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2 years ago

ASAP please. Not understanding

Mathematics

1 answer:

vivado [14]2 years ago

6 0

Bryan has 180 feet of fencing. he use the wall for one side of fencing

So he has to fence only 3 sides

he has to fence bottom side + left side+ right side of the wall

Let x be the width of the garden

Let y be the length

Perimeter of the garden = length + width + width

180 = y +x +x

180 = y+2x

so y = 180 - 2x

(a) Area of rectangle = Length * width

Area = y * x

Area = (180 -2x)* x

so area of the garden = -2x^2 +180x

(b)To find dimension to create largest are we find x coordinate of the vertex

formula is $x= \frac{-b}{2a}$

a= -2 and b = +180

$x= \frac{-180}{2(-2)}= 45$

So width = 45

We know length y = 180 - 2x= 180 - 2(45) = 90

Dimension with greatest area is

Length = 90 feet

width = 45 feet

= 90 * 45 = 4050 square feet

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where we use the power rule,

$\displaystyle \int x^n \, dx = \frac{x^{n+1}}{n+1} + C ~~~~ (n\neq-1)$

and a substitution to integrate the last term,

$\displaystyle \int \frac{dt}{1-3t} = -\frac13 \int \frac{du}u \\\\ = -\frac13 \ln|u| + C \\\\ = -\frac13 \ln|1-3t| + C ~~~ (u=1-3t \text{ and } du = -3\,dt)$

$\displaystyle \int \frac t{1+4t} \, dt = \frac14 \int \left(1 - \frac1{1+4t}\right) \, dt \\\\ = \frac14 \left(t - \frac14 \ln|1 + 4t|\right) + C \\\\ = \boxed{\frac t4 - \frac{\ln|1+4t|}{16} + C}$