A tennis ball has a radius of 3.4 cm. What volume of this cylinder is empty?
Answers
so, now, we simply get the volume of the cylinder, and then volume of the 3 balls, and subtract the volume of the balls from the cylinders, effectively making a hole in the volume of the cylinder, and what's leftover, is the empty area.
[tex]\bf \textit{volume of a cylinder}\\\\ V=\pi r^2 h~ \begin{cases} r=3.4\\ h=20.4 \end{cases}\implies V=\pi \cdot 3.4^2\cdot 20.4\implies V=235.824\pi \\\\ -------------------------------\\\\ \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}\qquad r=3.4\implies V=\cfrac{4\cdot \pi \cdot 3.4^3}{3}\implies V=\cfrac{157.216\pi }{3}[/tex]
[tex]\bf \textit{volume of the \underline{3 balls}}\quad 3\cdot \cfrac{157.216\pi }{3}\implies 157.216\pi \\\\ -------------------------------\\\\ \stackrel{\textit{volume of the cylinder}}{235.824\pi }-\stackrel{\textit{volume of the balls}}{157.216\pi }\implies 78.608\pi [/tex]
Answer:
Thanks to point
ok nerd
Related Questions
Solve the triangle. A = 46°, a = 31, b = 27
Answers
To solve the given triangle with A = 46°, a = 31, and b = 27, we use the Law of Sines to first find angle B, then use the sum of angles to find angle C, and finally, use the Law of Sines again to find side c.
Explanation:To solve the triangle with the given information A = 46°, a = 31, and b = 27, we need to use the Law of Sines or the Law of Cosines. Since we have one angle and the side opposite to it (a = 31), as well as another side (b = 27), we first need to find angle B using the Law of Sines:
\frac{\sin(A)}{a} = \frac{\sin(B)}{b}
\frac{\sin(46°)}{31} = \frac{\sin(B)}{27}
By solving for sin(B), we get:
\sin(B) = \frac{\sin(46°) * 27}{31}
Next, we calculate the value of sin(B) and then angle B. After that, we can find angle C by using the fact that the sum of angles in a triangle is 180°:
A + B + C = 180°
C = 180° - A - B
Once we have angle C, we can use the Law of Sines again to find side c:
\frac{\sin(C)}{c} = \frac{\sin(A)}{a}
By rearranging and solving for c, we get:
c = \frac{\sin(C) * a}{\sin(A)}
This process will give us the lengths of all sides and the measurements of all angles, thus solving the triangle.
Felipe has a job transporting soft drinks by truck. his truck is filled with cans that weigh 14 ounces each and bottles that weigh 70 ounces each. there is a combined total of 800 cans and bottles in his truck. let x be the number of 14 -ounce cans in his truck. write an expression for the combined total weight (in ounces) of the cans and bottles in his truck.
Answers
Let x be the number of 14-ounce cans
800-x be the number of bottles
Total weight=14*x+70*(800-x)=14x+56000-70x=56000-56x=56(1000-x)
A pet-sitting company charges $25 to board a pet for one day. It also charges all customers an extra $7.50 to trim the pet's nails once per stay.
How much will it cost to board a dog for two weeks?
A.
$57.50
B.
$65.00
C.
$357.50
D.
$455.00
Answers
2 weeks = 14 days
14 * 25 = 350
350 + 7.50 = 357.50
Answer is C
If P is the midpoint of ST, SP = x + 4, and ST = 4x, determine the length of ST
Answers
4x = 2(x + 4)
4x = 2x + 8
4x - 2x = 8
2x = 8
x = 8/2
x = 4
ST = 4x = 4*4 = 16 units
Answer:
ST = 16.
Step-by-step explanation:
Given : P is the midpoint of ST, SP = x + 4, and ST = 4x,
To find : Determine the length of ST.
Solution : We have given P is mid point of ST.
It mean P divide the ST in to two equal parts .
So, SP = PT .
We can say
ST = 2 SP .
Plug the given values SP = x + 4, and ST = 4x,
4x = 2 ( x +4).
4x = 2x + 8.
On subtracting both sides by 2x
4x -2x = 8.
2x = 8
On dividing both sides by 2
x = 4.
