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Mathematics

1 answer:

Sergio039 [100]3 years ago

8 0

All the information you need is in the quadratic trinomial ... Read from right to left:

Find factors of 49 which ADD (+) to give 14.

These will be 7 and 7 because: 7 × 7 = 49 and 7 + 7 = 14

The + sign shows that the signs in the brackets will be the SAME, the minus (-) shows that they will be negative:

( x − 7 ) ( x − 7 ) = ( x − 7 ) 2

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Find the measurements (the length L and the width W) of an inscribed rectangle under the line with the 1st quadrant of the x &am

Leni [432]

The question is incomplete. Here is the complete question.

Find the measurements (the lenght L and the width W) of an inscribed rectangle under the line y = - $\frac{3}{4}$ x + 3 with the 1st quadrant of the x & y coordinate system such that the area is maximum. Also, find that maximum area. To get full credit, you must draw the picture of the problem and label the length and the width in terms of x and y.

Answer: L = 1; W = 9/4; A = 2.25;

Step-by-step explanation: The rectangle is under a straight line. Area of a rectangle is given by A = L*W. To determine the maximum area:

A = x.y

A = x(- $\frac{3}{4}.x + 3$ )

A = - $\frac{3}{4}.x^{2} + 3x$

To maximize, we have to differentiate the equation:

$\frac{dA}{dx}$ = $\frac{d}{dx}$ (- $\frac{3}{4}.x^{2} + 3x$ )

$\frac{dA}{dx}$ = -3x + 3

The critical point is:

$\frac{dA}{dx}$ = 0

-3x + 3 = 0

x = 1

Substituing:

y = - $\frac{3}{4}$ x + 3

y = - $\frac{3}{4}$ .1 + 3

y = 9/4

So, the measurements are x = L = 1 and y = W = 9/4

The maximum area is:

A = 1 . 9/4

A = 9/4

A = 2.25

6 0

3 years ago

I need help can y'all help please

BartSMP [9]

Your domain is all positive numbers, and your range is all numbers. this is because no matter what you plug in for y, x will only ever get extremely close to 0, but never reach it or go below it, and if you put in large values of y x will get very big.