The change in volume of the sphere or best approximation to the increase in the volume of the sphere is 3.6π cubic inches.
How is volume of a sphere calculated?In simple words, when a sphere is placed in the space or three-dimension space, then the total space acquired by the sphere generally shows the volume of the sphere. The mathematical formula needed to determine the volume of a sphere is shown below,
[tex]V = \frac{4}{3} \pi r^3[/tex]
Calculation:Given- The initial radius of the sphere is r1 = 3 inch and the final radius of the sphere is r2 = 3.1 inch.
Now , the change in the radius of the sphere is [tex]dR =[/tex][tex]r2 - r1 =\\[/tex] 3.1 - 3 = 0.1 inch.
The mathematical expression of the volume of a sphere is shown below,
[tex]V = \frac{4}{3}\pi r^3[/tex] (here, [tex]r[/tex] is the radius of sphere)
Differentiate the above shown expression with respect to radius ([tex]r[/tex]) as shown below,
[tex]\frac{d}{dr} (V) = \frac{d}{dr} (\frac{4}{3} ) \pi r^3[/tex]
∴
dV/dR = 4/3 π × d/dR(r^3)
= 4/3 π × 3r^2
dV/dR = 4π r^2
∴ dV = 4π r^2 dR ................(1)
Substitute all values in equation (1) and calculate the approximation as shown below,
dV = 4π r^2 dR
= 4π (3)^2 × (0.1)
∴ dV = 3.6π cubic inches.
The change in volume of the sphere or best approximation to the increase in the volume of the sphere is 3.6π cubic inches.
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WILL MAKE BRAINLIEST
write the slope intercept form of the equation of each line
Answer:
15. C
16. A
Step-by-step explanation:
Good luck brotha!
A pitcher of mocktail contains 8 cups of pineapple juice and 2 cups of orange juice. How many cups of orange juice will be required to make a mocktail with 12 cups of pineapple juice?
Step-by-step explanation:
pineapple juice =8cups
orange juice =2cupspineapple juice =122x12=24
8×12=96
:. 96+24=120
moctail=120
.
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match each equation of the piecewise function represented in the graph to its corresponding piece of the domain.
Answer:
one is 3-x
two is 1
three is x
four is 5-x
hope it helps :)
Answer:
1: 3-x
2: 1
3: x
4: 5-x
Step-by-step explanation:
Hope this helped
Part A
What are the possible outcomes of rolling a six-sided die?
Answer:
the possible outcomes are :
one (1)two (2)three (3)four (4)five (5)six (6)Two numbers are missing from this table. How can the missing numbers be found?
a triangle has an angle that measures 50 degrees. the other two angles are in a ratio of 2:11. what are the measures of those two angles?
Answer:
2+11=13
180-50=130
130÷13=10
2×10=20
11×10=110
2=20°
11=110°
Solve for P.
S=A+1/2PL
9514 1404 393
Answer:
(b) P = 2(S -A) ÷ L
Step-by-step explanation:
Undo what is done to P.
[tex]S=A+\dfrac{1}{2}PL\qquad\text{given}\\\\S-A = \dfrac{1}{2}PL\qquad\text{subtract $A$}\\\\\dfrac{2}{L}(S-A)=P \qquad\text{multiply by $\dfrac{2}{L}$}\\\\\boxed{P=\dfrac{2(S-A)}{L}}[/tex]
Which key features of the graph of two parallel lines are the same and which as different?
Eli has $640 to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include tax.
He buys a new bicycle for $356.89.
He buys 2 bicycle reflectors for $16.70 each and a pair of bike gloves for $27.47.
He plans to spend some or all of the money he has left to buy new biking outfits for $74.08 each.
Write and solve an inequality which can be used to determine oo, the number of outfits Eli can purchase while staying within his budget.
PLEASE HELP! AHH I NEED HELP ASAP . PLUS ITS 6th GRADE MATH
The answer is 25
Combind like terms the 3z+z which equals 4z then subtract 25 from both sides. Meaning 25-25 and 125-25. After you minus you get 100. The set up should look like this: 4z=100 then you divide it by 4z on both sides your answer should be z=25.
Hope this helps!
How do I solve this?
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Answer:
b=-9
intersection point (3, -3)
Step-by-step explanation:
There are a couple of ways to do this. The method that does not involve calculus is to set the two equations equal and find 'b' such that there is exactly one solution.
x^2 -4x = y = 2x +b
In standard form, this is ...
x^2 -6x -b = 0 . . . . . . . we call this the "combined quadratic"
This will have one solution when the discriminant is zero. You may recall that the discriminant of quadratic ax^2 +bx +c is d = (b^2-4ac). We want ...
d = (-6)^2 -4(1)(-b) = 0
36 +4b = 0 . . . . . simplify
b = -36/4 = -9 . . . solve for b
Then the linear equation is ...
y = 2x -9
__
If the discriminant is zero, the solution to the "combined quadratic" is ...
x = -b/(2a) . . . . . . . . with a, b, c from the quadratic form (not y-intercept)
x = -(-6)/(2(1)) = 3
And the point of intersection of the line and the parabola is ...
y = 2(3) -9 = -3 ⇒ (x, y) = (3, -3)
__
The graph is attached.
PLEASE HELP!! I WILL GIVE BRAINLIEST IF YOU SHOW YOUR WORK!
Answer:
Step-by-step explanation: You would add 2 to your diameter to every circle which will lead to 17.5 as your radius. Then you would use the formula A=πr2.(r^2 is the same thing as the diamiter). This then will get you a circumfrence of 962.11.
Help me on this please
Answer:
uhhhh i dont know
Step-by-step explanation:
WILL GIVE BRAINLIEST!
