The volume of a cube depends on the length of its sides. This can be written in function notation as v(s). What is the best interpretation of v(4)=64

Answer:

7964

Step-by-step explanation:

A colony of bacteria that starts with 1 bacterium and doubles in number every half hour will contain approximately 281,474,976,710,656 bacteria at the end of 24 hours.

The number of bacteria in a colony that starts with 1 bacterium and doubles in number every half hour can be calculated using the formula 2ⁿ, where n is the number of generations. Since each generation is half an hour, there are 48 generations in 24 hours. Plugging in n=48 into the formula, we get 2⁴⁸, which is approximately 281,474,976,710,656 bacteria.

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#SPJ11

Answer:  Option 'C' is correct.

Step-by-step explanation:

Since we have given that

[tex]S_n=\sum^{\infty}_{n=1}4(\dfrac{1}{4})^{n-1}[/tex]

We need to find the value of S₄.

So, it means sum of 4 terms.

Here it form a geometric series:

a = 4 = first term

r = [tex]\dfrac{1}{4}[/tex] = Common ratio

And sum of n terms whose ratio is less than 1 is given by

[tex]S_n=\dfrac{a(1-r^n)}{1-r}\\\\S_4=\dfrac{4(1-\dfrac{1}{4}^{4})}{1-\dfrac{1}{4}}\\\\S_4=\dfrac{4(1-0.25^4)}{1-0.25}\\\\S_4=\dfrac{4(1-0.0039)}{0.75}\\\\S_4=5.3125\\\\S_4=5\dfrac{5}{16}[/tex]

Hence, Option 'C' is correct.

Answer:  Option 'C' is correct.

Step-by-step explanation:

Answer:

The answer is $686.584

Step-by-step explanation:

Given is, Cannon pays $8.05 per month for every $1,000, so we have a ratio:   8.05 / 1000  

Now, we will find the second ratio which is an unknown payment per month over the price:   x / 85290  

Equaling them to solve for x :

[tex]\frac{8.05}{1000}=\frac{x}{85290}[/tex]

[tex]1000x=8.05*85290[/tex]

[tex]1000x = 686584.50[/tex]

So, x = 686.584

Hence, the answer is $686.584

Step-by-step explanation: Apex 9/25/19

YES slay5 is correct the answer is : C. an inscribed angle

Answer:  C. An inscribed angle

Step-by-step explanation:

Central angle is an angle that is subtended by an arc in a circle, it is also known as the arc's angular distance.

Interior angle is an angle between two sides inside a polygon or a shape.

Inscribed angle is an angle formed by two chords in a circle which have a common endpoint, and by the inscribed angle theorem, the measurement of inscribed angle is half the measure of the intercepted arc.  

To catch up to your friend or not in a race explained with equations and steps.

The question is: Will you catch up to your friend? Explain.

Step-by-step explanation:

Friend's progress equation: y = 9x + 20

Your progress equation: y = 9x

To catch up, set the equations equal: 9x + 20 = 9x

Solve for x: 20 = 0 (This equation has no solution)

You will not catch up to your friend.

Answer:

b.1 over 3 to the 5th power.

Step-by-step explanation:

We are given that an expression

[tex]3^4\cdot 3^{-9}[/tex]

We have to find that which expression is equivalent to given expression

[tex]3^4\cdot 3^{-9}[/tex]

We know that [tex]a^b+a^c=a^{b+c}[/tex]

Using this identity

Then, we get [tex]3^4\cdot 3^{-9}=3^{4-9}=3^{-5}[/tex]

[tex]3^4\cdot 3^{-9}=\frac{1}{3^5}[/tex]

Using [tex]a^{-b}=\frac{1}{a^b}[/tex]

Hence, option b is true.

Answer:b.1 over 3 to the 5th power.

Final answer:

To solve the student's algebra problem, we defined variables, set up an equation based on the given conditions, and then solved for the larger number. Ultimately, we found the two numbers to be 33 and 16.

Explanation:

The student asked a problem that involves finding two numbers given that their sum is 49 and the smaller number is 17 less than the larger number. To solve this problem, we will use algebra.

Let the larger number be x and the smaller number be x - 17. According to the problem, the sum of these two numbers is 49:

x + (x - 17) = 49

Combine like terms: 2x - 17 = 49

Add 17 to both sides: 2x = 66

Divide by 2: x = 33

Since the larger number is 33, the smaller number is 33 - 17, which is 16.

Therefore, the two numbers are 33 and 16.

Here we want to find all the zeros of the function f(x) = 16*x^4 - 81.

The zeros are:

First, for a given function f(x), we define the zeros as the values of x such that:

f(x) = 0.

