An asprin tablet in a shape of a right circular cylinder has the height of 2/5 cm and the raidus of 1/2cm. the manufacturer also wishes to market the asprin in capsule form. The capsule is to be 5/3cm in total length, in the shape of a right cylinder with hemispheres attached to both ends . find a function that represents the volume of the capsule. fund the radius of the capsule so that it is the same volume of the tablet.

Answers

Answer 1

Answer:

The function that represents the volume of the capsule will be V = πr²h + (4/3)πR³. And the radius will be 19/30 cm.

What is the volume?

Volume is a measurement of three-dimensional space that is utilized.

An aspirin tablet in a state of a right round chamber has a level of 2/5 cm and a radius of 1/2cm. the producer additionally wishes to advertise the aspirin in container structure. The case is to be 5/3cm in complete length, looking like a right chamber with halves of the globe connected to the two finishes.

The radius of the hemisphere is calculated as,

R = [(5/3) - (2/5)] / 2

R = 19 / 30 cm

The function that represents the volume of the capsule is given as,

V = πr²h + 2[(4/3)πR³ / 2 + (4/3)πR³ / 2]

V = πr²h + (4/3)πR³

V = π(1/2)²(2/5) + (4/3)π(19/30)³

V = 0.1 π + 0.3387 π

V = 1.378 cm³

The function that represents the volume of the capsule will be V = πr²h + (4/3)πR³. And the radius will be 19/30 cm.

More about the volume link is given below.

brainly.com/question/1578538

#SPJ2

Answer 2

Answer: Volume of the tablet is height times pi r squared = .4cm x pi x .5^2 = pi cm^3So, the tablet has a volume of pi cubic centimeters (cc).We want the capsule to have the same volume. The two hemispherical ends put together make one sphere. The volume of a sphere is 4/3 pi r^3. And the cylindrical part is the same formula as the first one, but we don't know what r is,height x pi x r^2.pi cc = height x pie x r^2 + 4/3 pi r^3 Here, we took the value from the original problem and made it equal to the two ends of the capsule (together were the sphere) PLUS the rest (which is a cylinder.)Now, divide everything by pi to factor it out of the equation.cc = height x r^2 + 4/3 r^3 The problem told us that the total length is 5/3 cm, this means the cylinder height + the radius times two = 5/3. (Wish I could draw you a picture) So height in the equation at the beginning of this paragraph is 5/3 - 2r.Now we have volume in cc = (5/3 - 2r)r^2 + 4/3 r^3 =5/3r^2 - 2r^3 + 4/3r^3simplified by combining common terms, and written in standard form,volume in cc = 2 r^3 + 5/3 r^2 = 1 = r^2 ( r - 5/3) , factoring out the r^2.this means that r^2 is the reciprocal of r - 5/3, or r^2 = 1/(r - 5/3), and this is a quadratic equation.r^2 - r + .6 = 0 and r^2 -r + .25 = -.6 + .25 by completing the squareor (r - .25)^2 = -.35. Solve for r: square root of r - .25 = square root of .35 or .59r = .84 cm

Related Questions

A scientist has two solutions, which she has labeled Solution A 60% and Solution B 75% Each contains salt. She knows that Solution A is salt and Solution B is salt. She wants to obtain ounces of a mixture that is salt. How many ounces of each solution should she use
The center of a hyperbola is located at (0, 0). One focus is located at (0, 5) and its associated directrix is represented by the line y = . Given the standard form of the equation of a hyperbola, what are the values of a and b?
Points, in case you need to ask a question.
The sales tax in Bill's state is 6%. Bill bought a Scion having a sales tax of $820. What was the cost of the car? Round to the nearest dollar. A. $13,666 B. $13,668 C. $13,665 D. $13,667
When calculating simple interest, what must you do if you want to invest for months or weeks instead of years? a. Simple interest only pays yearly, so you should find another investment. b. The simple interest calculation does not use those units, so you should just calculate as normal. c. The units have changed, so the interest formula switches to I·t=P·r. d. Interest rates are annual, so you must convert the units into years

mike has 350.75 while jane has 250.25 .if they spent together a total amout of 295.50 and saved remaining amount how much they put together in the saving box?

