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Ipatiy [6.2K]
2 years ago
12

Y is directly proportional to the square root of x if y = 60 when x = 36 find x when y = 80

Mathematics
2 answers:
bearhunter [10]2 years ago
7 0

Answer:

x = 64

Step-by-step explanation:

Given y is directly proportional to \sqrt{x} then the equation relating them is

y = k\sqrt{x} ← k is the constant of proportion

To find k use the condition y = 60 when x = 36, then

60 = k \sqrt{36} = 6k ( divide both sides by 6 )

10 = k

y = 10\sqrt{x} ← equation of proportion

When y = 80 , then

80 = 10\sqrt{x} ( divide both sides by 10 )

8 = \sqrt{x} ( square both sides )

64 = x

butalik [34]2 years ago
6 0
Y = x^2
80 = x^2
x = √80
x = 8.94
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A rectangle has width that is 6 meters less than the length. The area of the rectangle is 280 square meters. Find the dimensions
salantis [7]

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<em><u>Solution:</u></em>

Let "a" be the length of rectangle

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Given that,

<em><u>A rectangle has width that is 6 meters less than the length</u></em>

Width = length - 6

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\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}\\\\\quad x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}

\mathrm{For\:}\quad a=1,\:b=-6,\:c=-280:\quad a_{1,\:2}=\frac{-\left(-6\right)\pm \sqrt{\left(-6\right)^2-4\cdot \:1\left(-280\right)}}{2\cdot \:1}

a =\frac{6 \pm \sqrt{36+1120}}{2}\\\\a = \frac{6 \pm \sqrt{1156}}{2}\\\\a = \frac{6 \pm 34}{2}\\\\Thus\ we\ have\ two\ solutions\\\\a = \frac{6+34}{2} \text{ or } a = \frac{6-34}{2}\\\\a = 20 \text{ or } a = -14

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