ST = 4 * 4 = 16.
Therefore, ST = 16.
D: Region D help please .....
Answers
The inequality y >= 3x+2 is the shaded region composed of regions A and D which are above the positive sloped line.
The overlapping region is region D. This region is found in BOTH shaded solution sets of the two inequalities.
This is why region D is the final answer.
The sum of two even numbers is even. the sum of 6 and another number is even. what conjecture can you make about the other number?
Answers
Answer: We can say that the other number is even since the sum of two even numbers is even.
The required conjecture is given as the other number must be an even number.
What is an even number?An even number is defined as a number that is a multiple of 2 is called even number, such as 2, 4, 6, 12, and so on.
What is arithmetic?In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
here,
The sum of two even numbers is even. Following the statement,
If the sum of 6 and another number is even, that another number must be even to get the sum of 6 and another number to be even, while 6 it self is an even number.
Thus, the required conjecture is given as the other number must be an even number.
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Math Help Please!!!
On a team’s opening day, fans in a baseball stadium were asked how many home games they plan to attend this season. The histogram shows the results. How many fans plan on attending fewer than 20 games?
Answers
Answer: 25
Step-by-step explanation:
Given : On a team’s opening day, fans in a baseball stadium were asked how many home games they plan to attend this season.
In the given histogram , it can be seen that the number of fans attending fewer than 10 = 8
And the number of fans attending between 10-20=17
Then, the number of fans attending fewer than 20 games =[tex]8+17=25[/tex]
Therefore, 25 fans plan on attending fewer than 20 games
How many even numbers can be formed from the digits 1,2,3,4,5?
Answers
The admission fee at a small fair is $1.50 for children and $4.00 for adults. on a certain day, 2200 people enter the fair and $5050 is collected. how many children and how many adults attended that day?
Answers
1.5x + 4y = 5050
x + y = 2200
From there solve the system of equations where x represents the number of children and y represent the number of adults.
x + y = 2200
x = 2200 - y
Plug "x" into the other system of equation.
1.5(2200-y) + 4y = 5050
3300 - 1.5y + 4y = 5050
2.5y = 1750
y = 700
Since you have the value for y, solve for x.
x + y = 2200
x + 700 = 2200
x = 1500
So, the solution is: 1500 children and 700 adults attended.
Just to check our answers:
1.5x + 4y = 5050
1.5(1500) + 4(700) = 5050
2250 + 2800 = 5050
5050 = 5050
A rectangle has area 64 m2. Express the perimeter of the rectangle as a function of the length L of one of its sides. State the domain of P
Answers
P = 2L + 2W
Since
A = LW = 64
W = 64/L
Substituting to the formula for perimeter would be,
P = 2L + 2(64/L)
P = 2L + 128/L
What is the surface area of this cone ?
Answers
A basketball player scored 29 points in a game. The number of three-point field goals the player made was 29 less than three times the number of free throws (each worth 1 point). Twice the number of two-point field goals the player made was 15 more than the number of three-point field goals made. Find the number of free-throws, two-point field goals, and three-point field goals that the player made in the game.
A-10 free throws; 1 two-point field goals; 8 three-point field goals
B-11 free throws; 8 two-point field goals; 4 three-point field goals
C-10 free throws; 9 two-point field goals; 3 three-point field goals
D-10 free throws; 8 two-point field goals; 1 three-point field goals
Answers
let y represent the number of two-point field goal.
let z represent the number of three-point shots made.
Then the correct system of linear equations is as follows:
x + 2y + 3z = 29 (The total number of points scored is 29.)
z = 3x - 29 (The number of 3-pointers was 29 less than 3 times the number of free throws.)
2y = z + 15 (Twice the number of 2-point shots made was 15 more than the number of 3-pointers.)
Solution:
This basketball player scored 10 points via free throws (10 at 1 point each), 16 points via 8 two-point shots made, and 3 points via 1 three-point shots made. So, in the choice its letter D.
Answer:
,
Step-by-step explanation:
The answer is D)
How many, and what type of, solutions does 6x2−2x+7=0 have?
