FILL IN THE BLANK. A balloon is being inflated. If its volume increases at the rate of 5 cm^3/sec, how fast is the radius growing longer when the radius is 6 cm? Answer in 3 decimal places, example is 0.123: ______ cm/sec
When the radius is 6 cm, the rate at which the radius is growing longer is approximately 0.011 cm/sec.
To find the rate at which the radius is growing when the radius is 6 cm, we need to relate the rate of change of volume to the rate of change of the radius.
The volume V of a sphere is given by the formula:
V = (4/3)πr³
Differentiating both sides of the equation with respect to time (t), we get:
dV/dt = 4πr²(dr/dt)
Given that dV/dt = 5 cm³/sec, we can plug in the value of r as 6 cm and solve for dr/dt.
5 = 4π(6)²(dr/dt)
Simplifying the equation:
5 = 144π(dr/dt)
Now, solve for dr/dt:
dr/dt = 5 / (144π)
Calculating the value:
dr/dt ≈ 0.011
Therefore, when the radius is 6 cm, the rate at which the radius is growing longer is approximately 0.011 cm/sec.
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What's the answer to this?
Answer:
Step-by-step explanation:is 10
Directions: Convert the equations from standard form to slope intercept form.
Answer:
Write in slope-intercept form, \(y=mx+b\).
5. \(y=2x+7\)
6. \(y=-\frac{5}{3} x+4\)
7. \(y=x-1\)
8. \(y=\frac{1}{3}x +5\)
9. \(y=\frac{4}{5}x -2\)
10. \(y=-\frac{7}{3}x + 6\)
if
f(x)=4x2−3x+7 , what is f(−2) ?
Answer:
D. 29 I just know the awnser sorry
To find the value of f(−2), we substitute −2 for x in the function f(x):
f(−2) = 4(-2)^2 − 3(-2) + 7
= 4(4) − 3(2) + 7
= 16 − 6 + 7
= 11
Therefore, f(−2) = 11.
Curt and Melanie are mixing 70% of blue paint and 30% of yellow paint to make seafoam green paint in a 1. 5 quarts bucket. Use the percent equation to find out how much yellow paint they should use
The amount of yellow paint Curt and Melanie should use is 0.45 quarts so that they can make 1.5 quarts bucket of seafoam green paint.We can use per cent equation.
Given that to make 1.5 quarts bucket of seafoam green paint Curt and Melanie have to mix 70 parts blue paint and 30 parts yellow paint.If 100 percent represent total paint then for 1.5 quarts we have to find the proportion of yellow paint.Let it be x.
30% / 100% =30 / 100 = x / 1.5 quarts.
We can reduce the equation further,
0.3 = x / 1.5.
0.3 * 1.5 = x
x = 0.45
We can also find blue paint proportion similar by substituting 30 per cent to 70 per cent.
As a result of our calculation, we found the amount of yellow paint to be 0.45 quarts.
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How much water should be added to 1 gallon of pure antifreeze to obtain a solution that is 95% antifreeze?
To obtain a 95% antifreeze solution,
(Simplify your answer.)
***
gallon(s) of water should be added.
4
Therefore, we need to add approximately 0.0526 gallons of water (which is equivalent to about 6.63 fluid ounces) to 1 gallon of pure antifreeze to obtain a solution that is 95% antifreeze.
What is equation?In mathematics, an equation is a statement that asserts the equality of two expressions. An equation typically consists of one or more variables, coefficients, and constants, and it can include mathematical operations such as addition, subtraction, multiplication, and division. The expressions on both sides of the equation are separated by an equal sign, indicating that they have the same value. The goal of solving an equation is to determine the value of the variables that make the equation true. Equations are used in many areas of mathematics and science to model real-world phenomena and solve problems.
Here,
Let's assume that we need to add x gallons of water to 1 gallon of pure antifreeze to obtain a solution that is 95% antifreeze. We know that the final solution will contain 1 gallon of antifreeze, and that this will be 95% of the total solution (the remaining 5% will be water). So, we can write:
1 gallon of antifreeze = 95% of (1 gallon of antifreeze + x gallons of water)
We can simplify this equation by converting 95% to a decimal:
0.95 × (1 gallon of antifreeze + x gallons of water) = 1 gallon of antifreeze
Now we can solve for x by isolating it on one side of the equation. First, let's distribute the 0.95:
0.95 gallons of antifreeze + 0.95x gallons of water = 1 gallon of antifreeze
Next, let's isolate x by subtracting 0.95 gallons of antifreeze from both sides:
0.95x gallons of water = 0.05 gallons of antifreeze
Finally, we can solve for x by dividing both sides by 0.95:
x = 0.05 gallons of antifreeze ÷ 0.95
x ≈ 0.0526 gallons of water
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In the equation: (16)^3=2^3/2x how could you solve for x?
