Mathematics College

The height of a grain of a cylindrical silo is is increasing at a constant rate of 4 feet per minute At what rate is the volume of grain in the cylinder if the radius of the silo is 10 feet? 
Just need the set up of the derivative 

Answers

Answer 1
the answer is 2 min and 30 sec

Related Questions

Jorge says there are 198 inches in 5.5 yards. Is he correct?

Answers

yess Jorge is correct
36 inches in 1 yard so
5 times 36=180
1/2 of 36( to get the.5) = 18
180+18= 198
so he is right

Of the 50 tables in a restaurant, 40% seat 2 people. The remaining tables seat 4 people. How many seats are there in the restaurant?

Answers

Okay. 40% of 50 is 20. 2 * 20 is 40. The other 30 tables seat 4 people. 4 * 30 is 120. 120 + 40 is 160. There are 160 seats in the restaurant.

Answer: 160 seats

Step-by-step explanation: Got it right on TTM

How much water should be added to 1 gallon of pure antifreeze to obtain a solution that is 35% antifreeze?

To obtain a 35% antifreeze solution, □ gallon(s) of water should be added
(Simplify your answer.)

Answers

Final answer:

To obtain a 35% antifreeze solution, you need to add approximately 1.857 gallons of water to 1 gallon of pure antifreeze.

Explanation:

To obtain a 35% antifreeze solution, you need to add a certain amount of water to 1 gallon of pure antifreeze. Let's assume that x gallons of water should be added. In a 35% antifreeze solution, the amount of antifreeze is 35% of the total solution. So, we can set up the following equation:

1 gallon of antifreeze = (35/100) * (1 + x) gallons of solution

Simplifying this equation, we get:

1 = 0.35 * (1 + x)

Now, let's solve for x:

Divide both sides of the equation by 0.35:

1/0.35 = 1 + x

2.857 = 1 + x

Subtract 1 from both sides of the equation:

2.857 - 1 = x

x = 1.857 gallons of water

Therefore, you need to add approximately 1.857 gallons of water to 1 gallon of pure antifreeze to obtain a 35% antifreeze solution.

Final answer:

To obtain a 35% antifreeze solution from 1 gallon of pure antifreeze, approximately 1.857 gallons of water needs to be added. This calculation is based on a simple concentration equation, resulting in the given ratio.

Explanation:

To calculate the amount of water to be added to 1 gallon of pure antifreeze to obtain a solution that is 35% antifreeze, we need to perform a simple concentration calculation.

We are starting with pure antifreeze, so it's 100% antifreeze. We want to end with a solution that is 35% antifreeze. Let's denote the amount of water added as x gallons. Because we are diluting the antifreeze, the total volume of the solution after adding water will be 1 gallon (the initial volume of the antifreeze) plus x gallons (the volume of water added).

The concentration of antifreeze after adding water is the volume of antifreeze divided by the total volume of the solution:

Concentration of antifreeze = Volume of antifreeze / Total volume of solution

Thus, 0.35 = 1 / (1 + x)

Multiplying both sides by (1 + x) and then by 0.35 we get:

1 = 0.35 * (1 + x)

Dividing by 0.35 and then subtracting 1:

x = 1 / 0.35 - 1

After calculating:

x ≈ 1.857 gallons

To obtain a 35% antifreeze solution, approximately 1.857 gallons of water should be added.

The LCD for the fractions 1/3, 3/4, 5/32, and 8/9 is

Answers

In order to find the least common denominator we need to find the common multiple between the denominators of 3, 4, 32, and 9 and once we get that we have our answer.

Answer: LCD is 288.
Hello There!

Factor them by their prime factors:
3  =  3
4 = 2 x 2 or 2²
32 = 2 x 2 x 2 x 2 x 2 or [tex] 2^{5} [/tex]
9 = 3 x 3 or 3²

Since you can divide 32 by 4 and 9 by 3, you only need to use 32 and 9.

LCD = 2 x 2 x 2 x 2 x 2 x 3 x 3
LCD = [tex] 2^{5} [/tex] x [tex] 3^{2} [/tex]
LCD = 288

Hope This Helps You!
Good Luck :) 

- Hannah ❤

The area of a regular octagon is 35 cm^2. What is the area of a regular octagon with sides five times as long?
A. 625 cm^2
B. 875 cm^2
C. 175 cm^2
D. 245 cm^2

I'm not very good at this kind of stuff :/

Answers

so... let's say the smaller regular octagon has sides of "x" long, then the larger octagon will have sides of 5x.

