If f(x) = x² + 1, then f(f(3)) = ?

Answer:17

Step-by-step explanation:

Convert the rational number to decimals, then solve it as a decimal instead, (with the optional choice of re-converting it back to rational).

a. U'(ct) = β(1 + r)U'(ct+1). This equation is known as the Euler equation, which represents the intertemporal marginal rate of substitution between consumption at time t and consumption at time t+1.

b. U'(c1) = β(1 + r)^2U'(c3). This relationship shows that the marginal utility of consumption at time 1 is equal to the discounted marginal utility of consumption at time 3.

c. C0 = ∑t=0[infinity]​(β(1 + r))^tct. This equation represents the sum of the discounted values of consumption at each period, where the discount factor β(1 + r) accounts for the diminishing value of future consumption.

d.  U0 = ∑t=0[infinity]​(β(1 + r))^tln(ct). This equation represents the sum of the discounted values of utility at each period, where the discount factor β(1 + r) reflects the time preference and the logarithmic utility function captures the agent's preference for consumption.

Y0 = y0 + (1 + γ)y1 + (1 + γ)^2y2 + ..., where γ represents the growth rate of income.

a. The optimization problem of the representative agent involves maximizing the present discounted value of utility subject to the period-by-period budget constraint. The Euler equation is derived as follows:

At each period t, the agent maximizes the utility function U(ct) = ln(ct) subject to the budget constraint ct = (1 + r)wt + yt, where wt is the agent's wealth at time t. Taking the derivative of U(ct) with respect to ct and applying the chain rule, we obtain: U'(ct) = β(1 + r)U'(ct+1). This equation is known as the Euler equation, which represents the intertemporal marginal rate of substitution between consumption at time t and consumption at time t+1.

b. The Euler equation between time 1 and time 3 can be written as U'(c1) = β(1 + r)U'(c2), where c1 and c2 represent consumption at time 1 and time 2, respectively.

Similarly, we can write the Euler equation between time 2 and time 3 as U'(c2) = β(1 + r)U'(c3). Combining these two equations, we fin

d U'(c1) = β(1 + r)^2U'(c3). This relationship shows that the marginal utility of consumption at time 1 is equal to the discounted marginal utility of consumption at time 3.

c. The present discounted value of optimal lifetime consumption can be written as C0 = ∑t=0[infinity]​(β(1 + r))^tct. This equation represents the sum of the discounted values of consumption at each period, where the discount factor β(1 + r) accounts for the diminishing value of future consumption.

d. The present discounted value of optimal lifetime utility can be written as U0 = ∑t=0[infinity]​(β(1 + r))^tln(ct).

This equation represents the sum of the discounted values of utility at each period, where the discount factor β(1 + r) reflects the time preference and the logarithmic utility function captures the agent's preference for consumption.

e. The present discounted value of lifetime income, denoted as Y0, can be expressed as Y0 = y0 + (1 + γ)y1 + (1 + γ)^2y2 + ..., where γ represents the growth rate of income. The income in each period is multiplied by (1 + γ) to account for the increasing income over time.

This assumption of income growth allows for a more realistic representation of the agent's economic environment, where income tends to increase over time due to factors such as productivity growth or wage increases.

for such more questions on  equation

https://brainly.com/question/17145398

#SPJ8

Answer:

The third answer is correct.

Step-by-step explanation:

You are going to translate the smaller quadrilateral (4 sided figure) to the larger quadrilateral.  Then you need the scale factor from the smaller figure to the larger.  

Side EF times the scale factor will give you side AB.  Let's call the scale factor s then our equation would be:

EF x s = AB  To find s divide both sides by EF

\(\frac{EF(s)}{EF}\) = \(\frac{AB}{EF}\)

s = \(\frac{AB}{EF}\)  This is our scale factor.

Helping in the name of Jesus.

The value of a(t) is -1 and b(t) is 55 + \(e^t\)

No, the given equation y' - y = 55 + \(e^t\) is not in the standard form of a first-order linear differential equation.

In the method for solving a first-order linear differential equation, an integrating factor is a function used to transform the equation into a form that can be easily solved.

For an equation in the standard form y' + a(t)y = b(t), the integrating factor is defined as:

μ(t) = e^∫a(t)dt

To solve the equation, you multiply both sides of the equation by the integrating factor μ(t) and then simplify. This multiplication helps to make the left side of the equation integrable and simplifies the process of finding the solution.

To put it in standard form, we need to rewrite it as y' + a(t)y = b(t).

