Determine the growth constant k, then find all solutions of the given differential equation. y' = 2.2y k=0 The solutions to the equation have the form y(t)= (Type an exact answer.)

The acceleration of the particle at \(t = 2\) seconds is \(4\) cm/s².

To find the acceleration of the particle at \(t = 2\) seconds, we need to differentiate the position function twice with respect to time. First, let's differentiate the position function \(s(t)\) once to find the velocity function \(v(t)\). Using the chain rule, we have:

\(\(v(t) = \frac{d}{dt}[(4t+1)^{3/2}]\)\)

To simplify the differentiation, we can rewrite the function as\(\(v(t) = (4t+1)^{3/2}\)\) . Applying the power rule, the derivative becomes:

\(\(v(t) = \frac{3}{2}(4t+1)^{1/2} \cdot 4\)\)

Simplifying further, we have:

\(\(v(t) = 6(4t+1)^{1/2}\)\)

Next, we differentiate the velocity function \(v(t)\) to find the acceleration function \(a(t)\):

\(\(a(t) = \frac{d}{dt}[6(4t+1)^{1/2}]\)\)

Using the power rule again, we get:

\(\(a(t) = 6 \cdot \frac{1}{2}(4t+1)^{-1/2} \cdot 4\)\)

Simplifying further, we have:

\(\(a(t) = 12(4t+1)^{-1/2}\)\)

Now we can find the acceleration at \(t = 2\) seconds by substituting \(t = 2\) into the acceleration function:

\(\(a(2) = 12(4 \cdot 2 + 1)^{-1/2}\)\)

\(\(a(2) = 12(9)^{-1/2}\)\)

Simplifying the expression, we have:

\(\(a(2) = \frac{12}{3} = 4\) cm/s²\)

Therefore, the acceleration of the particle at \(t = 2\) seconds is \(4\) cm/s².

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The distributive property is given as a(b + c) = ab + ac.

Solving for x :

\(5(4-3x)= - 10\\(5)(4) + (5)(-3x) = -10\\20 - 15x = -10\\20 + 10 = 15x\\30 = 15 x\\30/15 = x\\2 = x\)

5( 4 - 3x ) = -10

20 - 15x = -10

-15x = -10-20

15x=30

x= 30/ 15

x=2

Answer:

y = 17

Step-by-step explanation:

the initial value of the function is obtained when x = 0

• note that \(a^{0}\) = 1

then

y = 17\((1.24)^{x}\) ← substitute x = 0

y = 17\((1.24)^{0}\) = 17 × 1 = 17

initial value of the function is y = 17

Ans: 55°

Let's draw two parallel line intersecting angle x° and 45° as shown in the photo.

i) a=25° [Being Alternative Angle]

ii) d=15° [Being Alternative Angle]

iii) c= 45°-d[45°=c+d]

=45°-15°

=30°

iv)b=c[Being Alternative Angle]

v)x=a+b[Combining Angle a & b]

=25°+30°

=55°

Answer:

ED = 57 , AB = 19

Step-by-step explanation:

the midsegment FC is half the sum of the parallel bases , that is

\(\frac{AB+ED}{2}\) = FC

\(\frac{4x+3+18x-15}{2}\) = 38 ( multiply both sides by 2 )

22x - 12 = 76 ( add 12 to both sides )

22x = 88 ( divide both side by 22 )

x = 4

then

ED = 18x - 15 = 18(4) - 15 = 72 - 15 = 57

AB = 4x + 3 = 4(4) + 3 = 16 + 3 = 19

Answer:

The square root of 7

Step-by-step explanation:

Answer:

√7

Step-by-step explanation:

To find AC, use half of the base and the hight. Use the pythagorean theorm to help. 2^2+√3^2=x^2, 7=x^2, x=√7

answer is

because are complementary angles A and B

answer: 4.

The function f(x) = px, where p is a real number, is continuous on its domain by the definition of continuity, as for any ε > 0, there exists a δ > 0 such that |f(x) - f(a)| < ε whenever |x - a| < δ.

To prove that the function f(x) = px, where p is a real number, is continuous on its domain, we need to show that for any ε > 0, there exists a δ > 0 such that |f(x) - f(a)| < ε whenever |x - a| < δ.

Let's proceed with the delta-epsilon proof:

Given a value of ε > 0, we need to find a corresponding δ > 0. Let's choose δ = ε/|p|. Note that δ will be positive as ε and |p| are both positive.

Now, consider any two points x and a such that |x - a| < δ. We want to show that |f(x) - f(a)| < ε.