[tex]\bf \qquad \qquad \textit{ratio relations} \\\\ \begin{array}{ccccllll} &Sides&Area&Volume\\ &-----&-----&-----\\ \cfrac{\textit{similar shape}}{\textit{similar shape}}&\cfrac{s}{s}&\cfrac{s^2}{s^2}&\cfrac{s^3}{s^3} \end{array} \\\\ -----------------------------\\\\ \cfrac{\textit{similar shape}}{\textit{similar shape}}\qquad \cfrac{s}{s}=\cfrac{\sqrt{s^2}}{\sqrt{s^2}}=\cfrac{\sqrt[3]{s^3}}{\sqrt[3]{s^3}}\\\\ -------------------------------\\\\[/tex]

[tex]\bf \cfrac{small}{large}\quad \stackrel{area~ratio}{\cfrac{s^2}{s^2}}\implies \stackrel{area~ratio}{\cfrac{x^2}{(5x)^2}}\implies \stackrel{area~ratio}{\cfrac{x^2}{5^2x^2}}\implies \stackrel{area~ratio}{\cfrac{\underline{x^2}}{25\underline{x^2}}}=\stackrel{area~ratio}{\cfrac{35}{a}} \\\\\\ \cfrac{1}{25}=\cfrac{35}{a}\implies a=\cfrac{25\cdot 35}{1}[/tex]

there are 28 tables in the cafeteria.each table has 12 students sitting at it.fourth graders sit at 13 of the yables.fifth graders sit at the rest of the tables.how many fifth graders are there?

Answers

Hope this helps!

28 - 13 = 15
15 x 12 = 180 Fifth graders

solve using break apart strategy 132+42=

Answers

130+40=170
2+2=4
170+4=174

Catherine walks her dog 3/4 mile everyday. how far does she walk each day?

Answers

 3/4 mile            
If she were to walk her dog for a week then 5 1/4 miles.

Translate the phrase into a math expression. 
 
the quotient of twenty divided by four more than one



 
A.
(20 ÷ 4) + 1


 
B.
1 + (4 ÷ 20)


 
C.
(1 + 4) ÷ 20


 
D.
20 ÷ (1 + 4)

Answers

its d 20 / (1+4)...........................................................................



Classify the following triangle. Check all that apply

Answers

It is an acute triangle and a scalene triangle. It is acute because the angles are less than 90 degrees and it is scalene because all of the sides are not equal.

A students received a score of 50 on his history test. The test had a mean of 69 and a standard deviation of 10. Find the z score and assess whether his score is considered unusual.

Answers

[tex]z = \frac{x - mean}{stdev} \\ \\ z = \frac{50 - 69}{10} = -1.9[/tex]

The general rule is that 68% of all scores are within 1 z-score of the mean.
95% are within 2 z-scores of the mean.
99% are within 3 z-scores of the mean.

1.9 is pretty close to 2, so this means approximately only 5% of all scores are more unusual than this students' score.

What is the place value relationships of 8's in 6,588

Answers

The rightmost 8 is in the ones place and the 8 to the left of that is in the tens place.
Ones and tens
EXAMPLE
9-ones 
97- tens
987-hundreds and so on

Addison earn $25 Mowing her neighbors lawn. Then she loaned her friend $18, and got $50 from her grandmother for her birthday she now has $86. how much money did Addison have to begin with?

Answers

$29. 25-18+50=57. 86-57=29

If a 30 -meter pine tree casts a shadow of 30 meters, how far is the tip of the shadow from the top of the tree?

Answers

From the information given, this scenario creates a 45-45-90 triangle, allowing us to use the Pythagorean Theorem. 30^2+30^2=x^2. 30^2 is 900, so now you have 900+900=x^2. Add to make 1800=x^2. Now take the square root of both sides. It should come out to be about 42.43 meters.

The distance from the tip of the shadow to the top of the tree is 42.426 meters.

What is Pythagoras' theorem?

Pythagoras theorem is a relation between sides of a right-angle triangle.

It states that for a right-angle triangle the square root of Hypotenuse is equal to the sum of the individual base and perpendicular square.

So,

Hyp² = Base² + Perp²

Given the situation is making a right angle triangle with base and perpendicular as 30 meters.

By Pythagoras theorem,

Hyp² = Base² + Perp²

Hyp² = 30² + 30²

Hyp² = 1800

Hyp = 42.426 meter.

Hence "The distance from the tip of the shadow to the top of the tree is 42.426 meters".

To learn more about Pythagoras' theorem,

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Initially, a store has 35 train sets. The store sells 3 train sets each month.

What is the explicit rule for the number of train sets the store has after ‘n’ months?

Answers

The explicit rule is t=35-3(n)
Final answer:

The explicit rule for the remaining train sets after 'n' months is represented by the formula T(n) = 35 - 3n, where T(n) is the total number of train sets, and 'n' is the number of months.

Explanation:

The explicit rule for the number of train sets a store has after ‘n’ months, given that the store starts with 35 train sets and sells 3 each month, can be represented by a linear equation. The initial amount of train sets is the starting point, and the number of sets sold each month is the rate of change.

