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Andreas93 [3]
1 year ago
13

8. You have 160 meters of fencing to enclose a rectangular pen for your dog. To provide sufficient running

Mathematics
1 answer:
kolbaska11 [484]1 year ago
7 0

Perimeter is the sum of the length of the sides used to make the given figure. The length and the width of the rectangle are 60 meters and 20 meters, respectively.

<h3>What is the perimeter?</h3>

Perimeter is the sum of the length of the sides used to make the given figure.

Let the width of the rectangle be represented by x.

Given that the pen should be three times as long as it is width. Therefore, the dimensions of the rectangle can be written as,

Width of the rectangle = x

Length of the rectangle = 3x

Also, it is given that the perimeter of the rectangle should be equal to 160 meters, therefore, we can write,

Perimeter = 2(Length + Width)

160 = 2(3x + x)

160 = 2(4x)

160 = 8x

x = 160/8

x = 20 meters

Now, the dimensions of the rectangle can be written as,

Length = 3x = 3 × 20 meters = 60 meters

Width = x = 20 meters

Hence, the length and the width of the rectangle are 60 meters and 20 meters, respectively.

Learn more about perimeter here:

brainly.com/question/10466285

#SPJ1

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Formula for curvature for a well behaved curve y=f(x) is


K(x)= \frac{|{y}''|}{[1+{y}'^2]^\frac{3}{2}}


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{y}''=7e^{x}\\ {y}'=7e^{x}


k(x)=\frac{7e^{x}}{[{1+(7e^{x})^2}]^\frac{3}{2}}


{k(x)}'=\frac{7(e^x)(1+49e^{2x})(49e^{2x}-\frac{1}{2})}{[1+49e^{2x}]^{3}}

For Maxima or Minima

{k(x)}'=0

7(e^x)(1+49e^{2x})(98e^{2x}-1)=0

→e^{x}=0∨ 1+49e^{2x}=0∨98e^{2x}-1=0

e^{x}=0  ,  ∧ 1+49e^{2x}=0   [not possible ∵there exists no value of x satisfying these equation]

→98e^{2x}-1=0

Solving this we get

x= -\frac{1}{2}\ln{98}

As you will evaluate {k(x})}''<0 at x=-\frac{1}{2}\ln98

So this is the point of Maxima. we get y=7×1/√98=1/√2

(x,y)=[-\frac{1}{2}\ln98,1/√2]

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k(x)=0







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bus = 43

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Step-by-step explanation:

This can be solved using simultaneous equations

Let v represent the number of students that a van carries

Let b represent the number of students that a bus carries

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5v + 3b = 189  eqn 2

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Subtract equation 4 from 3

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Substitute for b in equation 1

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solve for v

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