8 A clock in the shape of an hour glass is made up of two identical cones
connected at their vertices. The radius of each cone is 7 centimeters. The
combined height of the two cones is 11.8 centimeters. What is the volume
of the clock?
Jason made a long Role hy ipining three different lengths of cylindrical poles
Answers
Answer:
The two cones are aligned on edge to edge so that the total volume of the hourglass becomes 2∗13πr2h
Step-by-step explanation:
a) When the sand has y units left in the upper cone the height of the cone becomes y, the radius remains 1cm.Now let's take the right triangle In the upper coneAnd by similar triangles property we found that the radius of the cone in which the amount of sand is left is y3 unitsNow the volume of the sand in the remaining part of the upper cone isπy32y which gives πy327Now if we apply the same similar triangle property with the cone in the below we find that the radius of the part it has filled up remains the same as y3unitsSo the volume it has filled is (3-y) from the top cone which says that the volume filled on the bottom cone has a height of (3-y)So therefore the volume of the frustum which it has filled up isπ3h(R2+r2+rR) {Is the volume of the frustum with two radii r and R with a height h}i.eπ3(3−y)(12+(y/3)2+(y/3))So now the total volume of the hourglass in terms of y is π3(3−y)(12+(y/3)2+(y/3))+πy327b) The next question tells us that when the height of the sand in the below cone reaches up a height of h centimetreswhich is exactly 3-y in the previous questionso substituting y = h-3 in the previous question we'll find the volume of the hourglass in terms of hπ(h−3)327+π3(6−h)(12+((h−3)/3)2+((h−3)/3)) .c) Total volume of the hourglass isV=V1+V2⇒3π4=πy327+π−π27(3−h)3Putting h=1We have the value of y as⇒3π4=π27y3+π+π278..............(1)⇒y=(54)13Differentiating the first equation with respect to t we have0=π9y2dydt+π9(3−h)2dhdtPutting values that dydt=−0.14inches/sec at h =1 and for ⇒y=(54)13We have0=π9(54)132∗(−0.14)+π922dhdt⇒0.1956π9=4π9dhdt⇒dhdt=0.19564⇒dhdt=0.0489
Related Questions
Which of the following expressions would give the number of ways to choose a group of 7 from a group
of 15?
151!/7!8!
7!/15!8!
7!15!7!
Answers
Answer:
A) 15!/(7!8!)Step-by-step explanation:
We are looking for the combination of 7 out of 15.
This is written as
15C7This is calculated as
15!/(7!(15-7)! = 15!/(7!8!)Correct choice is A
A sports store has a container of handballs: 4 blue, 5 red, 8 yellow 9 white and 11 green. If one ball is picked from the container at random,what is the probability that it will be yellow?
Answers
Answer:
8/37
Step-by-step explanation:
The total number of handballs in the container is
4+5+8+9+11 = 37
Since there are 8 yellow handballs, the probability of selecting a yellow handball is 8/37.
I need help with number 8….
Pls help
Answers
The equation properties are:
The distributive propertyThe associative property.The associative property.How to determine the properties?
The equations are given as:
3 * (6 + 2) = 3 * 6 + 3 * 25 * (7 * 8) = (7 * 5) * 85 * 3 * 7 = 7 * 3 * 5The distributive property of an equation states that:
a * (b + c) = ab + ac
This means that 3 * (6 + 2) = 3 * 6 + 3 * 2 is represented by the distributive property.
The associative property of an equation states that:
a * (b * c) = (a * b) * c
This means that 5 * (7 * 8) = (7 * 5) * 8 and 5 * 3 * 7 = 7 * 3 * 5 are represented by the associative property.
Read more about equation properties at:
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please i need someone to help me here
Answers
Answer:
See below ~
Step-by-step explanation:
No place where V has been marked∠EOF = 180° - 126° = 54°∠COE = ∠BOF = 126°∡CBF = 180°∡BCD = 54° + 63° = 117°∡BEF = 180° + 54° = 234°Which trigonometric function does the graph below represent?
Answers
Answer:
(d) 2sin(2θ +π/4) -1
Step-by-step explanation:
The graphed function has a midline of -1 (eliminates choice A). It will be a cosine function shifted right π/8 units, or a sine function shifted left π/8 units.