Answer:
x = 8
Step-by-step explanation:
16 is the same as 2^4
(2^4)³ = 2^3/2x
2^12 = 2^3/2x
as long as bases are both the same then set exponents equal
12 = \(\frac{3}{2}\)x
3x = 24
x = 8
Consider the proposed solution of the critical section problem listed below. Common variables flag 1 , and flag 2 are initially false. Does the code above guarantee mutual exclusion? If no, give an execution sequence where mutual exclusion is violated. If yes, give an explanation why all three requirements hold. Could deadlock occur? If no, explain why it cannot occur. If yes, give an execution sequence that leads to deadlock. Could bounded waiting occur? If no, explain why it cannot occur. If yes, give an execution sequence that allows bounded waiting.
Thread B has to wait until Thread A releases the resource by setting flag 1 to false. However, there is a bound on the waiting time, as Thread B will eventually enter the critical section once Thread A releases the resource.
The code provided does not guarantee mutual exclusion. Here's an execution sequence where mutual exclusion is violated:
1. Thread A executes line 3 and sets flag 1 to true.
2. Thread B executes line 5 and checks flag 1, which is true. Thread B enters the critical section.
3. Thread A executes line 6 and enters the critical section without being blocked, violating mutual exclusion.
Therefore, the code does not provide mutual exclusion as there is a scenario where multiple threads can simultaneously enter the critical section.
Deadlock cannot occur in this code because there is no circular dependency on resources. Deadlock typically occurs when two or more threads are waiting for each other to release resources they hold. In the given code, there is no such dependency or waiting involved, so deadlock cannot occur.
Bounded waiting can occur in this code, meaning there is a possibility that a thread may have to wait for a certain amount of time before entering the critical section. Here's an execution sequence that allows bounded waiting:
1. Thread A executes line 3 and sets flag 1 to true.
2. Thread B executes line 5 and checks flag 1, which is true. Thread B waits in a loop until flag 1 becomes false.
3. Thread A completes its critical section and sets flag 1 to false.
4. Thread B exits the loop and enters the critical section.
In this sequence, Thread B has to wait until Thread A releases the resource by setting flag 1 to false. However, there is a bound on the waiting time, as Thread B will eventually enter the critical section once Thread A releases the resource.
To ensure mutual exclusion and prevent deadlock, a proper synchronization mechanism such as locks or semaphores should be implemented in the code.
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Perform each matrix row operation and write the new matrix
Answer:
[4 -11 1 7 l -17]
[0 1 -1 -7 l 0]
[3 0 -2 2 l 12]
[4 1 5 3 l 7]
Step-by-step explanation:
This is Finite Math, I got this hehe :)
To find the answer, first you need to understand what R means.
It stands for "row". So R1 means "Row 1".
So: -3R1 + R3 means that you need to multiply -3 by all of the numbers in row 1 and then add all of the numbers in row 3
[0 3 1 -1 l 6]
[0 1 -1 -7 l 0]
[3 0 -2 2 l 12]
[4 1 5 3 l 7]
Then use ^^THAT^^ and apply the next set of instructions.
-4R1 + R4 means that you multiply -4 by all of the numbers in row 1 and then add all of the numbers in row 4:
[4 -11 1 7 l -17]
[0 1 -1 -7 l 0]
[3 0 -2 2 l 12]
[4 1 5 3 l 7]
why is this 536.82 can someone tell me what i plugged in wrong
in my calculator
2. What is the monthly mortgage payment if the beginning principal balance is $ 100,000 , the annual interest rate is 5 % , the loan term is 30 years, and the loan is fully amortizing?
The monthly mortgage payment for a $100,000 loan with a 5% annual interest rate and a 30-year fully amortizing term is approximately $536.82.
To calculate the monthly mortgage payment, we can use the formula for calculating the fixed monthly payment for a fully amortizing loan. The formula is: M = P * (r * (1 + r)^n) / ((1 + r)^n - 1)
Where:
M = Monthly mortgage payment
P = Principal balance
r = Monthly interest rate (annual interest rate divided by 12 and converted to a decimal)
n = Total number of monthly payments (loan term multiplied by 12)
Plugging in the given values into the formula:
P = $100,000
r = 0.05/12 (5% annual interest rate divided by 12 months)
n = 30 years * 12 (loan term converted to months)
M = 100,000 * (0.004166667 * (1 + 0.004166667)^(3012)) / ((1 + 0.004166667)^(3012) - 1)
M ≈ $536.82
Therefore, the monthly mortgage payment for a $100,000 loan with a 5% annual interest rate and a 30-year fully amortizing term is approximately $536.82.
