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Schach [20]
3 years ago
15

Kayla wants to find the width, AB, of a river. She walks along the edge of the river 100 ft and marks point C. Then she walks 22

ft further and marks point D. She turns 90° and walks until her location, point A, and point C are collinear. She marks point E at this location, as shown.
Mathematics
2 answers:
liubo4ka [24]3 years ago
8 0
You did not give me B, so I cannot help you with this question.
musickatia [10]3 years ago
5 0

Answer:

Given data

edge of the river=100 ft

angle=90

Width of AB=100+22sin90

Width of AB=122 ft

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Effectus [21]

Answer:

The dimension of the cardboard is 34 cm by 34 cm by 17 cm.

Step-by-step explanation:

Let the dimension of the cardboard box be x cm by y cm by z cm.

The surface area of the cardboard box without lid is

f(x,y,z)= xy+2xz+2yz.....(1)

Given that the volume of the cardboard is 19,652 cm³.

Therefore xyz =19,652

\Rightarrow z=\frac{19652}{xy}......(2)

putting the value of z in the equation (1)

f(x,y)=xy+2x(\frac{19652}{xy})+2y(\frac{19652}{xy})

\Rightarrow f(x,y)=xy+\frac{39304}{y})+\frac{39304}{x}

The partial derivatives are

f_x=y-\frac{39304}{x^2}

f_y=x-\frac{39304}{y^2}

To find the dimension of the box set the partial derivatives f_x=0 and f_y=0.Therefore y-\frac{39304}{x^2}=0

\Rightarrow y=\frac{39304}{x^2}.......(3)

and   x-\frac{39304}{y^2}=0

\Rightarrow x=\frac{39304}{y^2}.......(4)

Now putting the x in equation (3)

y =\frac {39304}{(\frac{39304}{y^2})^2}

\Rightarrow y=\frac{y^4}{39304}

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Then \Rightarrow x=\frac{39304}{34^2} =34 cm.

Putting the value of x and y in the equation (2)

z=\frac{19652}{34 \times 24}

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The dimension of the cardboard is 34 cm by 34 cm by 17 cm.

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3 years ago
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