__
The shift is accomplished by replacing θ with (θ -π/8) in the sine function, or (θ +π/8) in the cosine function. That means, we're looking for an expression that is either of ...
2(cos(2(θ-π/8)) -1 = 2cos(2θ -π/4) -1 . . . . . no match
or
2(sin(2(θ+π/8)) -1 = 2sin(2θ +π/4) -1 . . . . . matches choice D
_____
Additional comment
In the form ...
g(x) = K·f(C(x -A)) +B
the factor K is a vertical stretch factor, C is a horizontal compression factor, A is a right shift, and B is an up shift. In this function, we have its amplitude stretched by a factor of 2, a down shift of 1 unit, and a horizontal shift of π/8. The horizontal compression factor is 2.
__
The amount of horizontal shift for the cosine function is found at the peak nearest the y-axis. The amount of horizontal shift for the sine function is found at the upward midline crossing nearest the y-axis.
A linear model A. always predicts a straight line B. always predicts a curved line C. sometimes predicts a straight line and sometimes a curved line D. usually predicts a straight line
Answers
A linear model always represents a straight line which is x + y = c. Then the correct option is A.
What is the linear system?A Linear system is a system in which the degree of the variable in the equation is one. It may contain one, two, or more than two variables.
A linear model is given as
x + y = c
In the linear model, the power of the variable is one and the equation represents on the graph as a line.
More about the linear system link is given below.
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Simplify x = cos[2 arcsin(3/5)].
-7/25
7/25
4/5
Answers
Answer:
7/25
Step-by-step explanation:
Let [tex]\theta= \arcsin(\frac{3}{5})[/tex] so we have [tex]x=\cos(2\theta)[/tex]
As [tex]\cos(2\theta)=\cos^2\theta-\sin^2\theta[/tex], we'll have [tex]\cos[2\arcsin(\frac{3}{5})]=\bigr[\cos(\arcsin(\frac{3}{5}))\bigr]^2-\bigr[(\sin(\arcsin(\frac{3}{5}))\bigr]^2[/tex]
To determine [tex]\cos(\arcsin(\frac{3}{5}))[/tex], construct a right triangle with an opposite side of 3 and a hypotenuse of 5. This is because since [tex]\theta=\arcsin(\frac{3}{5})[/tex], then [tex]\sin\theta=\frac{3}{5}=\frac{\text{Opposite}}{\text{Hypotenuse}}[/tex]. If you recognize the Pythagorean Triple 3-4-5, you can figure out that the adjacent side is 4, and thus, [tex]\cos\theta=\frac{4}{5}=\frac{\text{Adjacent}}{\text{Hypotenuse}}[/tex]. This means that [tex]\cos(\arcsin(\frac{3}{5}))=\frac{4}{5}[/tex].
Hence, [tex]\cos[2\arcsin(\frac{3}{5})]=(\frac{4}{5})^2-(\frac{3}{5})^2=\frac{16}{25}-\frac{9}{25}=\frac{7}{25}[/tex]
If you shift the exponential parent function, f(x) = 2^x , right 2 units, what is the equation of the new function?
Answers
Answer:
[tex]g(x)=2^{x-2}[/tex]
Step-by-step explanation:
Translations
For [tex]a > 0[/tex]
[tex]f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}[/tex]
[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]
[tex]f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}[/tex]
[tex]f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}[/tex]
Parent function: [tex]f(x)=2^x[/tex]
Translated 2 units right: [tex]g(x)=f(x-2)=2^{x-2}[/tex]
We know the rule for shifting right(x is changed)
f(x) —» f(x-a)So
here
For a =2
f(x-2)[tex]\sf 2^{x-2}[/tex]The distribution of professional baseball player salaries has a mean of $3.2 million. an analyst believes that the mean salary for teams on the east coast is different. the analyst randomly selects 50 baseball players from teams on the east coast and records their annual salaries. the mean salary for the players in the sample is $3.9 million with a standard deviation of $2.1 million. a significance test at an alpha level alpha = 0.05 of produces a p-value of 0.02. what is the correct interpretation of the p-value?
a. assuming the true mean salary is $3.2 million, there is a 2% probability that the null hypothesis is true by chance alone.
b.assuming the true mean salary is $3.2 million, there is a 2% probability of getting a sample mean of $3.9 million by chance alone.
c.assuming the true mean salary is $3.2 million, there is a 2% probability of getting a sample mean at least as extreme as $3.9 million by chance alone.
d.assuming the true mean salary is $3.2 million, there is a 98% probability that a sample mean of $3.9 million or one more extreme will occur by chance alone.
