What are the slopes and y-intercept of a graph?

the rate of change of the radius at the instant the volume equals 36π cm³ is 7 / (36π) cm/sec.

The volume V of a sphere with radius r is given by the formula V = (4/3)πr³. We are given that the rate of change of the volume is 7 cm³/sec. Differentiating the volume formula with respect to time, we get dV/dt =(4/3)π(3r²)(dr/dt), where dr/dt represents the rate of change of the radius with respect to time.

We are looking for the rate of change of the radius, dr/dt, when the volume equals 36π cm³. Substituting the values into the equation, we have: 7 = (4/3)π(3r²)(dr/dt)

7 = 4πr²(dr/dt) To find dr/dt, we rearrange the equation: (dr/dt) = 7 / (4πr²) Now, we can substitute the volume V = 36π cm³ and solve for the radius r: 36π = (4/3)πr³

36 = (4/3)r³

27 = r³

r = 3  Substituting r = 3 into the equation for dr/dt, we get: (dr/dt) = 7 / (4π(3)²)

(dr/dt) = 7 / (4π(9))

(dr/dt) = 7 / (36π)

Learn more about volume here:

https://brainly.com/question/13338592

#SPJ11

Answer:

the answer is 12 degrees

The measure of angle ACB when the secant BC and the tangent AC intersect is 12°

When a secant and a tangent meet outside the circle, thwe product of the length of the secant and its external segment equals the square of the length of the tangent segment.

Therefore,

arc XA = 2(64) = 128 degrees.

Hence,

m∠C = 1 / 2 (152 - 128)

m∠C = 1 / 2 (24)

m∠ACB = 12°

Therefore, angle ACB is 12 degrees.

learn more on secant and tangent here: https://brainly.com/question/27248564

Answer:

no

Step-by-step explanation:

u r a n00b hahahahahahahahahahahahahaahahhaahahahahahahahahahahahahahahahahahahhahahau suk balz hhahahahahahahahahahahahahahaha

Answer:

you just put the point on the spot where x=2 and y=2

the red dot is the answer

Step-by-step explanation:

What is the question, is their answer options or...?

Answer:

See attached

Step-by-step explanation:

Disruptive selection is a type of natural selection that favors extreme values of a trait while reducing the fitness of individuals with intermediate values. This pattern occurs when the environment or selective pressures favor individuals at both ends of the phenotype distribution.

Disruptive selection occurs when individuals with extreme phenotypes have higher fitness compared to those with intermediate phenotypes. This can happen in various scenarios. For example, in a habitat with two distinct resource types, individuals with specialized traits for each resource type may have higher survival or reproductive success, leading to the maintenance of two distinct phenotypes.

In disruptive selection, the selection pressure against intermediate phenotypes reduces their fitness, causing a bimodal distribution where individuals at the extremes have higher relative fitness compared to those in the middle. Over time, disruptive selection can result in the divergence of the population into two or more distinct forms, potentially leading to the formation of new species if reproductive isolation occurs.

This type of selection can play a significant role in shaping the evolution and adaptation of populations by promoting and maintaining phenotypic diversity in response to selective pressures.

To learn more about disruptive selection, click here: brainly.com/question/29161682

#SPJ11

To test the convergence or divergence of the series ∑[infinity] k=1 k ln k / (k+1)^3, we can use the limit comparison test.

First, let's consider the general term of the series, a_k:

a_k = k ln k / (k+1)^3

To apply the limit comparison test, we need to find a comparison series whose convergence or divergence is known. We choose the series ∑[infinity] k=1 1 / k^2, which is a known convergent p-series with p = 2.