Then we must solve:

f(x) = 16*x^4 - 81 = 0

Solving this for x leads to:

16*x^4 = 81

x^4 =  81/16

x^2 = ±√(81/16) = 9/4

x = ±√±(9/4) = ±3/2 and ±(3/2)*i

So there are 4 zeros, and these are:

Where the two complex zeros come from evaluating the second square root on -9/4.

If you want to learn more, you can read.

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1 acre = 43560 square feet

43560 = 484 * X

X=43560/484 = 90

the width = 90 feet

Answer:

90 feet

Step-by-step explanation:

Answer:

In 2021 you would be 56 or 55 years old

Step-by-step explanation:

2021-1965=56 or the other way you could do it 52+4 because the other person said you would be 52 in 2017 so 4 years after you would be 55 or 56

Final answer:

To express -2 in trigonometric form, we find the magnitude (absolute value) and the argument (angle) of the complex number.

Explanation:

The trigonometric form of a complex number is expressed in the form r(cosθ + isinθ), where r is the magnitude of the complex number and θ is the argument or angle.

In this case, to express -2 in trigonometric form, we first find the magnitude, which is the absolute value of -2, so |-2| = 2. The argument can be found using the arctan function, which is θ = arctan(b/a), where a is the real part and b is the imaginary part.

For -2, the real part is -2 and the imaginary part is 0. Thus, the argument is θ = arctan(0/(-2)) = arctan(0) = 0. Therefore, -2 in trigonometric form is 2(cos0 + isin0), which simplifies to just 2.

Final answer:

To find the solutions of the equation 4x^4 - 4x^2 = 8, we can rearrange the equation and solve the resulting quadratic equation. The solutions are x = ±√2.

Explanation:

To find the solutions of the equation 4x^4 - 4x^2 = 8, we can rearrange the equation to get 4x^4 - 4x^2 - 8 = 0. This is a quadratic equation in terms of x^2. We can solve this quadratic equation by factoring or by using the quadratic formula.

Factoring the equation, we get (2x^2 - 4)(2x^2 + 2) = 0. Setting each factor equal to zero, we have 2x^2 - 4 = 0 and 2x^2 + 2 = 0.

Solving each equation separately, we get x^2 = 2 and x^2 = -1. Taking the square root of both sides, we get x = ±√2 and x = ±i. Therefore, the solutions of the original equation are x = ±√2.

The exact length of the curve [tex]\(y = 3 + 2x^\frac{3}{2}\)[/tex] over the interval [tex]\(0 \leq x \leq 1\)[/tex] is [tex]\(\frac{2}{27} (10\sqrt{10} - 1)\)[/tex].

To find the exact length of the curve [tex]\(y = 3 + 2x^\frac{3}{2}\)[/tex] over the interval [tex]\(0 \leq x \leq 1\)[/tex], we can use the formula for arc length of a curve:

[tex]\[ L = \int_{a}^{b} \sqrt{1 + \left(\frac{dy}{dx}\right)^2} dx \][/tex]

where a and b are the lower and upper bounds of the interval, respectively.

First, we need to find [tex]\(\frac{dy}{dx}\)[/tex], which represents the derivative of y with respect to x:

[tex]\[ \frac{dy}{dx} = \frac{d}{dx}(3 + 2x^\frac{3}{2}) = 0 + 3x^\frac{1}{2} = 3\sqrt{x} \][/tex]

Next, we substitute this derivative into the formula for arc length:

[tex]\[ L = \int_{0}^{1} \sqrt{1 + (3\sqrt{x})^2} dx = \int_{0}^{1} \sqrt{1 + 9x} dx \][/tex]

Now, we need to integrate [tex]\(\sqrt{1 + 9x}\)[/tex]L with respect to \(x\). We can do this by making a substitution. Let u = 1 + 9x, then du = 9dx and \(dx = \frac{du}{9}\). Substituting these into the integral, we get:

[tex]\[ L = \frac{1}{9} \int_{1}^{10} \sqrt{u} du \][/tex]

Now, we can integrate [tex]\(\sqrt{u}\)[/tex]:

[tex]\[ L = \frac{1}{9} \left[\frac{2}{3}u^\frac{3}{2}\right]_{1}^{10} = \frac{2}{27} \left[10^\frac{3}{2} - 1^\frac{3}{2}\right] \][/tex]

[tex]\[ L = \frac{2}{27} (10^\frac{3}{2} - 1) \][/tex]

[tex]\[ L = \frac{2}{27} (10\sqrt{10} - 1) \][/tex]

So, the exact length of the curve [tex]\(y = 3 + 2x^\frac{3}{2}\)[/tex] over the interval [tex]\(0 \leq x \leq 1\)[/tex] is [tex]\( \frac{2}{27} (10\sqrt{10} - 1) \)[/tex].

Answer:

1.1 × 103 feet per second