What is the volume of this container?

Answer:

[tex]\displaystyle \frac{dy}{dx} = \frac{-4}{3x^5}[/tex]

General Formulas and Concepts:

Calculus

Differentiation

Derivative Property [Multiplied Constant]:                                                           [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]

Basic Power Rule:

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle y = \frac{\frac{1}{x^4}}{3}[/tex]

Step 2: Differentiate

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

Unit: Differentiation

Answer:

[tex]y=x+3[/tex]

Step-by-step explanation:

What we need to know

1) Rewrite the equation x - y = 5 into slope-intercept form and identify the slope

[tex]x - y = 5[/tex]

Subtract both sides by x

[tex]x - y -x= -x+5\\-y= -x+5[/tex]

Divide both sides by -1

[tex]y= x-5[/tex]

Now, we can tell clearly that the slope (m) of this line is 1. Therefore, a line parallel to this would also have a slope of 1.

Plugging 1 as m into [tex]y=mx+b[/tex], we get:

[tex]y=x+b[/tex]

2) Find the y-intercept (b) of the line parallel to [tex]y= x-5[/tex] and find the final equation

[tex]y=x+b[/tex]

Plug in the given point (-5,-2)

[tex]-2=-5+b[/tex]

Add 5 to both sides

[tex]-2+5=-5+b+5\\3=b[/tex]

Therefore, the y-intercept of this line is 3. Now, plugging this back into our original equation, we get:

[tex]y=x+b\\y=x+3[/tex]

I hope this helps!

9514 1404 393

Answer:

  $12,720

Step-by-step explanation:

The amount is given by the formula ...

  A = P(1 +rt)

where P is the principal, invested at rate r for t years.

  A = $12,000(1 +0.06·1) = $12,720

The total amount after 1 year is $12,720.

Answer: C.) If the sum of the squares of the two shorter sides equals the square of the longest side, then the triangle is a right triangle.

Step-by-step explanation: i hope this helps! :)

The correct statement is (C)

The Pythagoras theorem states that if a triangle is right-angled (90 degrees), then the square of the hypotenuse is equal to the sum of the squares of the other two sides.

The Pythagoras theorem equation is expressed as, c2 = a2 + b2, where 'c' = hypotenuse of the right triangle and 'a' and 'b' are the other two legs. Hence, any triangle with one angle equal to 90 degrees produces a Pythagoras triangle and the Pythagoras equation can be applied in the triangle.

example:

The hypotenuse of a right-angled triangle is 16 units and one of the sides of the triangle is 8 units. Find the measure of the third side using the Pythagoras theorem formula.

Given : Hypotenuse = 16 units

Let us consider the given side of a triangle as the perpendicular height = 8 units

On substituting the given dimensions to the Pythagoras theorem formula

Hypotenuse2 = Base2 + Height2

162 = B2 + 82

B2 = 256 - 64

B = √192 = 13.856 units

So, Using the definition of Pythagoras theorem

the statement would be

If the sum of the squares of the two shorter sides equals the square of the longest side, then the triangle is a right triangle.

Learn more about pythagoras theorem here:

brainly.com/question/343682

#SPJ2

Answer:

is a function with a slope that is not constant.

Step-by-step explanation:

A linear function has a positive relationship and as such an increase in one variable (input variable) causes an increase in the other variable (output variable) i.e the variables are directly proportional. Thus, the graph of a linear function is a straight-line and its slope is always constant.

On the other hand, nonlinear function has a negative relationship and as such an increase in one variable (input variable) causes a decrease in the other variable (output variable) i.e the variables are inversely proportional.

This ultimately implies that, the graph of a nonlinear is a curved line and whose direction is constantly changing.

Hence, a nonlinear function is a function with a slope that is not constant. An example of a nonlinear function is a quadratic function or equation.

Answer:

D, (1,2)

Step-by-step explanation:

It all comes down to substitution. In this case the coefficient of x is 3 and the coefficient of y is 4. The format of these coordinates being (x,y).

