therefore: -1 = -8 + c
=> c = 7
Therefore equation: y = -4x + 7