The explicit rule for the number of train sets the store has after 'n' months can be represented by the linear function:

\[ T(n) = 35 - 3n \]

Here, \( T(n) \) represents the number of train sets after 'n' months, 35 is the initial number of train sets, and 3n represents the number of train sets sold each month. The negative coefficient (-3) indicates the decrease in the number of train sets each month. By plugging in different values for 'n', you can determine the number of train sets the store will have at any given month.

This is reflected in the equation:

T(n) = 35 - 3n

where T(n) represents the total number of train sets after n months, and n is the number of months that have passed.

Jasmine exchanges $100 for Yen before going to Japan if each US dollar is worth 87.747 Yen how many yen should Jasmine receive

Answers

100 * 87.747 = 8774.7

problem solving choose the correct answer that follows each sequence
3 4 6 9 13 18 24
.29
.31
.32
.33

Answers

31
it goes by 1 hen 2 then 3 then 4 then 5 then 6 then 7
you add each of the numbers to the last number

I need help with simplifying this question
43+a-2a
Thank you!!!!

Answers

The answer is 43 - a 
(Hope this helps you!)

The correct answer is 43-a. In other words, the result of simplifying algebraic expressions 43 + a - 2a is 43 - a.

To simplify the expression 43 + a - 2a, you can combine like terms.

The expression consists of three terms: 43, a, and -2a.

Starting with the numbers, 43 is a constant term and does not contain any variables. Since there are no other terms with numbers, 43 remains unchanged.

Next, let's simplify the terms with variables. We have a and -2a. To combine these terms, we can group them together as a single term.

The term with a is positive a, and the term with -2a is negative 2a. When we combine them, we subtract 2a from a. This gives us a - 2a, or -a.

Therefore, the simplified expression is 43 - a.

Therefore, the correct answer is 43-a. In other words, the result of simplifying algebraic expressions 43 + a - 2a is 43 - a.

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After you prove that two triangles are congruent, what would CPCTC be useful for?

Answers

Hello, 22Buckt CPCTC stands for "Corresponding parts of congruent triangles are congruent" this would be useful  after you prove that two triangles are congruent, is it asks to show that two angles or two sides are congruent.

Answer with explanation:

When we prove two triangles are congruent, either by following four congruent Axioms

1. S AS

2. SSS

3. A AS

4. A SA

Then C P CT C stands for Corresponding part of Congruent Triangles.

So, C P C TC is useful for proving , those corresponding parts of triangle that is side and Angles equal which are not used while proving Congruency of two triangles.

If sale price of a shirt after giving 8% is RS.161,then find the written price? (By the written price means cost price)

Answers


you can do it, man
I believe in you

To find the original cost price of a shirt on which an 8% discount was given, resulting in a sale price of Rs.161, the formula CP = Sale Price / (1 - (Discount Percent / 100)) is used, calculating the cost price as Rs.175.

If the sale price of a shirt after giving an 8% discount is Rs.161, to find the written price, or the cost price before the discount, we can use the formula for discount calculation. Let CP represent the cost price. The formula for calculating the sale price after discount is:

Sale Price = CP - (Discount Percent * CP) / 100

Here, the sale price is given as Rs.161, and the discount percent is 8%. Therefore, we can rearrange the formula to solve for CP:

CP = Sale Price / (1 - (Discount Percent / 100))

Plugging in the values gives us:

CP = 161 / (1 - (8 / 100)) = 161 / 0.92 = Rs.175

Therefore, the written price or the cost price of the shirt before the discount was applied is Rs.175.

Evaluate -(4/5) over 8/15

Answers

See picture for the answer.

What is the estimate 323 +151

Answers

There are multiple ways of doing this.  I would round off 323 to 300 and round off 151 to 150.  Then 323 + 151 is approx. equal to  300 + 150 = 450.

You could also find the estimate 320 + 150 = 470.

How can I find the exact distance between the points(√7,-√2)and (4√7,5√2)

Answers

[tex]\bf \textit{distance between 2 points}\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ \sqrt{7}}}\quad ,&{{ -\sqrt{2}}})\quad % (c,d) &({{4\sqrt{7}}}\quad ,&{{ 5\sqrt{2}}}) \end{array}~~~ % distance value d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2} \\\\\\ [/tex]

[tex]\bf d=\sqrt{[4\sqrt{7}-\sqrt{7}]^2~+~[5\sqrt{2}-(-\sqrt{2})]^2} \\\\\\ d=\sqrt{(4\sqrt{7}-\sqrt{7})^2~+~(5\sqrt{2}+\sqrt{2})^2}\implies d=\sqrt{(3\sqrt{7})^2~+~(6\sqrt{2})^2} \\\\\\ d=\sqrt{3^2\cdot 7~~+~~6^2\cdot 2}\implies d=\sqrt{63+72}\implies d=\sqrt{135} \\\\\\ \begin{cases} 135=5\cdot 3\cdot 3\cdot 3\\ \qquad 5\cdot 3^2\cdot 3\\ \qquad 15\cdot 3^2 \end{cases}\implies d=\sqrt{15\cdot 3^2}\implies d=3\sqrt{15}[/tex]

three adults and four children must pay $107. two adults and three children must pay $76. find the price of the adult ticks and the price of a childs ticket

Answers

assigning "a" as cost of adult tickets and "c" the cost of children's tickets.