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The scale factor from A DEF to A ABC is
6
5
ООО
4.5
Answer:
Between the edges of the first two triangles there is a ratio. To find this ratio, you need to ratio one edge of a small triangle to one edge of a large triangle. So 5/30=6/36=8/48=1/5. The ratio we want to find is 1/5 or 5.
find m<DCV and m<VBD
9514 1404 393
Answer:
m∠DCV = 50°m∠VBD = 50°Step-by-step explanation:
Arc DV is 100°, so any inscribed angle that intercepts that arc will have a measure that is half of 100°, or 50°.
Inscribed angles DCV and VBD both intercept arc DV, so both are 50°.
30 Points!!!
At a local college, only 30% of students live off campus. Of those who live off campus, 66% of those students work part-time. Of those who live on campus, 63% work part-time. The tree diagram shows how the college students are divided into subgroups.
The tree diagram shows college students branching off into two categories, off campus and on campus students. Off campus students branches off into two sub-categories, work part-time and do not work. On campus branches off into two subcategories, work part-time and do not work.
What is the percentage of students who live off campus and do not have a part-time job?
10.2%
25.9%
34%
44.1%
Answer:
A. 10.2% i believe is correct
Step-by-step explanation:
30% of students live off campus and and of those 66% have a part time job so that means 34% of students off campus do not have a part time job.
34% of 30% = .30 x .34 = .102 = 10.2%
so A. 10.2% should be the answer.
10.2% of students who live off campus and do not have a part-time job
What is Percentage?To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.
Given:
30% of students live off campus.
Of those who live off campus, 66% of those students work part-time.
so, the students off campus do not have a part time job.
= 100- 66
= 34%
Then, the percentage of students who live off campus and do not have a part-time job
= 34% of 30%
= 0.30 x 0.34
= 0.102
= 10.2%
Hence, 10.2% of students who live off campus and do not have a part-time job
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lots of point n brainliest SO help rq
Bruce invested a certain amount of money for five years at a rate of 2.25%. At the end of that time, he had earned $675 in interest. How much money was invested? (See Example 3 from your notes.)
a
$6000
b
$6675
c
$6750
d
$5645
Answer:
A. $6000Step-by-step explanation:
Let the invested amount is x.
Then the interest amount is:
x*5*2.25/100 = 6750.1125x = 675x = 675 / 0.1125x = 6000Correct choice is A
find f (5), f(x) =x^2-13t-30
Answer:
\(f(5) = -13t-5\)
Step-by-step explanation:
=> \(f(x) = x^2-13t-30\)
Put x = 5
=> \(f(5) = (5)^2-13t-30\)
=> \(f(5) = 25-30-13t\)
=> \(f(5) = -13t-5\)
Answer:
-13t - 5
Step-by-step explanation:
Put x as 5 and solve for the function.
f(5) = (5)² - 13t - 30
Splve for the exponent.
f(5) = 25 - 13t - 30
Add or subtract like terms.
f(5) = -13t - 5
which statement is false? NO LINKS AND NO BLANK ANSWERS
A) all squares are rectangles.
B) all squares are parallelograms.
C) all rhombuses are squares.
D) all rhombuses are parallelograms.
Answer:
C because not all rhombuses are squares
Suppose you invest $2000 at annual interest rate of 4.5 % How much money do you have in the account after five years?
Round two decimal places.
compounded weekly $ _____
compounded monthly $ _____
Answer:
if my math is correct
Step-by-step explanation:
2501.50
2504.65
A car travels 80 millimetres in 2 1/2 hours . What is it speed in kilometres per hour
Answer:
32 Kilometers
Step-by-step explanation:
A Car travels 80 Kilometers in 2 and Half hours.
1 Hour =60 minutes, 2 & Half hours= 2.5*60= 150 minutes
Kilometers travelled by Car in a hour= 80/150*60= 32 Kilometers
A 99-inch board is cut into two pieces. One piece is two times the length of the other. Find the length of the shorter piece.
Please help
Answer:
33 inches
Step-by-step explanation:
x=length of board
x+2x=99
3x=99
x=33
Answer:
33 inches
Step-by-step explanation:
The question above can be solved by using "algebraic expressions."
Let x be the length of the shorter piece.
Let 2x be the length of the longer piece.
