The rate at which the radius of the balloon is changing at the instant when the volume is 36π cubic inches is 1/3π inches per minute.
Change in volume of the sphere with temperature
The change in volume of the sphere with temperature is calculated as follows;
[tex]V = \frac{4}{3} \pi r^3\\\\[/tex]
Given;
[tex]\frac{dV}{dT} = 6 \ in^3/^0C\\\\\frac{dT}{dt} = 2 \ ^0C/\min[/tex]
Radius of the sphere when the volume of 36π cubic inches[tex]\frac{4}{3} \pi r^3 = 36 \pi\\\\r^3 = 27\\\\r^3 = 3^3\\\\r = 3 \ in[/tex]
Change in volume of the sphere with radius[tex]\frac{dV}{dr} = 4\pi r^2[/tex]
Rate at which the radius of the balloon is changing[tex]\frac{dV}{dT} \times \frac{dT}{dt} = \frac{dV}{dt} \\\\\frac{dV}{dt} = 6\ (in^3/^0C) \ \times 2\ (^0C/\min) = 12 \ \frac{in^3}{\min} \\\\\frac{1}{\frac{dV}{dr} } \times \frac{dV}{dt} = \frac{dr}{dt} \\\\\frac{dr}{dt} = \frac{1}{4\pi r^2} \times 12\\\\\frac{dr}{dt} = \frac{12}{4\pi r^2} \\\\Recall, \ r = 3 \ in\\\\\frac{dr}{dt} = \frac{12}{4\pi (3)^2} \\\\\frac{dr}{dt} = \frac{12}{36\pi }\\\\\frac{dr}{dt} = \frac{1}{3\pi} \ \frac{in}{\min}[/tex]
Thus, the rate at which the radius of the balloon is changing at the instant when the volume is 36π cubic inches is 1/3π inches per minute.
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agriculture can contribute to depletion of aquifers because _______
A. we wash our produce before eating it.
B. pesticides can runoff into oceans
C. irrigation water often comes from groundwater
D. animal waste runs off into surface waters
Answer:
B. pesticides can runoff into oceans
Why do people ask weird questions
How was you day? What is 12 + 20
Answer: It was okay, i took one of my standard assesments for writing i think i atleast passed.
Explanation:
Answer:
22
Explanation:
It was good! How was yours?
Why would safety be the number 1 priority in plant and soil science?
Answer:
If water and air deterioration have been described and studied for decades, soil contamination has become a priority only by late 1990s. Only in the last fifteen years, the importance of soil has been recognized as it represents the most important element for supporting life on Earth.2 Indeed, soil supports terrestrial ecosystems and human constructions, it regulates water cycle and carbon dynamics, decomposition takes place into the soil and the nutrients become available again. Soil provides food for human nutrition, and its quality represents a fundamental requirement for food safety, and therefore for animal and human health, even though not always this relationship is stressed enough
the name "Roy G.Biv"is one way to remember the colors of the light spectrum this is an example of
How does Truman’s speech reflect the consequences of atomic technology?
SAQ
Answer:
points giveaway !!!!
Explanation:
Follow me for points
The analysis used in the graphs has taken into account “data gaps, random instrument errors, uncertainties in ocean surface temperatures, and adjustments for urbanization over the land” (IPCC 2001 Climate Change—The Scientific Basis Report). Why do you think it is important for the scientists to take these uncertainties into account?
The reason why it is important for the scientists to take these uncertainties into account is because:
The uncertainty of data is vital for science due to the fact that it pushes scientists to be more involved in further investigation and research.
It is vital to understand that scientific uncertainty is not that there is flaws in your work but it it means there is an an absence of certainty and as such finding it is important so that it will not lead to bigger issues such as climate disasters.
What is the good about uncertainty?The Measurement of uncertainty is vital to risk assessment and decision making.
A lot of firms do make decisions a lot and on daily basis using reports that has quantitative measurement data. If measurement of the results are not right, the decision taken may have risks increase and as such it is good to investigate uncertainty.
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Suppose you are working on the balance sheet for your business. You need to determine your equity as an owner. Consider the following details: Total assets: $37,777 Total liabilities: $16,575 How would you determine your equity as the business owner? Explain the process you would take to determine the owner's equity. Provide two examples of assets and two examples of liabilities. Finally, provide the dollar value of owner's equity, given the dollar figures above.
Assuming Total assets is $37,777 and Total liabilities is $16,575. The dollar value of owner's equity is $21,202.
What is equity?Equity can be defined as total assets minus total liability.
Owner equity can be calculated using this formula
Equity=Total assets- Total liabilities
Equity=$37,777-$16,575
Equity=$21,202
Examples of assets are:
BuildingEquipmentExamples of liabilities are:
Interest payableAccrued wagesInconcludion the dollar value of owner's equity is $21,202.
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What is a right that you do not have yet as a U.S. citizen? What is a responsibility that you do not have yet?
Answer:
Below
Explanation:
Since you are in AP I'm going to assume you are under the age of eighteen, which means there are many rights you do not have. For ezample, you can not participate in our country's democratic practices by voting, you can't own property, you can't work full time, etc. A responsiblity that you do not have is you don't have any sort of military responsibilty. Say there is a war and a draft, anyone eighteen and over may become responsible to fight for their country, but you don't have to worry about that.
The form used by employees to determine how much of paycheck to withhold is a?
Answer:
I also think that is Form W-4 as the employer, the employee filling status, multiple job and others
Explanation:
-
Answer:
a W-4
Explanation:
3. Describe how the expanded
power of the president affected
the concept of checks and
balances.
A law can be vetoed by the President in the executive branch, but it can be overridden by the legislative branch with enough votes. The legislative branch has the authority to confirm Presidential appointments, manage the budget, and impeach and remove the President from office. The Checks and Balances system is linked to the separation of powers in the United States. The Checks and Balances system gives each part of government its own authority to keep the other branches in check and prevent one branch from becoming too strong. The president appoints federal officials, but the Senate must approve them. Within the legislative branch, each house of Congress acts as a check on the other's potential abuses of power. To become law, a measure must be passed by both the House of Representatives and the Senate in the same form.
Why Sigmund Freud personality development is referred to as psychodynamic
Answer:
Below
Explanation:
Freud's ideas focused heavily on the sub/unconscious. Unlike other psychologists, he believed the majority of a person lied their. So, in order for a person to be treated they needed to be "psychoanalyzed" or they psyche needed to be analyzed, which lead to the name as it was crucial in Freud's research.
what year does Haddow and Bullock present emergency management as disaster?
Answer:
2006
Explanation:
Haddow and Bullock (2006) [16] defined emergency management as dealing with hazards timely and taking action to avoid hazards.
Which of the following is NOT a main type of spring?
a:retractable
b:coiled
c:sinuous
d:wire
Answer:
it would be D
Explanation:
I’m pretty good at this point
Answer:
good that your good lol I'm happy that u are good
