Mathematics College

Look at the cups shown below (images are not drawn to scale): A cone is shown with width 2 inches and height 4 inches, and a cylinder is shown with width 2 inches and height 6 inches. How many more cubic inches of juice will cup B hold than cup A when both are completely full? Round your answer to the nearest tenth.

Answers

Answer 1

The formula for the volume of a cone is ...

... V = (1/3)πr²h = (1/3)π(d/2)²h = (π/12)d²h

for height h and diameter d.

Then the volume of the cone is ...

... V = (π/12)·(2 in)²·(4 in) = 4π/3 in³ ≈ 4.189 in³

___

The formula for the volume of a cylinder is ...

... V = πr²h = π(d/2)²h = (π/4)d²h

Then the volume of the cylinder is ...

... V = (π/4)·(2 in)²·(6 in) = 6π in³ ≈ 18.850 in³

_____

The difference in volume is ...

... 18.850 in³ - 4.189 in³ = 14.661 in³ ≈ 14.7 in³

Related Questions

Prove that for any positive integer n a field f can have at most a finite number of elements of multiplicative order at most n

Answers

Let's assume multiplicative order is infinite. Then [tex]x^k=1, \forall k=1(1)n[/tex]. In the field [tex]F[/tex] the solution of the polynomial [tex]x^k-1=0[/tex] can have at most [tex]k[/tex] distinct solutions. Hence for any [tex]k=1(1)n[/tex] we cannot have infinite roots. And thus the result follows.

Evaluate the integral by interpreting it in terms of areas. 0 4 + 36 − x2 dx −6

Answers

Answer: Split up the integral. â«(-6 to 0) [2 + sqrt(36 - x^2)] dx = â«(-6 to 0) 2 dx + â«(-6 to 0) sqrt(36 - x^2) dx. The first integral represents the area of a rectangle with base length 6 and height 2. ==> â«(-6 to 0) 2 dx = 6 * 2 = 12. The second integral you figured correctly to be (1/4) Ď€ * 6^2 = 9Ď€. So, the final answer is 12 + 9Ď€.

Final answer:

To evaluate the integral by interpreting it in terms of areas, we can break it down into two parts: the integral from 0 to 4 of 36 - x^2, and the integral from 0 to -6 of 36 - x^2. This represents the area between the curve and the x-axis.

Explanation:

To evaluate the integral by interpreting it in terms of areas, we can break it down into two parts: the integral from 0 to 4 of 36 - x^2, and the integral from 0 to -6 of 36 - x^2. Since the function is given as 36 - x^2, it represents the area between the curve and the x-axis. The integral from 0 to 4 represents the area between the curve and the x-axis above the x-axis, while the integral from 0 to -6 represents the area between the curve and the x-axis below the x-axis.

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Determine the quadrant when the terminal side of the angle lies according to the following conditions: sin (t) > 0, cos (t) < 0.

Answers

Check the problem again!Cosecant (csc) is the reciprocal of sine (sin) so they are always either both positive or both negative. Perhaps it should be sine < 0 and cosine > 0? In that case, sine is less than zero in quadrants 3 and 4, and cosine is greater than zero in quadrants 1 and 4, so this angle can only lie in quadrant 4. On the unit circle, remember that cosine is the x-coordinate of the terminal side of the angle and sine is the y-coordinate. Quadrant 1 is that where both sine and cosine are greater than zero. The rest of them are numbered consecutively going counter-clockwise; so quadrant 2 has cos < 0 and sin > 0, quadrant 3 has cos < 0 and sin < 0, and quadrant 4 has cos > 0 and sin < 0

Clay is playing darts. his dartboard contains ten equal-sized zones with point values from 1 to 10. write code that simulates his total score after 1000 dart tosses. make sure to use a for loop.

Answers

Instead of a real language, I'll use pseudo code here:

var TOTAL_SCORE = 0
for(var x; i<1000; i++) {
var SCORE rand.random_integer[from 1-10];
var TOTAL SCORE = TOTAL_SCORE + SCORE;
}

print(TOTAL_SCORE);

Answer:

Given parameters

Point values = 1 to 10 = 1,2,3...10

Dart tosses = 1000

Required:

Simulate total scores using a for loop

#This program is written using Python Programming Language

# Comments are used for explanatory purpose

#Program starts here

# The next line declares and initialize point_value as an array

point_value = make_array(1,2,3,4,5,6,7,8,9,10)

# The next line initializes total_score to 1

total_score =make_array(0)