Answers
Answer:
c
Step-by-step explanation:
An initial deposit of $6300.00 is made into a savings account that compounds 5.2% interest semi-annually. how much is in the account after 10 years?
question 1 options:
$414,740.48
$10,526.59
$10,459.19
$9,289.13
Answers
Answer:
$10459.19
Step-by-step explanation:
Find |27|.
27
-27
i don't get it.
Answers
Answer:
|27| is 27
Step-by-step explanation:
What are you trying to ask?
Answer:
27
Step-by-step explanation:
Always in absolute value, if the number inside it is negative it will be positive. But if a number is already positive it will stay positive. Absolute value is just another way of making things positive. So always nothing will ever be negative.
Dylan has 20x + 17 baseball cards. He gives 3x - 2 cards to his friend Tristan. How many cards does Dylan now have?
Answers
Answer:
17x-15
Step-by-step explanation:
I think.
Answer:
17x+19
Step-by-step explanation:
20x+17-(3x-2) (Set up the equation)
20x+17-3x+2 (Distribute the negative to both, double negative cancel out)
17x+19 (Combine Like terms)
How many whole numbers are there from 25 to 38?
Answers
Answer:
there is 13 whole number between 25 and 38
Open the document theres my question plss help
Answers
Answer: 55°
Step-by-step explanation:
The angle is in between 50° and 60°
Answer:
55°
Step-by-step explanation:
One ray lies on the 0° mark and the other lies on the 55° mark. To find the measure of the angle, find the difference between the greater angle and the lower angle. 55° - 0° = 55°
PLEASE HELP I WILL MARK BRAINLIEST PLS IT IS URGENT
It used to take Andie 45 seconds to swim 50 meters. Now she swims the same distance in 35 seconds. What is the percent increase in her speed? Round to the nearest whole percent.
Answers
35 is 78% of 45
Sure hope this helps you
PLEASE SOMEONE HURRY I NEED THE ANSWER PLS
7. After washing your hands there are 300 bacteria on your right hand. The amount of bacteria on each of
your hands is doubling each hour. When will the amount of bacteria on your right hand exceed 2000?
A) 2 hours
B) 2½ hours
C) 3 hours
D) 3½ hours
Answers
Answer: maybe c?
Step-by-step explanation:
Uh, 300+300 = 600
600+600= 1200
1200+ 1200= 2400
If a job has salary of $470 a week, how much would it pay for a year
Answers
Answer:
$22560
step 1
$270 × 4month
=$1880 for a month
step 2
$1880×12months
= $22560
X is greater than or equal -3 and less than 5
use x only once in your inequality
Answers
Answer:
[tex] - 3 \leqslant x \leqslant 5[/tex]
Ruby owns a small business selling bagels. She knows that in the last week 4
customers paid cash, 10 customers used a debit card, and 74 customers used a credit
а
card.
If next week, she is expecting 1600 customers, about how many would you expect to
pay with cash? Round your answer to the nearest whole number.
Answers
Answer:
73 people
Step-by-step explanation:
4/10/74=88
1600/88=18.18
18.18 x 4= 73
18.18 x 10= 182
18.18 x 74= 1345
Answer: 73
Step-by-step explanation:
A circle has an arc of length 36 with central angle 40°. Find the circumference of the circle.
Answers
Answer: 324.02
Step-by-step explanation:
Radius 51.57
A convenience store manager notices that sales of soft drinks are higher on hotter days, so he assembles the data in a table, shown above. Use technology to find the equation of the least squares regression line. Then use the regression equation to predict the number of cans sold on a day that is 90*F Round your answer to the nearest whole number.
Answers
The regression equation to predict the number of cans sold on a day that is 90°F will be 871.
What is the linear system?A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.
