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enyata [817]
3 years ago
9

Suppose that a dimension x and the area A of a shape are differentiable functions of t. Write an equation that relates to .

Mathematics
1 answer:
marusya05 [52]3 years ago
7 0

Complete question is;

Suppose that a dimension x and the area A = 2x² of a shape are differentiable functions of t. Write an equation that relates dA/dt to dx/dt.

Answer:

Step-by-step explanation:

Since A = 2x²

Let's differentiate both sides with respect to x.

dA/dx = 4x

Now, we want to find the relationship between dA/dt and dx/dt

dA/dt can be expressed as;

(dA/dt) = (dA/dx) × (dx/dt)

Thus;

dA/dt = 4x(dx/dt)

Thus, the equation that relates dA/dt to dx/dt is;

dA/dt = 4x(dx/dt)

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Answer:

7/12, 7/10, 5/6

Step-by-step explanation:

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Solve for x.<br> -4 &lt; 11 - 3.2
goldenfox [79]

Answer:

-4<11-(32/10)  

Inequality is always true

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "3.2" was replaced by "(32/10)".

Rearrange:

Rearrange the equation by subtracting what is to the right of the greater than sign from both sides of the inequality :

                    -4-(11-(32/10))<0  

Step by step solution :

Step  1  :

           16

Simplify   ——

           5  

Equation at the end of step  1  :

              16

 -4 -  (11 -  ——)  < 0  

              5  

Step  2  :

Rewriting the whole as an Equivalent Fraction :

2.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  5  as the denominator :

          11     11 • 5

    11 =  ——  =  ——————

          1        5    

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

2.2       Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

11 • 5 - (16)     39

—————————————  =  ——

      5           5  

Equation at the end of step  2  :

       39

 -4 -  ——  < 0  

       5  

Step  3  :

Rewriting the whole as an Equivalent Fraction :

3.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  5  as the denominator :

          -4     -4 • 5

    -4 =  ——  =  ——————

          1        5    

Adding fractions that have a common denominator :

3.2       Adding up the two equivalent fractions

-4 • 5 - (39)     -59

—————————————  =  ———

      5            5  

Equation at the end of step  3  :

 -59

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Step-by-step explanation:

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ollegr [7]

Answer:

4/3

Step-by-step explanation:

−x+

3

7

=2x−

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Step 1: Simplify both sides of the equation.

−x+

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=2x+

−25

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Step 2: Subtract 2x from both sides.

−x+

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Step 3: Subtract 3/7 from both sides.

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Step-by-step explanation:

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