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3 years ago

The radius of a circular puddle is growing at a rate of 25 cm/sec.

Mathematics

1 answer:

tatiyna3 years ago

8 0

Answer:

Step-by-step explanation:

a)area A=pi r^2

rate of change of area =dA/dt =2 pi r dr/dt

given dr/dt =25 ,r =50

rate of change of area =dA/dt =2 pi *50 *25 =2500pi=7854

area growing 7854 cm2/s

b)area A=pi r^2

rate of change of area =dA/dt =2 pi r dr/dt

given dr/dt =25 ,A =64

pi r^2 =64

=>r =8/√pi

rate of change of area =dA/dt =2 pi *(8/√pi) *25 =400√pi=708.98

area growing 708.98 cm2/s

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Which of the following is a solution of x2 + 6x = −18? x = 3 − 3i x = −3 + 3i x = −6 + 3i x = 6 − 3i

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Step 1 ) Move all terms right side of the equation.

$\displaystyle\ x^{2} + 6x = -18$

$\displaystyle\ x^{2} + 6x + 18 = -18 + 18$

$\displaystyle\ x^{2} +6x + 18 = 0$

Step 2 ) Apply quadratic formula. (Note: There are 2 solutions)

$\displaystyle\ x^{2} +6x + 18 = 0$

$\displaystyle\ x = \frac{-b\sqrt{b^{2}-4ac}}{2a}, \displaystyle\ x = \frac{-b-\sqrt{b^{2}-4ac}}{2a}$

$\displaystyle\ x = \frac{-6+\sqrt{6^{2}-4 * 18}}{2} , \displaystyle\ x = \frac{-6-\sqrt{6^{2}-4*18}}{2}$

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Step 3 ) Simplify.

$\displaystyle\ x = \frac{-6+6i}{2}$ ,

$\displaystyle\ x = \frac{-6-6i}{2}$

$\displaystyle\ x = -3+ 3i$ ,

$\displaystyle\ x = -3 - 3i$

Since the options only provide one of the answer we found, the answer is...

$\displaystyle\ x = -3 - 3i$

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d1i1m1o1n [39]

Number sentence is simply a sentence, that uses numbers and arithmetic signs.

The context that can be created from the sentence is: How many bits are there, in $32\frac 14$ bytes
The verbal meaning of $32\frac 14 \div \frac 18 = 258$ is: When $32\frac 14$ is divided by $\frac 18$ , the result is $258$

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$32\frac 14 \div \frac 18 = 258$

(a) Context or story

A context is as follows:

There are 8 bits in a byte; How many bits are there, in $32\frac 14$ bytes

(b) As a multiplication

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Change the division to multiplication as follows:

$32\frac 14 \times \frac 81 = 258$

(c) Verbal explanation how the numbers are related

When $32\frac 14$ is divided by $\frac 18$ , the result is $258$