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ryzh [129]
3 years ago
13

You have 72 feet of fencing to enclose a rectangular plot that borders on a river. if you do not fence the side along the river,

find the length and width of the plot that will maximize the area

Mathematics
1 answer:
vodka [1.7K]3 years ago
8 0
The area is maximized when half the fence is used along the river. The length and width of the plot are 36 ft and 18 ft.

_____
Let x represent the length of fence parallel to the river. Then the area (A) can be described by
.. A = x(72 -x)/2
This equation describes a downward-opening parabola with zeros at x=0 and x=72. Its vertex (maximum) is halfway between the zeros, at x=36.

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Determine whether the following sampling is dependent or independent. Indicate whether the response variable is qualitative or q
Margarita [4]

Answer:1. Dependent

2.Qualitative Variable

Step-by-step explanation:

Step 1--- Dependent

Reason-- The researcher considers a couple as a whole and The sampling is dependent because a spouce selected for one sample dictates or determines which individual to be in the second sample.

Step 2----Qualitative variable

Reason--- it classifies the individual spouce mental health based on mental health inventory of the couple

Because Qualitative variables are variables which can be placed according to characteristic or attribute, here the characteristics is mental health.

7 0
3 years ago
Read 2 more answers
Let the region R be the area enclosed by the function f(x)=ln(x) and g(x)= 1/2x-2. Find the volume of the solid generated when t
Neporo4naja [7]

Answer:

V=61.66

Step-by-step explanation:

This problem can be solved by using the expression for the Volume of a solid with the washer method

V=\pi \int \limit_a^b[R(x)^2-r(x)^2]dx

where R and r are the functions f and g respectively (f for the upper bound of the region and r for the lower bound).

Before we have to compute the limits of the integral. We can do that by taking f=g, that is

f(x)=g(x)\\ln(x)=\frac{1}{2}x-2

there are two point of intersection (that have been calculated with a software program as Wolfram alpha, because there is no way to solve analiticaly)

x1=0.14

x2=8.21

and because the revolution is around y=-5 we have

R=ln(x)-(-5)\\r=\frac{1}{2}x-2-(-5)\\

and by replacing in the integral we have

V=\pi \int \limit_{x1}^{x2}[(lnx+5)^2-(\frac{1}{2}x+3)^2]dx\\

V=\pi [28x+\frac{1}{x}+xln^2x-12xlnx-6lnx]  

and by evaluating in the limits we have

V=61.66

Hope this helps

regards

3 0
3 years ago
SOMEONE PLEASE PLEASE HELP I NEED THE ANSWERS YO BOTH PF THESE PLEASE
ella [17]

Answer:

1. c; 2. d

Step-by-step explanation:

1. 2*3 = 6

2. (1.43*1000)p + (2.2*1000) = (-4.001*1000)

8 0
2 years ago
9 is a member of A {1,3,8} intersecting D {3,9}
Jet001 [13]

The intersection of the two sets is the list of members that appear in both sets. That is {3}.

Your statement is FALSE.

5 0
3 years ago
How do you solve 28-2.2x=11.6x-54.8??
malfutka [58]
28 - 2.2x = 11.6x - 54.8
28 + 54.8 = 11.6x + 2.2x
82.8 = 13.8x
82.8 / 13.8 = x
6 = x
or x = 6 
6 0
3 years ago
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