Now, let's calculate the limit as k approaches infinity of the ratio between the general terms of the two series:

lim (k→∞) (a_k / (1/k^2))

= lim (k→∞) (k ln k / (k+1)^3) / (1/k^2)

= lim (k→∞) (k ln k / (k+1)^3) * (k^2 / 1)

= lim (k→∞) (k^3 ln k / (k+1)^3)

We can simplify this further by dividing both the numerator and the denominator by k^3:

= lim (k→∞) (ln k / (1+1/k)^3)

Now, as k approaches infinity, (1+1/k) approaches 1:

= lim (k→∞) (ln k / 1^3)

= lim (k→∞) ln k

The natural logarithm ln k grows without bound as k approaches infinity. Therefore, the limit of the ratio is infinity.

According to the limit comparison test, if the limit of the ratio is finite and positive, then both series converge or both series diverge. If the limit is zero or infinite, the conclusions may vary.

Since the limit of the ratio is infinite, we can conclude that the series ∑[infinity] k=1 k ln k / (k+1)^3 also diverges.

Therefore, the given series diverges.

learn more about convergence here

https://brainly.com/question/29258536?referrer=searchResults

#SPJ11

No, 25 is not a prime number. It can be divided by 5 without a remainder, so it has factors other than 1 and itself.

A prime number is a positive integer greater than 1 that has no positive integer divisors other than 1 and itself. In other words, a prime number can only be divided evenly by 1 and by itself. They are considered to be the "building blocks" of the natural numbers, and are important in number theory and other branches of mathematics.

The factors of 25 are 1, 5 and 25. Prime numbers are numbers that are divisible by only 1 and themselves. So 25 is not a prime number.

To know more on prime number

https://brainly.com/question/11799672

#SPJ4

Answer:

1: Narrower

2: Wider

Step-by-step explanation:

The magnitude of 'a' increases, the parabola becomes more and more wider.

A parabola is a curve where any point is at an equal distance from a fixed point (the focus), and a fixed straight line (the directrix).

Given is a parabola.

The parametric form of equation of parabola is given by -

y² = 4ax

Here, distance 'a' is called focus of parabola.

For a constant value of x - coordinate, take different values of 'a'. For constant x, we get the following relation -

y² \(\alpha\) a

As the magnitude of 'a' increases, the y coordinate increases and parabola becomes more and more wider.

Therefore,  the magnitude of 'a' increases, the parabola becomes more and more wider.

To solve more questions on parabola, visit the link below-

https://brainly.com/question/21685473

#SPJ5

Answer:

3.25

Step-by-step explanation:

Age and you can also use weight too

you can easily group people by their age and weight but not by eye color

example

age people

5 - 10 14

10 - 15 5

the table above shows that we have 14 people within the range of 5 to 10 years

and likewise the weight of the people can serve the same purpose

Answer:

5 pounds

Step-by-step explanation:

the volume of the container = 2*1.5*3.5= 10.5cubic foot.

Density of the content = 0.49 pound per cubic foot.

As already know,

Density = mass/ volume.

therefore, mass = density * volume.

mass of the content = 0.49 * 10.5 =5 pounds approximately

Answer:

50% chance

Step-by-step explanation:

if there are four balls there is a 50% chance she will pick the basket ball or the scoccer ball. Hope this helped.

Answer:

m'n' equals 13

Step-by-step explanation:

39 divided by 1/3 equals 13

Answer:

sagutan mo yan module mo yan wag kang umasa sa brainly

Answer:

Step-by-step explanation:

You want an equation and its solution for the distance from a building to the base of a ladder leaning at an angle of 71.6° to a point 12 ft up the side of the building.

The tangent function gives the relation between the legs of a right triangle:

  Tan = Opposite/Adjacent

In the attached diagram, that tells us ...

  tan(71.6°) = BL/BG

The equation that can be used to find the distance BG is ...

  tan(71.6°) = (12 ft)/BG

The solution to the equation is ...

  BG = (12 ft)/tan(71.6°) ≈ 4.0 ft

The bottom of the ladder is about 4.0 feet from the side of the building.

<95141404393>

Answer:

equilateral triangle all angles add up to 180 and are equal so each angle is 60 degrees

angles on a line add up to 180.

angle CBD = 180-60 = 120

DBC is an isosceles triangle so it's base angles are the same.

