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aniked [119]
3 years ago
12

Suppose f(x) varies directly with x and f (x) = 24 when x = 2.

Mathematics
1 answer:
serious [3.7K]3 years ago
5 0

Answer:

72

Step-by-step explanation:

Given that f(x) varies directly with x the the equation relating them is

f(x) = kx ← k is the constant of variation

To find k use the condition f(x) = 24 when x = 2

k = \frac{f(x)}{x} = \frac{24}{2} = 12

f(x) = 12x ← equation of variation

When x = 6, then

f(6) = 12 × 6 = 72

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Answer:

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3 years ago
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Reil [10]

<u>Answer:</u>

x = 5.00 cm

<u>Step-by-step explanation:</u>

• area of the rectangle = x   x   (x + 1)

                                     = x^2 + x

• area of the circle = π r²

                               = \frac{22}{7}   x   (x + 2)^2

                               = \frac{22}{7}   x   (x^2 + 4x + 4)

∴   x^2 + x   +    \frac{22}{7}   x   (x^2 + 4x + 4)  = 184  

⇒  x^2 + x      +   \frac{22}{7}  x^2   \space\ + \space\ \frac{88}{7} x \space\  +  \space\  \frac{88}{7} = 184

⇒  \frac{29}{7}x^2 \space\  +  \space\  \frac{95}{7}x \space\ - \frac{1200}{7} = 0

• Using quadratic formula, where

a = \frac{29}{7}

b = \frac{95}{7}

c = \frac{-1200}{7} ,

x=\frac{-b \pm \sqrt{b^2-4c}}{2}

x = \frac{-\frac{95}{7}\pm \sqrt{(\frac{95}{7})^2 - 4(\frac{29}{7})(\frac{-1200}{7} )  }  }{2(\frac{29}{7})}

x = 5.00   \space\   \space\ \space\ or  \space\ \space\ \space\   x = -8.28

As length (x) cannot be a negative number,

x = 5.00 cm

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2 years ago
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iVinArrow [24]

Answer:

x = \sqrt{99}

Step-by-step explanation:

Based on the Pythagoras theorem, where a and b are the legs of the triangle and c is the hypotenuse.

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Therefor x = \sqrt{99}

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3 years ago
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BigorU [14]

Answer:

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Step-by-step explanation:

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