A.) 2 nonreal solutions
B.) 2 irrational solutions
C.)2 rational solutions
D.) 1 rational solution
Answers
Answer:
Nope! The answer is 2 Nonreal Solutions i took the test! :)
Step-by-step explanation:
The given quadratic equation will have 2 nonreal solutions. The correct option is A.
What is a quadratic equation?
A quadratic equation is a polynomial with a degree of 2 or the maximum power of the variable is 2 in quadratic equations. It has two solutions as its maximum power is 2.
Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication and division.
Given that the quadratic equation is 6x²−2x+7=0. The equation can be solved as below;-
6x²−2x + 7 = 0
The equation will have two non-real values for x. The correct option is A.
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Point M is the midpoint of LN. LM = 7x - 12 and MN = 3x + 16. Find LM.
Answers
7x - 12 = 3x + 16 (LM=MN)
7x = 3x + 28
4x = 28
x = 7
Now that we know the value of x, we can find the value of LM by plugging the value in the equation.
LM = 7(7) - 12
LM = 49 - 12
LM = 37
an angle's measure is twice the measure of its complement. the larger angle is how many degrees greater than the smaller angle.
Answers
smaller angle = x
larger angle = 2x
x + 2x = 90
3x = 90
x = 90/3
x = 30° ← smaller angle
larger angle = 2x = 2 * 30 = 60°
larger angle - smaller angle = 60° - 30° = 30°
The larger angle is 30 degrees greater than the smaller angle.
If i was born in 2002 how old will i be in 2130
Answers
2130-2002=128. We use subtraction due to that we start in 2002 but end in 2130, and therefore find the difference
Please answer me this equation
Answers
Perimeter is a function of the number of hexagons.
[tex]p_1=6\\ p_2=2*6-1\\ p_3=3*6-2\\ p_4=4*6-3\\\\ \boxed{p_n=n*6-(n-1)}\ =6n-n+1=\boxed{5n+1}\\ [/tex]
The equation h(t)=−16t2+78t+45 gives the height of a firework, in feet, t seconds after it is launched from a platform. What is the height of the platform? Enter your answer in the box.
Answers
The height of the platform is 45 feet.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The equation h(t)=−16t² +78t+45 gives the height of a firework
When a firework is launched from a platform, its height at time t=0 seconds is equal to the height of the platform.
To find the height of the platform, we can substitute t=0 into the equation:
h(0) = -16(0)² + 78(0) + 45
h(0) = 0 + 0 + 45
h(0) = 45
Therefore, the height of the platform is 45 feet.
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In buffalo, New York, the temperature was -14F in the morning. If the temperature dropped 7F, what is the temperature now?
Answers
The initial temperature in Buffalo was -14°F. After a drop of 7°F, the new temperature would be -21°F.
Explanation:The student asked: In Buffalo, New York, the temperature was -14°F in the morning. If the temperature dropped 7°F, what is the temperature now? To solve this, we need to perform a simple subtraction operation. We begin with the initial temperature of -14°F and subtract the temperature drop of 7°F.
The calculation is as follows:
Initial temperature: -14°F
Temperature drop: -7°F
New temperature: -14°F - 7°F = -21°F
Therefore, after the temperature drop, the new temperature in Buffalo would be -21°F.
After the temperature in Buffalo dropped by 7°F from an initial -14°F, the current temperature is now -21°F.
Explanation:In Buffalo, New York, the temperature was -14°F in the morning. If the temperature dropped 7°F, to find the current temperature, you subtract 7 from -14. This calculation is as follows:
Starting temperature: -14°FTemperature drop: 7°FCurrent temperature: -14 - 7 = -21°FTherefore, the temperature now in Buffalo is -21°F.
Triangle PQR has vertices P(–2, 6), Q(–8, 4), and R(1, –2). It is translated according to the rule (x, y) → (x – 2, y – 16).
What is the y-value of P'?
Answers
Answer:
The answer is -10
Step-by-step explanation:
Which statements are true regarding the diagram
Answers
Complementary means equal to 90 degrees.
Supplementary means equal to 180 degrees.
Choice #1 is correct because the angles have to be equal to 90 degrees, and in the picture you can see that those two together are a right angle, which is 90 degrees.
Choice #2 is incorrect because on the picture it is obviously less than 180 degrees.