# Initialise number of toss

tosses = 1000

# Simulate using for loop iteration

for i in np.arange(tosses)

result = np.random.choice(point_value)

# get score after playing each toss

total_score=np.append(total_score, result)

#calculate totalscores after 1000 games

totalscore=sum(total_score)

#Output result

print("The total score after simulation of 1000 tosses is ")

print(totalscore)

#End of program

The price of stamps just increased by $0.03. Beth wants to send out 30 party invitations. Write a formula that will help her determine how much it will cost. Let’s let p=old price per stamp
t=total cost for stamps

Answers

t = 30 ( 0.03 + p )
hope it helps

the answer would be t=30x0.03p im pretty sure

Which expression is equivalent to −4.6+(−0.4)+(−7.2) ?

−(4.6−0.4)+(−7.2)

(4.6+0.4+7.2)

−4.6−(0.4+7.2)

(4.6+0.4)+(−7.2)

Answers

I took the test it's −4.6−(0.4+7.2)

The expression equivalent to −4.6+(−0.4)+(−7.2) is -4.6 - ( 0.4 + 7.2 )

Here,

The given expression is −4.6+(−0.4)+(−7.2)

We have to find expression equivalent to −4.6+(−0.4)+(−7.2)

What is Number system?

A number system is defined as a system of writing to express numbers. It is the mathematical notation for representing numbers of a given set by using digits or other symbols in a consistent manner.

Now,

The given expression is,

−4.6+(−0.4)+(−7.2) = -4.6 - 0.4 - 7.2

= -4.6 - (0.4 + 7.2) ( we take common negative sign )

Hence,

The expression equivalent to −4.6+(−0.4)+(−7.2) is -4.6 - ( 0.4 + 7.2 ).

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Compute the maximal area obtainable if we assume that the farmer builds a field in the shape of an isosceles triangle, where the two equal sides are the fenced sides, and the third side is the river.

Answers

Final answer:

The maximal area of an isosceles triangle-shaped field by the river is achieved when the triangle is also a right triangle. The area can be maximized by using the derivative of the area expression, considering the sides of the triangle and the fixed perimeter.

Explanation:

The question is asking to find the maximal area of an isosceles triangle-shaped field with two equal sides and the third side being the river.

To maximize the area of an isosceles triangle, the height of the triangle should be as large as possible, which occurs when the triangle is also a right triangle. The side opposite the right angle, which lies along the river, will be the base of the triangle.

By applying the Pythagorean theorem, if we have a fixed perimeter and the two equal sides are 'a' and 'a', and the base 'b' is along the river, we can express the area 'A' as A = (b/2) × √(a² - (b/2)²).

The area is maximized when the derivative of this area expression with respect to 'b' equals zero.

how do I set up 37 and 43

Answers

37)

keep in mind that the perimeter of a rectangle is length + length + width + width or P = 2l + 2w, or P = 2(l+w).

we know the perimeter of the box's width and length is 36, therefore then

[tex]\bf \stackrel{P}{36}=2(\stackrel{length}{l}+\stackrel{width}{w})\implies 18=l+w\implies \boxed{18-w=\stackrel{length}{l}} \\\\\\ V(w)=4(w)(18-w)\implies V(w)=-4w^2+72w[/tex]

check the first picture below.

now, that parabolic graph, goes up up up reaches a U-turn and the back down, so it has a "maximum" point, and that is when the volume is the highest, namely V(w).

[tex]\bf \textit{ vertex of a vertical parabola, using coefficients}\\\\ \begin{array}{lccclll} V(w) = &{{ -4}}w^2&{{ +72}}w&{{ +0}}\\ &\uparrow &\uparrow &\uparrow \\ &a&b&c \end{array}\qquad \left(-\cfrac{{{ b}}}{2{{ a}}}\quad ,\quad {{ c}}-\cfrac{{{ b}}^2}{4{{ a}}}\right) \\\\\\ {{ c}}-\cfrac{{{ b}}^2}{4{{ a}}}\implies \stackrel{maximum~volume}{0-\cfrac{72^2}{4(-4)}}[/tex]

43)

is pretty much the same thing, checking the vertex coordinates of the parabola, check the second picture below,

[tex]\bf h=64t-16t^2\implies h=-16t^2+64t+0\\\\\\ \textit{ vertex of a vertical parabola, using coefficients}\\\\ \begin{array}{lccclll} h = &{{ -16}}t^2&{{ +64}}t&{{ +0}}\\ &\uparrow &\uparrow &\uparrow \\ &a&b&c \end{array}\qquad \left(-\cfrac{{{ b}}}{2{{ a}}}\quad ,\quad {{ c}}-\cfrac{{{ b}}^2}{4{{ a}}}\right) \\\\\\ \stackrel{\textit{it takes this many seconds}}{-\cfrac{64}{2(-16)}}\qquad \qquad \stackrel{\textit{it went up this many feet}}{0-\cfrac{64^2}{4(-16)}}[/tex]

Find an equation in standard form for the hyperbola with vertices at (0, ±10) and asymptotes at y = ± five divided by six times x.. (2 points)

Answers

Refer to the diagram shown below.