Comparing the given equation with the standard form, we can identify:

a(t) = -1

b(t) = 55 + \(e^t\)

Therefore, The value of a(t) is -1 and b(t) is 55 + \(e^t\)

Learn more about integrating factor here

https://brainly.com/question/32554742

#SPJ4

Answer:

Row 15 is correct

Step-by-step explanation:

Pascal's triangle:  

                                              1                                            n = 0 , Row = 0

                                      1                 1                                  n = 1  , Row = 1

                             1               2                1                          n = 2 , Row = 2

                                               :

                                          .........

                                           .......

For n = 0, Row number 1  

For n = 1,  Row number 2

For n = 2, Row number 3

We make pascal's triangle but sum of above two number, write below.  

As we can see in pascal's triangle.  

Exponent represent the number of row.  

If binomial has exponent n then nth row of pascal's triangle use.  

For  

Here power is 15  

So, we have to use 15 row of pascal's triangle.  

Hence, Row 15 is correct

Answer:

the second part is 16

Step-by-step explanation:

The value of \(y\) will be \(4\sqrt{3}\) .

Triangle is a three sides two dimensional surface having three angles.

We have,

\(\triangle MRN\) , \(\triangle RSM\) and \(\triangle RSN\),

And, \(NS =6,\ SM=2,\ RM=x,\ NR=y,\ RS=z\)

Now,

We have right angle \(\triangle MRN\),

Using Pythagoras theorem,

\(x^2+y^2=8^2\)

\(x^2+y^2+=64\\)     \(.....(i)\)

Now, We have right angle \(\triangle RSN\),

Again Using Pythagoras theorem,

\(z^2+6^2=y^2\)

⇒\(z^2=y^2-36\)     \(.....(ii)\)

Now, We have right angle \(\triangle RSM\),

Again Using Pythagoras theorem,

\(z^2+2^2=y^2\)

⇒\(z^2=x^2-4\)     \(.....(iii)\)

Now comparing equation \((ii)\) and equation  \((iii)\),

We get,

\(x^2-4=y^2-36\)

We get,

\(x^2-y^2=-36+4\)

\(x^2-y^2=-32\)     \(.....(iv)\)

Now,

Adding equation \((i)\) and equation  \((iv)\), i.e.

\(x^2+y^2+=64\)

\(x^2-y^2=-32\)

We get,

\(2y^2=96\)

\(y^2=48\)

\(y=\sqrt{48}\)

\(y=4\sqrt{3}\)

So, the value of \(y\) is \(4\sqrt{3}\)

Hence, we can say that the value of \(y\) will be \(4\sqrt{3}\)  which is given in option (b).

To know more about Triangle click here

https://brainly.com/question/2773823

#SPJ2

Answer:

its c

Step-by-step explanation:

taking test rn

Answer: 2.25

Step-by-step explanation:

Answer:

answer 215 nickels

Step-by-step explanation:

Answer:

the graph will be an exponential function that crosses the y-axis at about (0, -4).

Step-by-step explanation:

Answer:

The answer is the first graph.

Step-by-step explanation:

I just did the quiz

Answer:

y = 45x miles

Step-by-step explanation:

Speed is the rate of change of distance with time. Mathematically,

speed = distance/time

Given that Darla travels at a constant speed of 45 miles per hour and for y miles, it takes her x hours then

45 = y/x

multiply both sides by x

45x = y

then the number of miles (y) Darla can drive in x hours

y = 45x (in miles)

The interval of convergence is (-2, 14)., the radius of convergence is 8.

To find the radius of convergence, we take half the length of the interval of convergence: Radius of Convergence = (14 - (-2))/2 = 16/2 = 8. Hence, the radius of convergence is 8.

To find the radius of convergence and interval of convergence of the series, we will use the ratio test. Consider the series:

∑ [(√n)/(8^n)] * [(x-6)^n]

Let's apply the ratio test:

lim┬(n→∞)⁡(|(√(n+1))/(8^(n+1)) * ((x-6)^(n+1))| / |(√n)/(8^n) * ((x-6)^n)|)

Simplifying this expression, we get:

lim┬(n→∞)⁡(|√(n+1)/(√n) * ((x-6)/(8))|)

Since we are interested in finding the radius of convergence, we want to find the limit of this expression as n approaches infinity:

lim┬(n→∞)⁡(|√(n+1)/(√n) * ((x-6)/(8))|) = |(x-6)/8| * lim┬(n→∞)⁡(√(n+1)/(√n))

Now, let's evaluate the limit term:

lim┬(n→∞)⁡(√(n+1)/(√n)) = 1

Therefore, the simplified expression becomes:

|(x-6)/8|

For the series to converge, the absolute value of (x-6)/8 must be less than 1. In other words:

|(x-6)/8| < 1

Simplifying this inequality, we have:

-1 < (x-6)/8 < 1

Multiplying each part of the inequality by 8, we get:

-8 < x-6 < 8

Adding 6 to each part of the inequality, we have:

-8 + 6 < x < 8 + 6

Simplifying, we obtain:

-2 < x < 14

Therefore, the interval of convergence is (-2, 14).