Choice #3 is correct (same reason #1 is correct)
Choice #4 is correct because we can see that HNL is a straight line, which is equal to 180, and the angles add up toe the line HNL.
Choice #5 is incorrect because MNG was already a 90 degree angle, so adding another angle would not make it a right angle again.
I hope this helps!!
Answer:
A. AngleGNH and AngleHNJ are complementary.
C.AngleKNL and AngleLNM are complementary.
D.mAngleHNK + mAngleKNL = 180°
Step-by-step explanation:
24 divided by 2 find the qoutient
Answers
24/2 = 12
the quotient is 12
Answer: So your answer is 12 for 24 divided by 2 which gives you 12 I hope this helps
Step-by-step explanation:
24 divided by 2 = 12
12 times 2= 24
Or 2 times 12 = 24
A machine manufactures wheels with a diameter of 70 cm. It is acceptable for the diameter of a wheel to be within 0.02 cm of this value. Write and solve an absolute-value equation to find the minimum and maximum acceptable diameters.
Answers
It is acceptable for the diameter to be within 0.02 cm of the expected value.
Therefore the acceptable values for the diameter, d, are
[tex]d \pm 0.02 = 70[/tex]
The minimum acceptable value of d is obtained from
d + 0.02 = 70
d = 69.98 cm
The maximum acceptable value of d is obtained from
d - 0.02 = 70
d = 70.02 cm
Answer:
Minimum acceptable diameter = 69.98 cm
Maximum acceptable diameter = 70.02 cm
To find the minimum and maximum acceptable diameters for wheels manufactured by a machine with a 70 cm diameter tolerance set within 0.02 cm, an absolute-value equation is used to determine the range of acceptable values.
The question is: A machine manufactures wheels with a diameter of 70 cm, and it can be within 0.02 cm of this value. To find the minimum and maximum acceptable diameters, we need to set up an absolute-value equation.
Let x be the diameter of the wheel.The absolute-value equation is |x - 70| ≤ 0.02.Solving this equation, the minimum acceptable diameter is 69.98 cm, and the maximum acceptable diameter is 70.02 cm.what number fills in the blank to complete the factorization of 3x+24?
Answers
Answer:
Complete factorization of 3x+24 is:
3(x+8)
Step-by-step explanation:
we have to completely factorize:
3x+24
Taking 3 common in the above expression
3(x+8)
This cannot be factorized further
Hence, complete factorization of 3x+24 is:
3(x+8)
Find f(x) and g(x) so the function can be expressed as y = f(g(x)). There may be more than one possible decomposition.
y = (x^3 + 1)^2
Answers
and f(x) would be (x + 1)^2
Simplify -4/7 + (-4/3)
Answers
- 12/21 - 28/21 = -40/21
your answer is -1 19/21
hope this helps
Which function grows at the fastest rate for increasing values of x?
p(x)=5x3+3
f(x)=8x2−3x
h(x)=2x
g(x)=19x
Answers
And btw answer is p(x)
The function which has the fastest rate for increasing values of x are:
[tex]p(x)=5x^3+3[/tex]
Step-by-step explanation:We are given four polynomial functions as:
[tex]p(x)=5x^3+3\\\\\\ f(x)=8x^2-3x\\\\\\h(x)=2x\\\\\\g(x)=19x[/tex]
Now as we know that if the degree of the polynomial increases the function becomes more extreme i.e. it increases very quickly with the increasing value of x.
Hence, among the given options the function which has the fastest rate of increase is:
[tex]p(x)=5x^3+3[/tex]
( Since, it's degree is 3 which is highest as compared to the other polynomials (one of degree 2 and 2 of degree 1) )
Find the value of tan θ given cot θ=5/7.
Answers
In the expression 12 + 7, the values on the right and left of the + symbol are called _____ .
Answers
In the expression 12 + 7, the values on the right and left of the + symbol are called operands.
What are operands?A mathematical object upon which an operator acts.
Given that, an expression 12+7,
In maths, the values that an operator acts on are called operands. In this case, 12+7 are the operands.
Hence, the asked statement is operands.
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Keiko runs 10 miles in 75 minutes. at the same rate, how many miles would she run in 69 minutes?