Answer:
-11
Step-by-step explanation:
<h3><u>Option A</u></h3>
is the required equation to calculate width of rectangular frame that has a total area of 140 square inches.
<h3>
<u>Solution:</u></h3>
Given that,
Length of a rectangular frame is given as 2x + 10
Width of the rectangular frame is given as 2x + 6
Total area = 140 square inches
<em><u>The area of rectangular frame is given as:</u></em>

Plugging in values, we get

This is the required equation to calculate width of rectangular frame
Solve the above quadratic equation to get the value of "x"

<em><u>Use the quadratic equation formula:</u></em>

Here a = 4 ; b = 32 ; c = -80


x = 2 or x = -10
Now measurement cannot be negative, so taking the positve value of "x", we can calculate the width
So put "x" = 2
Width of the rectangular frame = 2x + 6 = 2(2) + 6 = 10
Thus the width of frame is 10 inches
Answer:
C:a = 9 in., b = in.
Step-by-step explanation:
The square root of 2 is added on the hypotenuse of a triangle with the angles 45-45-90 while(in this case) a and b are equal
The ODE is exact, since


so there is solution
such that


Integrating both sides of the first PDE wrt
gives

Differentiating both sides wrt
gives


Then the solution to the ODE is

# # #
Alternatively, we can see that the ODE is homogeneous, since replacing
and
reduces to the same ODE:



This tells us we can solve by substituting
, so that
, and the ODE becomes



which is separable as

Integrating both sides gives


and solving in terms of
,



If it is rotated along AB it would be a cone