180-120= 60

60/2=30

The isosceles triangle ΔDBC have equal base angles.

The measure of angle C is 30 degrees

ΔADB is an equilateral triangle.

So, we have:

\(\mathbf{\angle ADC = \angle BAD = \angle DBA = 60}\)

Next, we calculate \(\mathbf{\angle DBC}\)

\(\mathbf{\angle DBC =180 - \angle DBA}\) -- angle on a straight line

So, we have:

\(\mathbf{\angle DBC =180 - 60}\)

\(\mathbf{\angle DBC =120}\)

ΔDBC is an isosceles triangle.

So, we have:

\(\mathbf{\angle C = \angle D}\)

This is then calculated as:

\(\mathbf{\angle C + \angle C = 180 - 120}\)

\(\mathbf{2\angle C = 60}\)

Divide both sides by 2

\(\mathbf{\angle C = 30}\)

Hence, the measure of angle C is 30 degrees

Read more about triangles at:

https://brainly.com/question/2456591

1) the displacement of the particle over the interval [0, 2] is 2 meters.

2) the total distance traveled by the particle over the interval [0, 2] is 4 meters.

What is the quadratic equation?

The solutions to the quadratic equation are the values of the unknown variable x, which satisfy the equation. These solutions are called roots or zeros of quadratic equations. The roots of any polynomial are the solutions for the given equation.

Question 1: To compute the displacement of the particle over [0, 2], we need to find the net change in position. The displacement can be calculated by integrating the velocity function over the given interval.

Given velocity function v(t) = 3t² - 2t - 1, we integrate it with respect to t over the interval [0, 2]:

Displacement = ∫[0 to 2] v(t) dt

Let's calculate the integral:

Displacement = ∫[0 to 2] (3t² - 2t - 1) dt

To find the antiderivative, we integrate each term separately:

Displacement = ∫[0 to 2] (3t²) dt - ∫[0 to 2] (2t) dt - ∫[0 to 2] (1) dt

Simplifying further:

Displacement = [t³] evaluated from 0 to 2 - [t²] evaluated from 0 to 2 - [t] evaluated from 0 to 2

Displacement = (2³) - (2²) - (2) - ((0³) - (0²) - (0))

Displacement = 8 - 4 - 2 - (0 - 0 - 0)

Displacement = 8 - 4 - 2

Displacement = 2 meters

Therefore, the displacement of the particle over the interval [0, 2] is 2 meters.

Question 2: To compute the total distance traveled by the particle over [0, 2], we need to find the sum of the absolute values of the velocity function integrated over the given interval.

Given velocity function v(t) = 3t² - 2t - 1, we integrate the absolute value of the velocity function over the interval [0, 2]:

Total Distance = ∫[0 to 2] |v(t)| dt

Let's calculate the integral:

Total Distance = ∫[0 to 2] |3t² - 2t - 1| dt

To find the integral, we consider different cases based on the sign of the velocity function within the interval [0, 2].

Case 1: When v(t) ≥ 0

Within the interval [0, 2], the velocity function 3t² - 2t - 1 is positive or zero. So we can directly integrate it:

∫[0 to 2] (3t² - 2t - 1) dt

Using the same steps as in Question 1, we find the integral to be (2 meters).

Case 2: When v(t) < 0

Within the interval [0, 2], the velocity function 3t² - 2t - 1 is negative. To consider the absolute value, we negate the velocity function:

∫[0 to 2] -(3t² - 2t - 1) dt

Using the same steps as in Question 1, we find the integral to be (-2 meters).

Total Distance = |2 meters| + |-2 meters| = 2 meters + 2 meters = 4 meters

Therefore, the total distance traveled by the particle over the interval [0, 2] is 4 meters.

Hence, 1) the displacement of the particle over the interval [0, 2] is 2 meters.

2) the total distance traveled by the particle over the interval [0, 2] is 4 meters.