Finally, to find the radius of convergence, we take half the length of the interval of convergence:

Radius of Convergence = (14 - (-2))/2 = 16/2 = 8

Hence, the radius of convergence is 8.

Learn more about convergence here:

https://brainly.com/question/31401345

#SPJ11

y = (-1/2)x + 4 is the equation for the linear function with an x-intercept of 8 and a y-intercept of 4.

We are aware that lines might have several kinds of equations; the typical form is

The equation of a line in slope-intercept form is Ax + By + c = 0, and

y = mx + b.

m is the slope, and b is the y-intercept.

The y-intercept, or (0,b), is the point where the line crosses the y-axis at x = 0. The slope represents the rate of change of the y-axis relative to the x-axis.

Given, An x-intercept for a linear function is 8, and a y-intercept is 4.

The two points on the line are therefore (8, 0) and (0, 4).

Slope(m) is now equal to (4 - 0)/(0 - 8).

m slope = 4/8.

slope(m) equals -1/2.

With a y-intercept of 4, it represents the value of b in the equation y = mx + b.

Consequently, the equation is y = (-1/2)x + 4 is linear.

To learn more about slope-intercept form refer,

brainly.com/question/3605446

#SPJ4

The company's total amount of income that is earned is $136,500.

Profit is the difference between revenue and expenses. Income is the total revenue that is earned by a company before any deductions. Expenses include all the cost incurred in running a business. Income is the sum of profit and expenses. A venture is profitable only if the revenue is greater than expenses.

Profit = income - expenses

Income = profit + expenses

$35,000 + 101,500 = $136,500

To learn more about profit, please check: brainly.com/question/26181966

#SPJ1

Answer:

see below

Step-by-step explanation:

Kiara, as she was only over by 5.5, Wes, as he was less than by 22.7 lbs, and Natalie, as she was over only by 14.7 lbs

a) No, p1 = 20, p2 = 19.50 is not a Nash Equilibrium.

b) Yes, there is a Nash Equilibrium in which Firm 2 makes a positive profit.

c) Player 1 has infinitely many strategies.

d) Yes, p1 = 15, p2 = 15 is a Nash Equilibrium.

e) No, p1 = 21, p2 = 21 is not a Nash Equilibrium.

Nash Equilibrium is a state of a strategic game where no player has an incentive to deviate from his or her chosen strategy after considering the strategies of other players. A game has more than one Nash equilibrium if players are unable to agree on a cooperative strategy to play.

Finding Nash Equilibrium

Learn more about Nash equilibrium at

https://brainly.com/question/32714160

#SPJ11

Answer:

-2, 10

Step-by-step explanation:

From the image, I'm pretty sure it's asking you to find where the line can be "cut" into to make it symmetrical. If this is true, you would need to find a half way mark in the graph, or try and plot this on the graph.

We have explained the ASA rule of congruency of the triangle

What is an ASA congruency of triangles?

ASA Congruence. Angle-Side-Angle. If two angles in one triangle are congruent to two angles of a second triangle, and also if the included sides are congruent, then the triangles are congruent.

If a triangle PQR is congruent to a triangle ABC, we write it as ∆ PQR ≅ ∆ ABC.

Note that when ∆ PQR ≅ ∆ ABC, then sides of ∆ PQR fall on corresponding equal sides of ∆ ABC and so is the case for the angles.

This means that PQ covers AB, QR covers BC, and RP covers CA;

∠P, ∠Q, and ∠R cover ∠A, ∠B, and ∠C respectively.

Also, between the vertices, there is an existence of one-one correspondence.

That is, P corresponds to A, Q corresponds to B, R corresponds to C and it is written as

P↔A, Q↔B, R↔C

Under this condition, the correspondence ∆ PQR ≅ ∆ ABC is true but is not correct for the correspondence ∆QRP ≅ ∆ ABC.