Four people are running for sheriff. A survey was randomly conducted in the countyand the results were recorded in the graphIf there are approximately 5,000 registered voters, how many more volers would be expected to vote for Ben than for Scott?
A.) 4
B.) 210
C.)500
D.) 400
Answer:
I'm not sure how to answer this.
Step-by-step explanation:
Is this the full question? The context seems to be missing something. Who are Ben and Scott and who are the other 2 candidates?
Maybe post another question and rephrase it.
I need to know how to solve for this.
9514 1404 393
Answer:
use the rules of exponents
Step-by-step explanation:
The applicable rules of exponents are ...
(a^b)(a^c) = a^(b+c)
(a^b)/(a^c) = a^(b-c)
(a^b)^c = a^(bc)
(ab)^c = (a^c)(b^c)
__
Applying these to the left-side expression, we can simplify it so it looks like the right side expression.
[tex]\dfrac{(12x^5)(2x^7)}{(2x^2)^3}=\dfrac{12\cdot2x^{5+7}}{2^3x^{2\cdot3}}=\dfrac{24x^{12}}{8x^6}\\\\=3x^{12-6}=\boxed{3x^6}[/tex]
For the following right triangle, find the side length x, Round your answer to the nearest hundredth.
12
x
16
Answer:
10.6. (3s.f.)
Step-by-step explanation:
If the sum of six consecutive odd integers is 480, what is the smallest of the six integers
Answer:
90
Step-by-step explanation:
Answer:
191
Step-by-step explanation:
Find the volume of a cone with a base diameter of 8 cm and a height of 6 cm.
The volume of a cone is equal to 13 times the area of the base πr2 π r 2 times the height h . Substitute the values of the radius r=6 and height h=8 into the formula to find the volume of the cone. Pi π is approximately equal to 3.14
1 . What is the distance between the two points.
(0,5 1,3), (-0,4, -1,3) ?
2. What is the distance between the two points
(6, -3), (2, -4)
Sin(2/3+3/5) help please
Answer:
Answer ≈ 0.022
Step-by-step explanation:
For these types of questions with sin cos or tan, you will need to use a calculator. There is no other way as far as I have seen on the internet to solve this type of problem. Anyways, what you have to do is take your calculator and put in:
sin
sin(2/3+3/5) exactly like that
and the calculator will give this to you:
0.022105703 which you can then round up.
I hope this answer helped you out. If it did I would greatly appreciate it if you could check out my channel The Game Rater(or Nitro Studios the name might change). I would really appreciate that. Thanks.
-Nitroid444The population of a southern city follows the exponential law. If the population doubled in size over 19 months and the current population is 50,000, what will the population be 5 years from now?
Answer:19=2x/yr..(407936.5)
Step-by-step explanation:
guys help this makes no sense you will get lots of points for a real answer
Three more than four times the difference of x and 2 is 36
Answer:
3+4 (x - 2) =36 x= 10.25
Step-by-step explanation:
Amber coaches soccer and volleyball. She coaches both sports for a total of 10 hours each day. The soccer practice lasts 1 hour more than twice as long as the volleyball practice. Part A: Write a system of equations to model the situation. Use v for the number of hours Amber coaches volleyball in a day and s for the number of hours she coaches soccer. ( Part B: How many hours each day does Amber spend coaching each sport? Show your work. ( Will Mark Brainliest. Only answer if your 100% sure. This is very important).
Step-by-step explanation:
part a: Total is 10 hours
soccer: 2v + 1
volleyball: v
part b: 10 = 2v + 1
-2v = -10 +1
-2v = -9
v = -9 ÷ -2
v = 4.5
volleyball is 4.5 hours
if soccer is one hour longer than volleyball then soccer is 5.5 hours
4.5 + 5.5 is a total of 10 hours :)
There are 6 softball teams. There are a total of 48 children on all the teams. There are an equal number of children on each team.
Choose the number sentence which represents the number of children on each team.
Answer:
I divide 48/6=8 that is the only one that make sense for me becuase 6x8=48
Step-by-step explanation:
THE TOPIC IS: AREA OF CIRCLES!! PLEASE HELP ME WITH THIS QUESTION!!! WHATS THE ANSWER?? I WILL GIVE YOU BRAINLIEST AND A THANKS!!! AND PLS PUT AN EXPLANATION!! THANK YOU
Answer:
Step-by-step explanation:
6) diameter = 2 cm
Radius is half of diameter
r = 2 /2 = 1 cm
Area of circle = πr² {Plugin r = 1 in the formula}
= π*1²
= π cm²
7) r = 7.4 cm
Area = πr²
= π * 7.4*7.4
= 54.76π cm²
What fraction of 2 minutes is 6
seconds?
Answer:
1/20 of 2 minutes = 6 seconds
Answer:
1/20; 0.05; 5%
Step-by-step explanation:
Well, 2 minutes is 120 seconds, 6/120 simplified is 1/20, and decimal form would be 0.05, which is 5%
If 20 out of 25 students in a P.E. class are boys, what percent of the class is made up of boys?
20 points! Please help though-
Answer:
t = 7
Step-by-step explanation:
t( 5 /7 ) = 5
Hope it helped.
Answer:
7
Step-by-step explanation:
Well its worth 5 but its an easy question so its nothing really.
Well isolate the variable by performing inverse operations which in this case is diving 5 by 5/7 which is 7.
t=7
Simplify the variable expression below as much as possible.
(4.5)x+ 3x + 2
Answer:
23x +2
Step-by-step explanation:
20x + 3x + 2 = 23x + 2, also close ur curtains ouch
Based on the information given, the value of the expression is 23x + 2.
From the information given, the expression that was given is (4.5)x+ 3x + 2. This simply means that one has to multiply the values in the bracket first and solve it. This will be:
= (4 × 5)x + 3x + 2
= 20x + 3x + 2
= 23x + 2
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