In the diagram, the two vertices are located at (0, a) and (0, -a).
The equation for the parabola is
[tex] \frac{y^{2}}{a^{2}} - \frac{x^{2}}{b^{2}} =1[/tex]
The asymptotes have the equations
[tex]y= \pm \frac{a}{b} x[/tex]

For the given problem,
The vertices are located at (0, +/-10).
Therefore a = 10.

The asymptotes are
[tex]y = \pm \frac{5}{6} x[/tex]
Therefore
[tex] \frac{a}{b} = \frac{10}{b} = \frac{5}{6} \\\\ 5b = 60 \\\\ b =12[/tex]

Answer:
The equation of the parabola is
[tex] \frac{y^{2}}{100} - \frac{x^{2}}{144} =1[/tex]

HELP ASA AND EXPLAIN!!
there is 2 attachments btw pppllzzz explain both of them

Answers

First problem.

3a - 4 <= 5

Add 4 to both sides.

3a <= 9

Divide both sides by 3.

3a/3 <= 9/3

a <= 3

Second problem.

n/(-3) + 5 > 4

Subtract 5 from both sides

n/(-3) > -1

Multiply both sides by -3.
When you multiply or divide both sides of an inequality by a negative number, the inequality sign switches direction.

n/(-3) * (-3) < -1 * (-3)

n < 3

What is 0.003 of 1/10 as much as

Answers

The answer to this is 0.03

Find the general solution of the given differential equation. x2y' + x(x + 2)y = ex

Answers

[tex]x^2y'+x(x+2)y=e^x[/tex]
[tex]x^2e^xy'+x(x+2)e^xy=e^{2x}[/tex]
[tex]\bigg(x^2e^xy\bigg)'=e^{2x}[/tex]
[tex]x^2e^xy=\dfrac{e^{2x}}2+C[/tex]
[tex]y=\dfrac{e^x}{2x^2}+\dfrac C{x^2e^x}[/tex]

Which equation has no solution? 4(x + 3) + 2x = 6(x + 2) 5 + 2(3 + 2x) = x + 3(x + 1) 5(x + 3) + x = 4(x + 3) + 3 4 + 6(2 + x) = 2(3x + 8)

Answers

Answer:

the answer is 5+2(3+2x)=x +3 (x+1)

Step-by-step explanation:

The equation second 5+2(3+2x)=x +3 (x+1) has no solution.

We have given that,

4(x + 3) + 2x = 6(x + 2)

5 + 2(3 + 2x) = x + 3(x + 1)

5(x + 3) + x = 4(x + 3) + 3

4 + 6(2 + x) = 2(3x + 8)

We have determine which equation has no solution.

When equation has no solution?

The constants are the numbers alone with no variables. If the coefficients are the same on both sides then the sides will not equal, therefore no solutions will occur.

Therefore the equation second has no solution

[tex]5+2\left(3+2x\right)=x+3\left(x+1\right)[/tex]

[tex]4x+11=x+3x+3[/tex]

[tex]4x+11=4x+3[/tex]

[tex]4x+11-11=4x+3-11[/tex]

[tex]0=-8[/tex]

[tex]\mathrm{The\:sides\:are\:not\:equal}[/tex]

Therefore the second equation has no solution.

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A total of 428 tickets sold for the school play. They were either adults tickets or student tickets. The number of students tickets sold was three times the number of adult tickets sold. How many adults tickets were sold.

Answers

107 Adult tickets were sold.

Total tickets sold = 428

428÷4=107 (split into four equal groups)

107×3=321 (amount of student tickets sold) (this is 3/4 of the total amount sold)

107×1=107 (amount of adult tickets sold) (this is 1/4 of the total amount sold)

321+107=428 (amount of tickets sold total)

321 (amount of student tickets sold) is three times the number of adult tickets sold. (107) 107×3=321

Final answer:

107 adult tickets were sold for the school play.

