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Mademuasel [1]
4 years ago
9

(URGENT) need answer for today​

Mathematics
1 answer:
Harman [31]4 years ago
8 0

<u>Given</u>:

Given that a basketball court is in the shape of a rectangle that is 94 feet long and 50 feet wide.

We need to determine the length of the diagonal to the court.

<u>Length of the diagonal:</u>

The length of the diagonal can be determined using the Pythagorean theorem.

Thus, we have;

d^2=l^2+w^2

where d is the diagonal, l is the length and w is the width of the rectangle.

Substituting the values, we have;

d^2=94^2+50^2

d^2=8836+2500

d^2=11336

d=\sqrt{11336}

d=106.5

Thus, the length of the diagonal of the court is 106.5 feet.

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A cardboard box without a lid is to have a volume of 19,652 cm3. Find the dimensions that minimize the amount of cardboard used.
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}

\Rightarrow y^3= 39304

⇒y=34 cm

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}

  =17 cm.

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

4 0
3 years ago
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Answer:

Step-by-step explanation:

m+3 < 5

Isolate the m by subtracting 3

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m = 1-1/it doesn't matter because the answer will be zero!!

Now for slope intercept form:

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y = 0x + b; take one of your points and plug it in:

1= 0(2)+ b

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