1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
qwelly [4]
2 years ago
13

A cube with edges of length x centimeters has volume v(x)=x^3 at the instant when x=2, what is the rate of change of x, in centi

meters per minute, with respect to time?
Mathematics
2 answers:
PtichkaEL [24]2 years ago
8 0

Answer:

The rate of change of x, in centimeters per minute, with respect to time is found to be :

\frac{2}{3}

Step-by-step explanation:

Edge length of the cube is given to be x centimeters

V(x) = x^3 ...........(1)\\\\\text{At any instant when x = 2}\\\\V(2) = 2^3= 8\:\:cm^3\\\\\implies\frac{dv}{dt}=8\\\\\text{Now, differentiating (1) w.r.t. t}\\\\\frac{dv}{dt}=3\cdot x^2\cdot\frac{dx}{dt}\\\\\implies 8=3\cdot x^2\cdot \frac{dx}{dt}\\\\\text{When x = 2}\\\\\implies\frac{dx}{dt}=\frac{8}{3\times 4}\\\\\implies\frac{dx}{dt}=\frac{2}{3}

Hence, the rate of change of x, in centimeters per minute, with respect to time is found to be :

\frac{2}{3}

Margarita [4]2 years ago
5 0
Dv/dt=40    dv/dt=3x^2dx/dt
40=3x^2dx/dt
40=12dx/dt
10/3=dx/dt
You might be interested in
What is the solution to equation 3 1/2 + p = 5 1/4?
Tatiana [17]

<em>The</em><em> </em><em>value</em><em> </em><em>of</em><em> </em><em>p</em><em> </em><em>is</em><em> </em><em>1</em><em> </em><em>3</em><em>/</em><em>4</em>

<em>Look</em><em> </em><em>at</em><em> </em><em>the</em><em> </em><em>attached</em><em> </em><em>picture</em>

<em>Hope</em><em> </em><em>it</em><em> </em><em>will</em><em> </em><em>help</em><em> </em><em>you</em>

<em>Good</em><em> </em><em>luck</em><em> </em><em>on</em><em> </em><em>your</em><em> </em><em>assignment</em>

8 0
3 years ago
Read 2 more answers
$248.62 rounded to the nearest dollar
nata0808 [166]

$249.......................................

7 0
3 years ago
Read 2 more answers
Write a unit test for addinventory(). call redsweater.addinventory() with parameter sweatershipment. print the shown error if th
Katena32 [7]
<span>#include <iostream> using namespace std; class InventoryTag { public: InventoryTag(); int getQuantityRemaining() const; void addInventory(int numItems); private: int quantityRemaining; }; InventoryTag::InventoryTag() { quantityRemaining = 0; } int InventoryTag::getQuantityRemaining() const { return quantityRemaining; } void InventoryTag::addInventory(int numItems) { if (numItems > 10) { quantityRemaining = quantityRemaining + numItems; } } int main() { InventoryTag redSweater; int sweaterShipment = 0; int sweaterInventoryBefore = 0; sweaterInventoryBefore = redSweater.getQuantityRemaining(); sweaterShipment = 25; cout << "Beginning tests." << endl; // FIXME add unit test for addInventory /* Your solution goes here */ cout << "Tests complete." << endl; return 0; }</span>
5 0
3 years ago
Find the length of the missing side in the figure below. a = _______ cm.
WITCHER [35]

Answer:

\frac{2 \sqrt{177} }{5}

or

5.32cm correct to 2 decimal places

Step-by-step explanation:

This is a right angled triangle from what I know so we have to apply pythagoras theorem.

{7.1}^{2}  =  {a}^{2}  +  {4.7}^{2}

we need to rearrange this to find a²

{a}^{2}  =  {7.1}^{2}  -  {4.7}^{2}

a =  \sqrt{ \frac{708}{25} }

This can either be written as a fraction or decimal.

a =  \frac{2 \sqrt{177} }{5}

OR

a = 5.32

correct to 2 decimal places

5 0
1 year ago
A cell phone company charges $100 to activate a phone line and then $50 a month after that. Which of the following functions rel
Flura [38]
Y= 100+50x should be a correct function
4 0
2 years ago
Other questions:
  • Kohls sells casual shirts for 9$ and polo shirts for 18$. Total sales were 1,080 and customers bought 4 times as many casual shi
    6·1 answer
  • Simplify the following expression<br> 2x − 6y + 3x2 + 7y − 14x
    10·1 answer
  • If the cost for manufacturing x units of a certain product is given c=x^2 +25x +30 find the number of units manufactured at a co
    12·1 answer
  • In triangle JKL, sin(b°) = three fifths and cos(b°) = four fifths. If triangle JKL is dilated by a scale factor of 2, what is ta
    8·1 answer
  • 9 × [(21 − 4) − 9 what is the answer when you find out pls let me know!!!
    14·1 answer
  • PLEASE HELP
    12·1 answer
  • Which ordered pair is a solution to the system of equalities y&lt;3x y&lt;5
    13·1 answer
  • Can I get some help with these questions?​
    6·1 answer
  • 3. The number which when substituted in a polynomial makes its value zero.​
    13·2 answers
  • 8⁄9 ÷ 1⁄3 what is the answer please
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!