Explanation:

Let's denote the number of adult tickets sold as x. According to the given information, the number of student tickets sold is three times the number of adult tickets sold. So, the number of student tickets sold would be 3x. The total number of tickets sold is 428, so we can set up the equation:

x + 3x = 428

Combining like terms, we have:

4x = 428

Dividing both sides of the equation by 4, we find:

x = 107

Therefore, 107 adult tickets were sold.

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A white-tailed deer can sprint at speeds up to 30 miles per hour. American bison can run at speeds up to 3,520 feet per minute. Which animal is faster and by how many miles per hour? There are 5,280 feet in one mile. 1)A deer is 10 miles per hour faster than a bison. 2)A bison is 10 miles per hour faster than a deer. 3)A deer is 0.66 miles per hour faster than a bison. 4)A bison is 0.66 miles per hour faster than a deer.

Answers

b i belive xd have to ad 20 words

The second option is the correct answer. A bison is 10 miles per hour faster than a deer.

Suppose another sample of 41 students is to be randomly selected from this population. find the probability that the mean of this sample is greater than 110.

Answers

<110 greater then 110

what is 75% of 400? Write an evaluate an expression to find the answer. Then explain how to use the model to justify the answer

Answers

Answer:

Step-by-step explanation: love your self

What is 225 percent as a decimal or fraction in simpilist form

Answers

225/100

225 ÷ 25 = 9
100 ÷ 25 = 4

So, 225% as a fraction in it's simplest form would be 9/4

If you want 225% as a decimal:

225/100
225 ÷ 100 = 2.25

So, 225% as a decimal in its simplest form would be 2.25

I really hope this helped you! c:

{$7.04,$7.04,$7.05,$11.99,$12.50,$12.99,$9.98,$9.99,$8.51,$11.95}
What is the mode?
What is the median?
What is the mean?
What is the IQR?

Answers

Final answer:

The mode of the given data set is $7.04, the median is $9.99, the mean is $9.634, and the IQR is $3.48.

Explanation:

The mode of the given set is $7.04, as it occurs the most number of times.

The median is $9.99, which is the middle value when the data is arranged in ascending order.

The mean can be calculated by finding the sum of all the values and dividing it by the total number of values. In this case, the mean is $9.634.

The IQR (Interquartile range) is the difference between the third quartile and the first quartile. To find the IQR, we need to first calculate the quartiles. First, we arrange the data in ascending order: $7.04, $7.04, $7.05, $8.51, $9.98, $9.99, $11.95, $11.99, $12.50, $12.99. The first quartile is the average of the 3rd and 4th values, which is $8.51. The third quartile is the average of the 8th and 9th values, which is $11.99. Therefore, the IQR is $11.99 - $8.51 = $3.48.

How many five digit zip codes are possible if digits cannot be repeated?

Answers

1st digit - 0-9 = 10 numbers

2nd digit = 9 numbers

3rd digit = 8 numbers

4th digit = 7 numbers

5th digit = 6 numbers

10 * 9 * 8 * 7 * 6 = 30,240 zip codes

Solve the equation. 6^2x-4=14701 to 4 decimal places. (Doing Logs)

Answers

6^(2x-4) = 14701

Take the log on both sides to find x.

log[6^(2x-4) = log(14701)

(2x-4)log6 = log(14701)

Take it from here.

A coin is tossed 5 times. let x count the number of heads tossed. determine x hhtht ( ).

Answers

Given that x counts the number of heads tossed

If the sequence of the results of the coin toss is HHTHT, it can be seen that there are 3 heads tossed.

Therefore, x(HHTHT) = 3

Given that x counts the number of heads tossed

If the sequence of the results of the coin toss is HHTHT, it can be seen that there are 3 heads tossed.

Therefore, x(HHTHT) = 3 i that help u

How do transformations affect the logarithmic graph?

Answers

Transformations of log graphs follow the same rules as do other transformations.

Begin with the example y=log x and its graph. Then the graph of y=log (x-a) is the same as that of y=log x, except that the whole graph is translated to the right by a units.

What specifically would you like to know beyond this?

How many solutions does the following equation have?

|3x + 12| = 18 (5 points)

No solution
One solution
Two solutions
Infinitely many solutions

Answers

It is an absolute value equation so there will be 2 solutions
x = -10
x = 2

An implicit equation for the plane passing through the point (-1,-4,5) that is perpendicular to the line l(t) = <1+2t,1+t,5+3t> is

Answers

Final answer:

The implicit equation of the plane is 2x + y + 3z - 14 = 0, found using the direction vector of the line as the normal vector for the plane and the given point to determine the specific plane equation.