To learn more about the quadratic equation visit:

brainly.com/question/28038123

#SPJ4

Answer: 9

Step By Step: 2 exponent 5= 32 then subtract it with 4+3 exponent 2 which gives you 13.

32-13=19

Labor content (labor dollar per unit) is the total cost of labor required to produce one unit of a product. It can be calculated by dividing the total labor cost by the number of units produced.

In this scenario, we are given that an employee produces 17 parts during an 8-hour shift and earns $109 per shift.

To calculate the labor content, we first determine the labor cost per hour. This is done by dividing the total amount earned in the 8-hour shift by 8.

Labor cost per hour = $109 ÷ 8 = $13 per hour

Next, we calculate the number of parts produced per hour by dividing the total number of parts produced (17) by the duration of the shift (8 hours).

Parts produced per hour = 17 ÷ 8 = 2.125 parts per hour

Finally, we calculate the labor cost per part by dividing the labor cost per hour by the number of parts produced per hour.

Labor cost per part = $13 ÷ 2.125 = $6.12 per part

Therefore, the labor content (labor dollar per unit) of the product is $6.12 per part.

Learn more about labour content

https://brainly.com/question/14701647

#SPJ11

Answer:

id k if it's right but i hope this helps :)

Step-by-step explanation:

Answer:

a function of an angle, or of an abstract quantity, used in trigonometry, including the sine, cosine, tangent, cotangent, secant, and cosecant, and their hyperbolic counterparts.

Step-by-step explanation:

Answer:

AC = 18, EB = 5 Step-by-step explanation:In a rhombus, AE = CE, and DE = BE. However, AE or AC ≠ DE or BE.

CE = AE

    = 9

AC = CE + AE

    = 9 + 9

    = 18

DE = BE

    = 5

i am gonna have to go with B

The function f(x) = x^3 - 3x^2 - 6x + 5 has an inflection point at (1, -3). The function is concave up for x > 1 and concave down for x < 1.


To find the intervals on which the function f(x) = x^3 - 3x^2 - 6x + 5 is concave up or down, we need to analyze the second derivative of the function. Let's begin by finding the second derivative:

f'(x) = 3x^2 - 6x - 6 (first derivative)

f''(x) = 6x - 6 (second derivative)

To determine the intervals of concavity, we need to find where the second derivative changes sign.

Setting f''(x) = 0 and solving for x:

6x - 6 = 0

x = 1

The inflection point occurs at x = 1. Now, we can analyze the concavity on either side of the inflection point.

For x < 1:

Choosing a test point, let's evaluate f''(0):

f''(0) = 6(0) - 6 = -6

Since f''(0) is negative, the function is concave down for x < 1.

For x > 1:

Choosing another test point, let's evaluate f''(2):

f''(2) = 6(2) - 6 = 6

Since f''(2) is positive, the function is concave up for x > 1.

Therefore, we have the following intervals:

Concave up: (1, ∞)

Concave down: (-∞, 1)

The inflection point of f is (1, f(1)) = (1, 1 - 3 - 6 + 5) = (1, -3).

To know more about inflection point, refer here:

https://brainly.com/question/32521033#

#SPJ11

The volume of the rectangular pyramid with a length of 8m, width of 5m and height of 12m is 160 m³.

A rectangular pyramid is simply a three-dimentional object with a rectangular shaped base and triangular shaped faces that correspond to each side of the base.

The volume of rectangular pyramid is expressed as;

V = (1/3) × l × w × h

Where l is the base length, w is the base width and h is the height of the pyramid.

From the diagram:

Length l = 8 meters

Width w = 5 meters

Height h = 12 meters

Volume V = ?

Plug the given values into the above formula and solve for the volume:

V = (1/3) × l × w × h

V = (1/3) × 8 × 5 × 12

V = 160 m³

Therefore, the volume of the pyramid is 160 m³.

Learn more about volume of pyramids here: brainly.com/question/21308574

#SPJ1