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andrezito [222]
3 years ago
13

A rectangle has side lengths, L and W, and a diagonal, d. Complete the equations to answer the questions below.

Mathematics
1 answer:
Alexxandr [17]3 years ago
6 0

Answer:

Step-by-step explanation:

I think your question is missed of key information, allow me to add in and hope it will fit the original one.  Please have a look at the photo

My answer:

a.How are L and W, and d related?

Because  L and W, and  d are the 3 size of an right-triangle. So we use pytagon theorem to fill in the blank:

d^{2} = L^{2} + W^{2}

b. If L is 7 units long and W is 5 units long, how long is d

Once again, we use pytagon theorem to find out d

d^{2} = L^{2} + W^{2}

<=> d^{2} = 7^{2} + 5^{2}

<=> d^{2} = 74

<=> d = \sqrt{74}

Hope it will find you well.

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Answer:

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4 years ago
Find the equation of the sphere if one of its diameters has endpoints (-8, -3, -10) and (-6, 1, -4) which has been normalized so
alex41 [277]

Answer:

The  equation is  x^2 + y^2    +z^2 + 14 x  + 3y \ + 14z  + 86.25=0

Step-by-step explanation:

From the question we are told that  

    The  diameter endpoints is   (-8, -3, -10) and (-6, 1, -4)

Generally the equation of a sphere with center coordinates (a, b , c ) and  radius  r   is mathematically represented as

           (x -  a )^2  + (y -b )^2  + (z -c)^2 =  r^2

Now since we are given the endpoints of the diameter then we can obtain the center coordinates as follows

         (a, b , c) =  [ \frac{ -8 +(-6)}{2}  ,  \frac{-3 + (1)}{ 2}  , \frac{ -10 + (-4)}{2} ]

         (a, b , c) =  [ -7 ,  -1.5  , -7 ]

Now the length of the diameter is evaluated as

    |d| =  \sqrt{ (-8 - (-6 ))^2 + ( -3 - (1) )^2 + ( -10 - (-4))^2 }

   |d| =  \sqrt{56 }

   |d| =   \sqrt{4 *  14 }

   |d| = 2  \sqrt{  14 }

Now the radius is mathematically represented as

    r = \frac{|d|}{2}

    r = \frac{ 2 \sqrt{14} }{2}

    r =  \sqrt{14}

So

   (x -  -7 )^2  + (y --1.5 )^2  + (z --7)^2 = ( \sqrt{14} )^2

   (x +7 )^2  + (y +1.5 )^2  + (z +7)^2 = 14

    x^2 + 14 x + 49  + y^2 + 3y + 2.25   +z^2 14z + 49 = 14

    x^2 + y^2    +z^2 + 14 x  + 3y \ + 14z  + 86.25=0

4 0
4 years ago
The simplified form of (4/7)¯³​
Lemur [1.5K]
343/64


Step by step explanation This is how I got the answer to your question and I gave you the solution I hope this helps you out
5 0
3 years ago
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In-s [12.5K]

Answer: 105.26

Step-by-step explanation: 9263/88=105.26

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Margie's car can go 32 miles on a gallon of gas, and gas currently costs $4 per gallon. How many miles can Margie drive on $20 w
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