Using the definition of f(x) = px, we can calculate:

|f(x) - f(a)| = |px - pa| = |p(x - a)|

Since |x - a| < δ, we know that |x - a| < ε/|p|. Multiplying both sides by |p| gives:

|p(x - a)| < |p| * (ε/|p|)

The |p| terms cancel out:

|p(x - a)| < ε

Since ε > 0, |p(x - a)| < ε implies that |f(x) - f(a)| < ε.

Therefore, for any ε > 0, we have found a δ = ε/|p| such that |f(x) - f(a)| < ε whenever |x - a| < δ. This satisfies the definition of continuity.

Hence, we have proven that the function f(x) = px, where p is a real number, is continuous on its domain.

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Answer:

assuming the poor grammar you mean he owed his friend 7$, bought a 9$ album with his 20$ allowance.

9 + 7 = 16

20 - 16 = 4

he's got $4.00 left.

The theoretical probability of spinning a number less than 7 is 5/6, or approximately 83.3%.

The process for calculating the theoretical probability of spinning a number less than 7 is as follows: First, count the number of outcomes on the spinner that are less than 7. In this case, there are 5 outcomes (numbers 1-6) that are less than 7. Then, count the total number of outcomes on the spinner. In this case, there are 6 total outcomes (numbers 1-6). Finally, calculate the probability of the event by dividing the number of outcomes less than 7 by the total number of outcomes. In this case, 5/6 = 83.3%. Therefore, the theoretical probability of spinning a number less than 7 is 5/6, or approximately 83.3%.

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The derivative of the function y = x(6x + 1)⁵ is: dy/dx = (6x + 1)⁵ + 30x(6x + 1)⁴

To find the derivative of the given function, we can apply the rules of differentiation. Using the product rule, we differentiate each term separately and then add them together.

For the first term x, the derivative is simply 1.

For the second term (6x + 1)⁵, we apply the chain rule. The derivative of (6x + 1)⁵ with respect to x is 5(6x + 1)⁴ multiplied by the derivative of the inner function 6x + 1, which is 6.

Multiplying these derivatives together, we get (6x + 1)⁵ * 6 = 6(6x + 1)⁵.

For the third term x(6x + 1)⁴, we again apply the product rule. The derivative of x is 1, and the derivative of (6x + 1)⁴ is 4(6x + 1)³ multiplied by the derivative of the inner function 6x + 1, which is 6.

Multiplying these derivatives together, we get x * 4(6x + 1)³ * 6 = 24x(6x + 1)³.

Finally, we add the derivatives of each term to get the derivative of the entire function: dy/dx = (6x + 1)⁵ + 30x(6x + 1)⁴.

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Complete question:

Use the rules of differentiation to find the derivative of the function y= x(6x + 1)⁵

(6x + 1)⁵ + 30x(6x + 1)⁴

(6x + 1)⁴ (36x + 1)

x-1/6

No correct answer provided.

The domain of the function is:

h > 0, only integers.

Then the correct option is the first one.

For a function f(x), we define the domain as the set of the possible values of x that we can use as inputs in the given function.

Here the function is:

f(h) = 6*h + 12

Where h is the number of packages that you buy.

Then h can be only integers larger than zero (as you can't buy half a package or something like that).

Then we conclude that the correct option is the first option.

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Answer:

please see photo above for details

Answer:

what are the choices?

Step-by-step explanation:

Answer:

\(m=0\)

General Formulas and Concepts:

Pre-Alg

Alg I

Step-by-step explanation:

Step 1: Define

Point (-6, -7)

Point (5, -7)

Step 2: Find slope m

This means that our line is a horizontal line.

Answer:

0/11

Step-by-step explanation:

You want to do y2-y1/x2-x1=m

So you would -7-(-7)/5-(-6)

Which equals 0/11

Hope this helps!

If E is not closed or is not bounded, then there may not be some positive number c so that f(e) > c for all e ∈ E .

Suppose that E is not closed, then there exists a limit point a of E such that a ∉ E. For this limit point a, we can choose a sequence of points in E that converges to a. Since f(x) > ε for all x ∈ E ∩ (e − ε, e + ε), we have that f(x) > ε for all x in the sequence that converges to a.

However, since a is not in E, we cannot find an ε > 0 such that f(x) > ε for all x ∈ E ∩ (a − ε, a + ε), so we cannot find a positive number c such that f(e) > c for all e ∈ E.