A convenience store manager notices that sales of soft drinks are higher on hotter days, so he assembles the data in the table, shown above. Use technology to find the equation of the least-squares regression line.
Then the regression line will be passing through (55, 340) and (84, 780). Then we have
y - 340 = 15.17(x - 55)
Then the regression equation to predict the number of cans sold on a day that is 90°F will be
y - 340 = 15.17 (90 - 55)
y = 871
More about the linear system link is given below.
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Cost of a CD: $23.50
Markup: 63%
Discount: 50%
Answers
To find the cost after a percent of it was added, we just need to multiply the two together and add.
=
$
23.50
+
(
$
23.50
⋅
(
63
%
100
)
)
(we divide by 100 to get the number out of a percent)
=
$
23.50
+
(
$
23.50
⋅
0.63
)
=
$
23.50
+
$
14.81
=
$
38.31
Ok now that we have the number after the price increase, we now need to find the final answer after a discount of
50
%
(do the exact same idea as above but switch the sign)
=
$
38.31
−
(
$
38.31
⋅
(
50
%
100
)
)
=
$
38.31
−
(
$
38.31
⋅
0.5
)
=
$
38.31
−
$
19.16
=
$
19.15
HEEEEEELP
Solve for x. Leave your answer in simplest radical form.
Answers
Answer:
Here is the answer hope it helps:)
Help me solve the volume for the sphere?
Answers
Answer:
38.77 yd³
Step-by-step explanation:
The volume of the sphere can be determined by using the formula 4πr³/3.
[Where "r" is the radius of the circle].
We are given that:
Radius of circle = 2.1 yd
When we substitute the radius in the formula, we get;
⇒ 4 × π × (2.1)³/3
Let π be substituted as 3.14. Then;
⇒ 4 × π × (2.1)³/3
⇒ 4 × (3.14) × (2.1)³/3
When evaulating the cube of 2.1, we get;
⇒ 4 × (3.14) × (2.1)³/3
⇒ 4 × (3.14) × (2.1) × (2.1) × (2.1)/3
When simplified, we get;
⇒ 4 × (3.14) × (2.1) × (2.1) × (2.1)/3
⇒ 4 × (3.14) × (2.1) × (2.1) × (0.7)
⇒ 4 × (3.14) × (4.41) × (0.7)
⇒ (12.56) × (4.41) × (0.7)
⇒ 38.77272 ≈ 38.77 yd³ (Rounded to nearest hundredth)
Therefore, the volume of the sphere is 38.77 yd³.
What is the value of x?
99°
35°
81
55
46
134
Answers
Answer: 46
Step-by-step explanation:
The angles add to form a straight angle, so x+99+35=180. It follows that x=46.
Which two Integers is 29 between
Answers
Answer:
28 < 29 < 30
Step-by-step explanation:
29 - 1 = 28
29 + 1 = 30
Then
The integer 29 is between the two integers 28 and 30
Please answer the question
Answers
45/50
explanation:
If there are 50 numbers in a hat, and 5 of them are the number 10. 50 - 5 = 45 which means 45 of the numbers are not 10. Therefore the probability of not drawing 10 would be 45/50.
Which parallelogram has an area of 60 square units?
Answers
Answer:
Finding the area of each parallelogram, applying the formula, it is found that the parallelogram D has an area of 60 square units
Step-by-step explanation:
Similarly to a rectangle, the area of a parallelogram is given by height multiplied by base, that is:
In item A, the height is of 15 units and the base is of 10 units, thus, the area, in square units, is of .
In item B, the height is of 6 units and the base is of 10.2 units, thus, the area, in square units, is of .
In item C, the height is of 15 units and the base is of 15 units, thus, the area, in square units, is of .
In item D, the height is of 10 units and the base is of 6 units, thus, the area, in square units, is of , which means that this is the correct option.
The area of a square with side length of 5 cm is ___________ cm.
Answers
Answer:
25cm
Step-by-step explanation:
5 x 5 its not that hard
2 cm
6 cm
6 cm
What is the surface area of the solid above?
O A. 14 cm2
O B. 120 cm2
O C. 56 cm2
O D. 84 cm2
Answers
Answer:
O B. 120 cm2
Step-by-step explanation:
2×(6×6 + 6×2 + 6×2) = 120 centimeters2
