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2 years ago

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100 POINTS TO ANYONE WHO ANSWER THISS!!! An oil slick is expanding as a circle. The radius of the circle is increasing at the ra

te of 20 meters per day. Express the area of the circle as a function of d, the number of days elapsed.

1 answer:

Dima020 [189]2 years ago

3 0

Answer:

circle area = 400*d^2

Step-by-step explanation:

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<img src="https://tex.z-dn.net/?f=%5Cfrac%7Bb%5E%7B-2%7D%20%7D%7Bb%5E%7B4%7D%20%7D" id="TexFormula1" title="\frac{b^{-2} }{b^{4}

MAXImum [283]

Answer: $\frac{1}{b^6}$ or $b^{-6}$

Step-by-step explanation:

$\frac{b^-2+2}{b^4+2}$ Add the exponent two to both sides. After adding -2 and 2 you get 0 and any number raised to the zero power is one. And 4 plus two is 6

$\frac{b^0}{b^6}$ = $\frac{1}{b^6}$

3 0

3 years ago

Solve the proportion x/6 = 4/5

luda_lava [24]

Answer:

x/6 = 4/5

x(5) = 6(4)

5x=24

x=24/5

Let me know if this helps!

3 0

2 years ago

kherson [118]

Answer:

Point N(4, 1)

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Multiplication Property of Equality
Division Property of Equality
Addition Property of Equality
Subtraction Property of Equality<u> </u>

<u>Algebra I</u>

Coordinates (x, y)
Functions
Function Notation
Terms/Coefficients
Anything to the 0th power is 1
Exponential Rule [Rewrite]: $\displaystyle b^{-m} = \frac{1}{b^m}$
Exponential Rule [Root Rewrite]: $\displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}$

<u>Calculus</u>

Derivatives

Derivative Notation

Derivative of a constant is 0

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Derivative Rule [Chain Rule]: $\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)$

Step-by-step explanation:

<u>Step 1: Define</u>

<u /> $\displaystyle y = \sqrt{x - 3}$ <u />

<u /> $\displaystyle y' = \frac{1}{2}$ <u />

<u />

<u>Step 2: Differentiate</u>

[Function] Rewrite [Exponential Rule - Root Rewrite]: $\displaystyle y = (x - 3)^{\frac{1}{2}}$
Chain Rule: $\displaystyle y' = \frac{d}{dx}[(x - 3)^{\frac{1}{2}}] \cdot \frac{d}{dx}[x - 3]$
Basic Power Rule: $\displaystyle y' = \frac{1}{2}(x - 3)^{\frac{1}{2} - 1} \cdot (1 \cdot x^{1 - 1} - 0)$
Simplify: $\displaystyle y' = \frac{1}{2}(x - 3)^{-\frac{1}{2}} \cdot 1$
Multiply: $\displaystyle y' = \frac{1}{2}(x - 3)^{-\frac{1}{2}}$
[Derivative] Rewrite [Exponential Rule - Rewrite]: $\displaystyle y' = \frac{1}{2(x - 3)^{\frac{1}{2}}}$
[Derivative] Rewrite [Exponential Rule - Root Rewrite]: $\displaystyle y' = \frac{1}{2\sqrt{x - 3}}$

<u>Step 3: Solve</u>

<em>Find coordinates</em>

<em />

<em>x-coordinate</em>

Substitute in <em>y'</em> [Derivative]: $\displaystyle \frac{1}{2} = \frac{1}{2\sqrt{x - 3}}$
[Multiplication Property of Equality] Multiply 2 on both sides: $\displaystyle 1 = \frac{1}{\sqrt{x - 3}}$
[Multiplication Property of Equality] Multiply √(x - 3) on both sides: $\displaystyle \sqrt{x - 3} = 1$
[Equality Property] Square both sides: $\displaystyle x - 3 = 1$
[Addition Property of Equality] Add 3 on both sides: $\displaystyle x = 4$

<em>y-coordinate</em>

Substitute in <em>x</em> [Function]: $\displaystyle y = \sqrt{4 - 3}$
[√Radical] Subtract: $\displaystyle y = \sqrt{1}$
[√Radical] Evaluate: $\displaystyle y = 1$

∴ Coordinates of Point N is (4, 1).

Topic: AP Calculus AB/BC (Calculus I/II)

Unit: Derivatives

Book: College Calculus 10e

4 0

2 years ago

4.5 is 8.2 what is the sum

antiseptic1488 [7]

Answer:

12.7

Step-by-step explanation:

4 0

2 years ago

certain computer virus can damage any file with probability 35%, independently of other files. Suppose this virus enters a folde

Ksivusya [100]

Answer:

0.623 is the probability that between 800 and 850 files get damaged.

Step-by-step explanation:

We are given the following information:

We treat virus can damage computer as a success.

P( virus can damage computer) = 35% = 0.35

The conditions for normal distribution are satisfied.

By normal approximation:

$\mu = np = 2400(0.35) = 840\\\sigma = \sqrt{np(1-p)} = \sqrt{2400(0.35)(1-0.35)} = $$23.36$

We have to evaluate probability that between 800 and 850 files get damaged.

$P(800 \leq x \leq 850) = P(\displaystyle\frac{800 - 840}{23.36} \leq z \leq \displaystyle\frac{850-840}{23.36}) = P(-1.712 \leq z \leq 0)\\\\= P(z \leq 0.428) - P(z < -1.712)\\= 0.666 - 0.043 = 0.623 = 62.3\%$

$P(800 \leq x \leq 850) = 62.3\%$

0.623 is the probability that between 800 and 850 files get damaged.

8 0

2 years ago