Now suppose that E is not bounded. Then for every positive number M, there exists a point e ∈ E such that |e| > M. We can choose ε = |e|/2, and then we have that f(x) > ε for all x ∈ E ∩ (e − ε, e + ε). However, since E is not bounded, we can always choose M large enough so that ε = |e|/2 > M, and then we cannot find a positive number c such that f(e) > c for all e ∈ E.

Therefore, if E is not closed or is not bounded, then there may not be some positive number c so that f(e) > c for all e ∈ E.

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Answer:5*(x-2)^2 + 5

Step-by-step explanation:that would be the answer 5x^2-20x+25

Answer:

Its A. Just had this question

Step-by-step explanation:

Answer:

3/4

Step-by-step explanation:

Answer:

132 degrees

Step-by-step explanation:

the angles of measure 2 and 3 have to add up to 180 degrees (because that's the angle of a straight line, which 2 and 3 make together)

180-48=132

Answer:

it's b. y= \(y= e^{b}+3\) on edg2020

Transformed functions are functions that are modified by some transformation. In this question the transformation of y=\(e^x\) that is  y = \(e^x\)+ 3.

Therefore, the transformation of the given function y= \(e^x\) that is "y = \(e^x\) + 3".

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Given :

m||n, interior angles are (2x-26) and (7x+8).

To Find :

Find the value of x.

Solution :

We know, alternate interior angle of a triangle are supplement to each other.

So, (2x-26) + (7x+8) = 180°

9x - 18° = 180°

9x = 198°

x = 22°

Therefore, the value of x is 22°.

Answer:

value of x is 22°

Step-by-step explanation:

Correct answer

The correct answer is c. Learning curves are important for estimating performance improvement as workers become experienced.

Learning curves are often used in project management to estimating the time, effort, and resources required to complete a task or project. They help to estimate how long it will take for a worker or team to become proficient at a task or process, based on the amount of time and effort that they have put into it.

This can be helpful in estimating performance improvement as workers become more experienced and efficient in their work. The concept of a learning curve is a curved line that represents the rate of improvement over time, which is why the term "curve" is relevant. While learning curves do involve some math, they are not primarily focused on helping new PMs understand required math, nor are they used for visualization of curved mechanical parts or estimating cost improvement as parts become "broken in."
Learning curves are important for:
c. estimating performance improvement as workers become experienced.
Learning curves represent the progress made in a skill or job over time, whereas a curve illustrates the relationship between experience and efficiency. As workers become more experienced, their performance typically improves, which can be estimated using a learning curve in various industries and tasks.

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a) Yes, researchers can assume an approximation to the normal distribution.

b) The probability of observing 7 cases of caesarian in a sample of 16 is calculated using the binomial distribution.

To determine if researchers can assume an approximation to the normal distribution, we need to check if the sample size is sufficiently large. The sample size in this case is 16, and the probability of undergoing a caesarian is

7/16 = 0.4375.

We check the conditions np ≥ 10 and n(1-p) ≥ 10. For np, we have 16 * 0.4375 = 7, which is greater than 10. For n(1-p), we have

16 * (1 - 0.4375) = 9,

which is also greater than 10.

Since both np and n(1-p) are greater than 10, researchers can assume an approximation to the normal distribution for their investigation.

To calculate the probability of observing 7 cases of caesarian in a sample of 16, we use the binomial distribution. The probability is calculated as P(X = 7) = C(16, 7) * (0.327)⁷ * (1 - 0.327)⁽¹⁶⁻⁷⁾.

Evaluating this expression gives us the probability of observing the specific results seen in the sample.

Therefore, researchers can assume an approximation to the normal distribution, and the probability of observing the specific results in the sample can be calculated using the binomial distribution.

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Answer:

A.

Step-by-step explanation:

i'm 99% sure

Answer:

A. y = 0.5x

Step-by-step explanation:

i got it right

Answer:

a screw is a simple machine that works as a modified inclined plane. You can think of the thread of the screw as an inclined plane wrapped around the shaft of the screw. The slope of the screw is the distance for one complete rotation while the height of the inclined plane is the distance between the threads, known as pitch. The relationship between the pitch and circumference of the screw gives the mechanical advantage.

Answer:

Yupll have to use a calculator to get the answer for this type of question

Answer: The population after five years = 9967

Step-by-step explanation:

The exponential equation for population decay : \(P=A (1-r)^t\), where A = initial population r= rate of decay , t= time

Given: A= 42000, r= 25%= 0.25, t= 5

then

\(P=42000(1-0.25)^5\\\\=42000(0.75)^5\\\\=42000(0.2373046875)\\\\\approx9967\)

Hence, The population after five years = 9967