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4 years ago

Y varies inversely with X. When X=5, Y=4, What is the value of Y when X increases to 7.

Mathematics

1 answer:

Anna35 [415]4 years ago

3 0

Step-by-step explanation:

y is inversely to x

to remove inversely we use constant so let constant be k

y=k/x. (1)

now let find value of k

X=5, Y=4

put these in above equation(1)

4=k/5

4×5 =k

20=k

now when x increase to 7

x=5 increase to 7 x=12

now let find value of y put value of x and k in equation (1)

y=20/12

y=5/3

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TiliK225 [7]

parallelogram

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area=b times h

area = 16(9)=144cm2

2 TRAPEZOID

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3 years ago

A piece of wire 25 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral tria

fomenos

Answer:

Wire used for square is 7.55 m.

Step-by-step explanation:

Let the length of wire cut for square be 'x'.

Given:

Total length of the wire = 25 m

Length of wire for square = 'x'

Length of wire for equilateral triangle = $25-x$

Now, area of square (a) = $x^2$

Area of equilateral triangle (e) is given as:

$e=\frac{\sqrt3}{4}(25-x)^2$

Now, total area (A) is given as:

$A=a+e\\\\A=x^2+\frac{\sqrt3}{4}(25-x)^2$

Now, in order to maximize 'A', the derivative of area with respect to 'x' must be 0.

∴ $\frac{dA}{dx}=0$

$\frac{d}{dx}(x^2+\frac{\sqrt3}{4}(25-x)^2)=0\\\\2x-\frac{\sqrt3}{2}(25-x)=0\\\\2x+\frac{x\sqrt3}{2}=\frac{25\sqrt3}{2}\\\\x(2+\frac{\sqrt3}{2})=\frac{25\sqrt3}{2}\\\\x(4+\sqrt3)=25\sqrt3\\\\x=\frac{25\sqrt3}{4+\sqrt3}=7.55\ m$

Therefore, the length of the wire that is cut for square should be 7.55 m for maximum area.

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koban [17]

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Step-by-step explanation:

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