Answers

Answer:

305.5

Step-by-step explanation:

350.75 + 250.25 = 601

601 - 295.50 = 305.50

What are the constraints of using transportable tablespaces? (Choose two.) A) The source and target character sets must match. B) The source and target database versions must match. C) The source and target platforms must match. D) The source and target time zone versions must match.

Answers

Answer:

The answer is B

Step-by-step explanation:

I took the assignment

4. Find the sum of the first eighteen terms of the arithmetic sequence whose nthterm is an = 15 + 8n.
a. 1438
b. 1638
c. 1836
d. 1783

Answers

Answer:

The sum of first eighteen terms of the arithmetic sequence is $\mathbf{S_(18)=1638}$

Option B is correct option.

Step-by-step explanation:

We need to find the sum of the first eighteen terms of the arithmetic sequence whose nth term is an = 15 + 8n

The formula used to calculate sum of arithmetic sequence is: $S_n=(n)/(2)(a_1+a_n)$

Finding a₁ by putting n=1

$a_n=15+8n\na_(1)=15+8(1)\na_(1)=15+8\na_(1)=23$

We have $a_1=23$

Finding 18th term n=18

$a_n=15+8n\na_(18)=15+8(18)\na_(18)=15+144\na_(18)=159$

So, the sum of first eighteen terms of the arithmetic sequence is:

$S_n=(n)/(2)(a_1+a_n)\nS_(18)=(n)/(2)(a_1+a_(18))\nS_(18)=(18)/(2)( 23+159)\nS_(18)=9(182)\nS_(18)=1638$

So, the sum of first eighteen terms of the arithmetic sequence is $\mathbf{S_(18)=1638}$

Option B is correct option.

Which number is equivalent to 3⁴÷3² This problem comes straight from a standardized test given in New York in 2014.

Answers

Answer:

Step-by-step explanation:

3^4 / 3^2 = 3^(4 - 2)

= 3^2
= 9

Tim has developed a money saving strategy that uses the formula S=450+100r.a. Give a possible interpretation of Tim's strategy.

b. What do the slope and S-intercept of the graph of the relation represent, base on the interpretation from part a.?

c. If Tim plans to stop his savings once he has accumulated $1250, what are the domain and range of this relation.

Answers

Answer:

Step-by-step explanation:

Given that Tim has developed a money saving strategy that uses the formula S=450+100r.

a) 450 will be savings always and for every r an additional 100 would be saved

b) Slope = 100 represents the increase of S for a unit increase of 1.

S intercept = 450 is the savings even when r=0

c) Since max savings is 1250 and min is 450

Range = (450,1250)

For 450 range, domain r =0 and for range 1250, domain r = 8

Domain =(0,8)

A) For 100R, that might mean every week, he is putting 100 dollars away for an interpretation.
B) The Slope represents the time it takes to make 100 dollars, and S represents the total amount of money Tim has.
C) If Tim got to 1250 dollars, it would be 8 for R. So 8 would be the domain and 1250 for the range.

Solve the system of equations algebraically. Show all of your steps.
y=x^2+2x
y=3x+20

Answers

do you have to get both x and y?

Answer:

x = -4

Y = 8

Step-by-step explanation:

Other Questions

Help with these 2 questions please?? Check my answers. The height of a triangle is 13 in. less than its base. If the area of the triangle is 24 in2, what is the length of the base? 3 in.10 in.<------16 in.21 in.Madison hits a tennis ball with an initial velocity of 18 m/s straight up into the air. When she hits the ball, it is 1.2 m above the ground. Which equation can be used to find the time, t, it takes for the ball to reach the ground? –4.9t2 + 18t + 1.2 = 0–16t2 + 18t + 1.2 = 0<-------–4.9t2 + 1.2t + 18 = 0–16t2 + 1.2t + 18 = 0

Which of the following is the solution to (x-13)<18

The variables x and y are directly proportional, and y = 2when x = 3. What is the value of y when x = 9 ?

Find the value of the sec 19° using your calculator.A. 0.989 B. 0.946 C. 1.058 D. 1.011