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anygoal [31]
3 years ago
11

A=1/2b(c+d) solve for c

Mathematics
1 answer:
TiliK225 [7]3 years ago
5 0

Answer:

c = \frac{2A}{b} - d

Step-by-step explanation:

Multiply both sides by 2 to eliminate the fraction

2A = b(c + d) ← divide both sides by b

\frac{2A}{b} = c + d ← subtract d from both sides

\frac{2A}{b} - d = c

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Steve likes to entertain friends at parties with "wire tricks." Suppose he takes a piece of wire 60 inches long and cuts it into
Alex_Xolod [135]

Answer:

a) the length of the wire for the circle = (\frac{60\pi }{\pi+4}) in

b)the length of the wire for the square = (\frac{240}{\pi+4}) in

c) the smallest possible area = 126.02 in² into two decimal places

Step-by-step explanation:

If one piece of wire for the square is y; and another piece of wire for circle is (60-y).

Then; we can say; let the side of the square be b

so 4(b)=y

         b=\frac{y}{4}

Area of the square which is L² can now be said to be;

A_S=(\frac{y}{4})^2 = \frac{y^2}{16}

On the otherhand; let the radius (r) of the  circle be;

2πr = 60-y

r = \frac{60-y}{2\pi }

Area of the circle which is πr² can now be;

A_C= \pi (\frac{60-y}{2\pi } )^2

     =( \frac{60-y}{4\pi } )^2

Total Area (A);

A = A_S+A_C

   = \frac{y^2}{16} +(\frac{60-y}{4\pi } )^2

For the smallest possible area; \frac{dA}{dy}=0

∴ \frac{2y}{16}+\frac{2(60-y)(-1)}{4\pi}=0

If we divide through with (2) and each entity move to the opposite side; we have:

\frac{y}{18}=\frac{(60-y)}{2\pi}

By cross multiplying; we have:

2πy = 480 - 8y

collect like terms

(2π + 8) y = 480

which can be reduced to (π + 4)y = 240 by dividing through with 2

y= \frac{240}{\pi+4}

∴ since y= \frac{240}{\pi+4}, we can determine for the length of the circle ;

60-y can now be;

= 60-\frac{240}{\pi+4}

= \frac{(\pi+4)*60-240}{\pi+40}

= \frac{60\pi+240-240}{\pi+4}

= (\frac{60\pi}{\pi+4})in

also, the length of wire for the square  (y) ; y= (\frac{240}{\pi+4})in

The smallest possible area (A) = \frac{1}{16} (\frac{240}{\pi+4})^2+(\frac{60\pi}{\pi+y})^2(\frac{1}{4\pi})

= 126.0223095 in²

≅ 126.02 in² ( to two decimal places)

4 0
3 years ago
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Ede4ka [16]

Answer:

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Step-by-step explanation:

3 0
3 years ago
How do you find the derivative of 1/logx?
valentina_108 [34]

The derivative of 1/logx is With the chain rule.

1log(x)=log(x)−1 is ,= -1xlog(x)2 .

The by-product of logₐ x (log x with base a) is 1/(x ln a). Here, the thrilling issue is that we have "ln" withinside the by-product of "log x". Note that "ln" is referred to as the logarithm (or) it's miles a logarithm with base "e".

The by-product of 1/log x is -1/x(log x)^2. Note that 1/logx is the reciprocal of log.

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5 0
11 months ago
Need help ASAP ? <br>3/4×20
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3/4 x 20

3/4 x 20/1

3 x 20 = 60

4 x 1 = 4

60 / 4 = 15

8 0
3 years ago
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For the inverse variation equation xy = k, what is the constant of variation, k, when x = 7 and y = 3? three-sevenths seven-thir
vova2212 [387]

The value of the constant k when the value of x and y is 7 and 3 respectively in the equation xy=k is 21.

<h3>What is an equation?</h3>

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The value of the constant k when the value of x and y is 7 and 3 respectively in the equation xy=k can be written as,

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Hence, the value of the constant k when the value of x and y is 7 and 3 respectively in the equation xy=k is 21.

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1 year ago
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