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Alex777 [14]
2 years ago
9

Solve the system ... y=3x-8 and y=-9x+4

Mathematics
1 answer:
natita [175]2 years ago
7 0
1] y - 3x = -8
[2] y + 9x = 4

-3x + y = -8 9x + y = 4

Solve equation [2] for the variable y


[2] y = -9x + 4

// Plug this in for variable y in equation [1]

[1] (-9x+4) - 3x = -8
[1] - 12x = -12
// Solve equation [1] for the variable x


[1] 12x = 12

[1] x = 1
// By now we know this much :

y = -9x+4
x = 1
// Use the x value to solve for y

y = -9(1)+4 = -5

{y,x} = {-5,1}
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A rectangle has one side of 8 cm. How fast is the diagonal of the rectangle changing at the instant when the other side is 6 cm
lisov135 [29]
<h2>The diagonal is increasing at 1.8 cm/minute.</h2>

Step-by-step explanation:

Let l be one side,w be other side and s be diagonal.

We have

             s² = l² + w²

We have

          l = 8 cm

          w = 6 cm

           s² = l² + w²  

           s² = 8² + 6²

           s² = 100

           s = 10 cm

Taking derivative with respect to time in s² = l² + w²

           s^2=l^2+w^2\\\\2s\frac{ds}{dt}=2l\frac{dl}{dt}+2w\frac{dw}{dt}\\\\s\frac{ds}{dt}=l\frac{dl}{dt}+w\frac{dw}{dt}\\\\\frac{dw}{dt}=3cm/min\\\\\frac{dl}{dt}=0cm/min\\\\10\frac{ds}{dt}=8\times 0+6\times 3\\\\\frac{ds}{dt}=1.8cm/min

The diagonal is increasing at 1.8 cm/minute.

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