3a + 4c = 107
2a + 3c = 76

elimination method
2(3a + 4c = 107)
-3(2a + 3c = 76)

6a + 8c = 214
-6a - 9c = -228
----------------------
0 - c = - 14
c = 14

Then 2a + 3(14) = 76
2a = 76 - 42
2a = 34
a = 34/2
a = 17


hat is the solution set of the following equation? -8x + x + 15 = -7x + 12 Ø {} {all reals}

Answers

-8x + x + 15  = -7x + 12
-7x + 15 = -7x + 12

First of all, we need to put the variables apart and the numbers apart. So we add 7x on both sides:
-7x + 7x + 15 = -7x + 7x + 12
0x + 15 = 0x + 12
15 = 12

This answer is impossible since 15 can never be equal to 12. So there are no values of x that can make the equation true.

Hope this helps! :)

Factor the expression using the GCF. 2+8

Answers

2: 1,2
8: 1,2,4,8
Greatest common factor is 2.

So the factored expression would be 2(2) + 8(2)= 10(2)
Final answer:

The expression '2+8' simplifies to 10. Factoring using the Greatest Common Factor (GCF) is commonly used with expressions that contain variables.

Explanation:

The expression you're looking to factor, 2+8, does not really involve any complex mathematical concepts, and there's no variable to enable factoring in its usual way. However, we can simplify it by adding the numbers. So, 2+8 equals to 10. Factoring using the greatest common factor(GCF) is most often used when you're handling expressions that involve variables, for instance, 2x + 8x. In this case, the GCF would be 2x, and the expression would factor to 2x(1 + 4).

Learn more about Factoring Using GCF here:

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The manufacturers of m&m's claim that 20% of the milk chocolate m&m candies are orange. find the mean and standard deviation of the sampling distribution of the sample proportion of orange m&m's for samples of size 100. use two decimal places.

Answers

The mean of a sampling distribution of a sample with proportion, p and sample size, n is given by [tex]\mu=np[/tex].

The standard deviation of a sampling distribution of a sample with proportion, p and sample size, n is given by [tex]\sigma= \sqrt{np(1-p)} [/tex]

Given that the manufacturers of m&m's claim that 20% of the milk chocolate m&m candies are orange. The proportion is p = 0.2

The mean of the sampling distribution of the sample proportion of orange m&m's for samples of size 100 is given by [tex]\mu=100(0.2)=20[/tex]

The standard deviation of the sampling distribution of the sample proportion of orange m&m's for samples of size 100 is given by [tex]\sigma= \sqrt{100(0.2)(1-0.2)} = \sqrt{16} =4[/tex]

i need to know what t is but i don't understand how to get it

Answers

[tex]\bf \cfrac{7+3t}{4}=-\cfrac{t}{8}\impliedby \textit{first off cross-multiply} \\\\\\ 8(7+3t)=4(-t)\implies 56+24t=-4t\implies 24t+4t=-56 \\\\\\ 28t=-56\implies t=-\cfrac{56}{28}\implies t=-2[/tex]

If one of the purple-flowered progeny plants is selected at random and self-fertilized, what is the probability it will breed true? if one of the purple-flowered progeny plants is selected at random and self-fertilized, what is the probability it will breed true? 2/3 3/4 1/4 1/3

Answers

This is in reality a biology question given a lot of biology related information is not given in the problem.
However, I will provide the answer by making biology-related assumptions.
1. The genotype of the purple-flowered progeny is Pp
2. The purple-flower phenotype is recessive.

If self fertilized, both "parents" have genotype Pp
The punnett square is as follows:

         P      p
P     PP    Pp
p     Pp     pp

Since purple-flowers are recessive, only PP will come out purple, hence the probability is 1/4.

How do you write 960,060 in expanded form

Answers

900,000 + 60,000 + 60

hope this helps

Answer:

[tex]900000 + 60000+60[/tex]

Step-by-step explanation:

write 960,060 in expanded form

In 960,060, from left to right

0 is in ones place is 0

6 is in tens place is 6 times 10 = 60

6 is in ten thousands place is 6 times 10000= 60000

9 is in hundred thousands place 9 times 100000= 900000

So the expanded form of the given number is

[tex]900000 + 60000+60[/tex]

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