Explanation:

To find an implicit equation for the plane passing through the given point (-1,-4,5) and perpendicular to the given line, we need to determine the direction vector of the line which will also serve as the normal vector to the plane. The equation of the line is given as l(t) = <1+2t, 1+t, 5+3t>, which suggests that the directional vector of the line (and thus the normal vector of the plane) is <2, 1, 3>.

Now, the general equation of a plane in 3D space can be given by Ax + By + Cz + D = 0, where <A, B, C> is the normal vector to the plane. Thus, substituting the normal vector and the given point into this equation will allow us to find the value of D and hence the implicit equation of the plane. In this case, the equation is given by:

2(x + 1) + 1(y + 4) + 3(z - 5) = 0, simplifying this gives:

2x + y + 3z - 14 = 0,

which is the implicit equation of the desired plane.

Final answer:

The implicit equation of the plane passing through the point (-1, -4, 5) and perpendicular to the line ℒ(t) is 2x + y + 3z - 9 = 0.

Explanation:

To find an implicit equation for a plane that is perpendicular to a given line, we first need the direction vector of the line. The line ℒ(t) = <1+2t, 1+t, 5+3t> has a direction vector of <2, 1, 3>, which also serves as the normal vector of the plane. The normal vector (A, B, C) and a point (x0, y0, z0) on the plane can provide an equation via the dot product: A(x - x0) + B(y - y0) + C(z - z0) = 0.

For the given point (-1, -4, 5), the equation becomes 2(x + 1) + 1(y + 4) + 3(z - 5) = 0. Simplifying, we get:

2x + 2 + y + 4 + 3z - 15 = 0

2x + y + 3z - 9 = 0

This is the implicit equation of the plane that passes through the point (-1, -4, 5) and is perpendicular to the given line.

A student expressed a sum of two whole numbers as 3 x (2 + 5). What were the two whole numbers?

Answers

your answer is 6 + 15, because the two numbers had a common factor, and could use distribute law to find the results.

What is the inverse of the statement? A number that has exactly two distinct factors is prime.

Answers

If an angle doesn’t have two distinct factors, it isn’t prime.

Answer:

The inverse statement is

"A number that does not has exactly two distinct factors is not prime"

Step-by-step explanation:

Given a statement we have to tell the inverse of that statement.

The given statement is

"A number that has exactly two distinct factors is prime".

We have to write the inverse of the above statement.

The inverse of the statement is

"A number that does not has exactly two distinct factors is not prime"

Foston is between library and West Quan and is 4 inch away from the library on the map how far is Boston from West qual

Answers

Boston would be 8 inches away on a map from WQ, because the library is in between Boston and WQ, and the library is 4 inches away from Boston, so, logically, it would be about 4 inches away from WQ, too.

Thus, Boston is 8 inches away from WQ.

Final answer:

Boston is 4 inches away from West Quan.

Explanation:

Foston, positioned between the Library and West Quan on the map, is noted as being 4 inches away from the Library. Given that Library and West Quan lie on the same line, it can be inferred that Foston and West Quan share the same 4-inch separation. Consequently, the distance from Boston to West Quan is deduced to be 4 inches. This deduction is based on the assumption that the spatial relationship between Foston, Library, and West Quan forms a straight line. Therefore, the proximity of Foston to the Library serves as a reference for determining the distance between Foston and West Quan, establishing it at 4 inches.

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Your great aunt sally loans you $5000 for three years and asks that you repay it with annually compounding interest at the rate of 8% per year. how much do you repay her after three years?

Answers

$1,875
5,000÷8×3=1,875

The gasoline tank of a minivan holds 18 gallons. How many quarts can the tank hold?

Answers

72 quarts
1 gallon = 4 quarts
18 times 4 = 72 quarts.

To convert 18 gallons to quarts, multiply by the conversion factor of 4 quarts per gallon, giving a result of 72 quarts.

The gasoline tank of a minivan holds 18 gallons. To determine how many quarts it can hold, we need to use the conversion factor that 1 gallon is equivalent to 4 quarts. Since we are converting from a larger unit to a smaller unit, we will multiply the number of gallons by 4.

18 gallons x 4 quarts/gallon = 72 quarts

Therefore, the minivan's gasoline tank can hold 72 quarts of gasoline.

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