1. Plug in your x value (1 in this circumstance) and solve:

3(1) + 4y < 12

3 + 4y < 12

2. Plug in your y value (2 in this circumstance) and solve:

3 + 4(2) < 12

3 + 8 < 12

3. Solve

3 + 8 = 11

11 < 12

Answer:

A sample of 153 is needed.

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.9}{2} = 0.05[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.05 = 0.95[/tex], so Z = 1.645.

Now, find the margin of error M as such

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

Standard deviation is 15 for the population of all adults.

This means that [tex]\sigma = 15[/tex]

We wish to find the sample size necessary to estimate the mean IQ score of statistics students. Suppose we want to be 90% confident that our sample mean is within 2 IQ points of the true mean.

This means that a sample of n is needed.

n is found when M = 2. So

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

[tex]2 = 1.645\frac{15}{\sqrt{n}}[/tex]

[tex]2\sqrt{n} = 1.645*15[/tex]

Simplifying both sides by 2

[tex]\sqrt{n} = 1.645*7.5[/tex]

[tex](\sqrt{n})^2 = (1.645*7.5)^2[/tex]

[tex]n = 152.2[/tex]

Rounding up:

A sample of 153 is needed.

Answer:

The blank for the computers will be 20 because they are multiply each number by 2. The top blanks will be 4 and 16

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

B, C, D are all symmetrical

Answer:

a

Step-by-step explanation:

since B, C, D are all symmetrical it should be a

Answer:

$30.96

Step-by-step explanation:

I hope this helps

Answer:

105, I think if not please tell me it isn't!

Answer:

2/5 i think not sure

Step-by-step explanation:

Answer:

There is a 40% chance of the person pulling out a penny.

Step-by-step explanation:

Out of 5 coins, 2 of them are pennies. This is 2 out of 5.

2 out of 5 is a fraction, 2/5.

2/5 in percent form is 40%.

Answer:

486

Step-by-step explanation:

The solid is a cube. The faces of a cube are 6 congruent squares.

side = 9 ft

surface area = 6 * side²

SA = 6 * (9 ft)²

SA = 486 ft²

Answer:

80b-16

Step-by-step explanation:

16(5b-1)

Answer:

x > 5

Step-by-step explanation:

–3(2x – 5) < 5(2 – x)

-6x + 15 < 10 - 5x

-6x + 5x < 10 - 15

-x < -5

x > 5

Answer: is D on khan academy

Answer:

[tex]1st \: = 16.3pints \: \\ 2nd \: = 23.7pints \\ \\ [/tex]

Answer:

Leon's jersey has a prime number

Step-by-step explanation:

Answer:

x = 1/3 , 5

Step-by-step explanation:

Factoriza y establece cada factor igual a cero.

Answer:

15-6

Step-by-step explanation:

if it helps don't forget to like and mark me

x=-9

Hope this helps :T

Answer:

d) 72/100

Step-by-step explanation:

the first grid is 42/100 so you add the 3/10 which 3/10 is equal to 30/100 the grid is just simplified. Once you add 42/100 and 30/100 it equals to 72/100. Hope this is helps you !

Answer:

72/100

Step-by-step explanation:

There is 40 whole and 30 whole which equals 70. Plus 2 which is 72 so the answer is 72/100

Answer:

43 FT^2

Step-by-step explanation:

3.14159265359 x 3.7^2

Pi times the radius squared

Answer:

2/11

Step-by-step explanation:

2 3/4 = 11/4

1/2 x 4/11 = 4/22 *when you divide a something by a fraction, you flip that fraction to get its reciprocal*

4/22 simplified is 2/11

Answer: x^3+8x^2-79x-182

Step-by-step explanation:

(x+13)(x+2)(x-7)=x^3+8x^2-79x-182

Answer:

I think the answer is 11i

there is the correct answer.

Answer:

B

Step-by-step explanation:

College Board

Answer:A

Step-by-step explanation:

● Alternate interior angles are always equal.