Let's solve.
x + 2x = 99 (inches)3x = 99x = \(\frac{99}{3}\)x = 33The length of the shorter piece is 33 inches.
Let's get the length of the longer piece.
2x = ?2(33) = 66The length of the longer piece is 66 inches.
Let's check.
x + 2x = 99 inches
33 + 66 = 99
99 = 99
The answer is correct.
As an estimation we are told £3 is €4.
Convert £54.20 to euros.
Give your answer rounded to 2 DP.
Answer:
72.27 euros
(54.20 X 4) / 3
if the classroom supplies, outdoor games, toys for the playground and paint for all three classrooms are represented by 3x2, xy3, 2x3y, and 4xy respectively, multiply the polynomial expressions. write your answer in descending order according to the x variable. please use the palette below to enter your answer.
To represent outside games, playground equipment, and paint for all three classrooms, multiply the polynomial expressions by 3x2, xy3, 2x3y, and 4xy, accordingly.
This polynomial's formula is 12x^5y^3 + 24x^4y^3 + 18x^3y^3
Numerous branches of mathematics and science use polynomials. used to approximate other functions in calculus and numerical analysis to approximate other functions in calculus and numerical analysis. From straightforward word problems to intricate scientific conundrums, polynomial equations are utilized to represent a broad variety of topics.Algebraic varieties and polynomial rings, two core concepts in algebra and algebraic geometry, are constructed using polynomials in higher mathematics.
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What is the area of this figure?
4 mm
2 mm
3 mm
9 mm
2 mm
11 mm
Answer:
A = (1/2)(4)(5) + 7(7) + 3(2) = 65 mm^2
Which of the following is the quotient of the rational expressions shown
below?
2x^3/x+5 divided by x-5/3x-1
Answer:
6x^4 - 2x^3/ x^2 - 25
Step-by-step explanation:
On A
Find the next two terms in this
sequence.
50, 40, 31, 23, 16, | ? ],[?]
Answer:
8, 0
Step-by-step explanation:
Whats 36/2/3 simplify
Answer:
6
Step-by-step explanation:
This is calculated in order from left to right. This is same as: (36/2)/3
36/2/3= 18/3=6Note:
It would be calculated as below if the parenthesis was differently applied:
36/(2/3) = 36* 3/2 = 54Answer:
6
Step-by-step explanation:
3 + 10x+ 4x as an algebradic expression
Answer: 10x² + 3x + 4
Step-by-step explanation: I hate math.
Please help i need this done like within at least an hour
Answer:
2.475
Step-by-step explanation:
12 divide into 29.7 goes 2.475 times
use the illustration from the other example and you should be able to do it
12 into 29 goes twice
subtract 29-24 to get 5
bring down the 7 to get 57
12 into 57 goes four times
57-48 = 9
bring down a zero to get 90
12 into 90 goes seven times
90-84 = 6
12 into 60 is 5
18÷29.70= 0.40
that should be right
PLEASEEEEE I NEED HELP WITH THIS!!
Solve for x.
5
6X 30
7 1
X+ x =
5*= -52
x =
(Type an integer or a simplified fraction.)
Answer:
x = 60
Step-by-step explanation:
A 6-pack of bouncy balls costs $2. 76. What is the unit price?
A 6 pack of bouncy ball costs 2.76$ and the unit price of a bouncy ball is $0.46
To find the unit price of the bouncy balls, we need to divide the total cost by the number of bouncy balls in the pack. Since there are 6 bouncy balls in the pack and the cost is $2.76, we can calculate the unit price as follows: Unit price = total cost ÷ number of units
Unit price = $2.76 ÷ 6
Unit price = $0.46
Therefore, the unit price of a bouncy ball is $0.46.
Unit price is a measure of the cost of a single unit of a product. It is calculated by dividing the total cost of a product by the number of units in the package. The unit price is helpful when comparing the costs of different package sizes or brands of the same product. It allows consumers to make informed decisions about their purchases based on the value they receive for their money. Unit pricing is required by law in some countries, including the United States, to ensure transparency in pricing and to protect consumers from deceptive marketing practices. Overall, knowing the unit price of a product can help consumers save money and make more informed purchasing decisions.
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Solve the system by substitution (show your work)
Y=3x+14
Y=-4x
Step-by-step explanation:
y = 3x + 14
y = -4x
substitution means that we use the information of one equation in the other equation to reduce it to one equation in one variable. with the solution of that we go into the other equation and solve for the second variable.
in our case we use the second equation directly in the first and get
-4x = 3x + 14
-7x = 14
x = -2
and now, with this x = -2 we go to the second equation
y = -4×-2 = 8