Hence, we have explained the ASA rule of congruency of the triangle

To learn more about the ASA rule of congruency of the triangle, visit:

https://brainly.com/question/3168048

#SPJ4

Answer:

Elena will run 6 miles in 1.5 hours

Jada will walk 3 miles in 1.5 hours

Step-by-step explanation:

Multiply: 4*1.5=6 (Elena's)

Multiply:2*1.5=3  (Jada's)

Elena will run 6 miles in 1.5 hours

Jada will walk 3 miles in 1.5 hours

Hope this helped!! :)

Stay safe and have a wonderful day/night!!!!!

Brainliest?!?!

Please correct me if I'm wrong

Answer:

Area of the semi-circle:

(1/2)π(2^2) = 2π = 6.28 square centimeters

Area of the triangle:

(1/2)(4)(5.7) = 11.4 square centimeters

Total area:

6.28 + 11.4 = 17.68 square centimeters

The correct answer is D. f(x) = 11x - 4 and g(x) = (x + 4)/11

To determine which pair of functions are inverses of each other, we need to check if the composition of the functions results in the identity function, which is f(g(x)) = x and g(f(x)) = x.

Let's test each option:

Option A:

f(x) = x/2 + 15

g(x) = 12x - 15

f(g(x)) = (12x - 15)/2 + 15 = 6x - 7.5 + 15 = 6x + 7.5 ≠ x

g(f(x)) = 12(x/2 + 15) - 15 = 6x + 180 - 15 = 6x + 165 ≠ x

Option B:

f(x) = ∛3x

g(x) = (x/3)^3 = x^3/27

f(g(x)) = ∛3(x^3/27) = ∛(x^3/9) = x/∛9 ≠ x

g(f(x)) = (∛3x/3)^3 = (x/3)^3 = x^3/27 = x/27 ≠ x

Option C:

f(x) = 3/x - 10

g(x) = (x + 10)/3

f(g(x)) = 3/((x + 10)/3) - 10 = 9/(x + 10) - 10 = 9/(x + 10) - 10(x + 10)/(x + 10) = (9 - 10(x + 10))/(x + 10) ≠ x

g(f(x)) = (3/x - 10 + 10)/3 = 3/x ≠ x

Option D:

f(x) = 11x - 4

g(x) = (x + 4)/11

f(g(x)) = 11((x + 4)/11) - 4 = x + 4 - 4 = x ≠ x

g(f(x)) = ((11x - 4) + 4)/11 = 11x/11 = x

Based on the calculations, only Option D, where f(x) = 11x - 4 and g(x) = (x + 4)/11, satisfies the condition for being inverses of each other. Therefore, the correct answer is:

D. f(x) = 11x - 4 and g(x) = (x + 4)/11

for such more question on inverses

https://brainly.com/question/15066392

#SPJ8

Answer:

The shape is a Dodecagon

The statistical method that would be best to use in this situation is b) Regression analysis.

Regression analysis is a statistical technique used to examine the relationship between a dependent variable (in this case, the number of students registering each semester) and one or more independent variables (such as time, semester, or any other relevant factors). By analyzing past data on the number of students registering each semester, regression analysis can help identify trends, patterns, and the average number of students registering.

Using regression analysis, the university can estimate the average number of students registering each semester based on historical data and use this information to plan how many classes to run in the upcoming semester. It allows for a quantitative analysis and prediction based on the relationship between variables, making it a suitable choice for estimating the average number of students in this scenario.

Hence the answer is Regression analysis.

Learn more about Regression analysis click;

https://brainly.com/question/31873297

#SPJ12

Answer:

Step-by-step explanation:

Rocio ha gastado mas. El cubo de Jaime esta mas lleno.

Rocio gasto otro poco mas porque 3 esta mas grande que 2

The reasons for each statement about the given triangle are as follows:

Congruent triangles are two triangles that are the same size and shape. Two congruent triangles remain congruent even if we flip, turn, or rotate one of them. Two triangles must have the same angles and, as a result, must be congruent if their sides are the same.

Given, A triangle PWZ in that base ∠1 and ∠2 are same and the distance between W and Z from X and Y are the same where XY is the base of another triangle inside the ΔPWZ.

For ΔPWZ

We know PWZ is an isosceles triangle since its two angles are the same.

thus another ΔPXY is on the same base of ΔPWZ and also at the same distance from its point Hence, these triangles are congruent triangles.

Looking at that perspective, we can say that ∠1 and ∠2 are pairs of alternate angles and are congruent.

∠1 ≅ ∠2

The same with ∠3 and ∠4.

∠3 ≅ ∠4

Therefore, As a result, according to the ASA Theorem, the Triangles are congruent. The two angles and the side they encompass are comparable.

Learn more about congruent triangles here:

https://brainly.com/question/12413243

#SPJ1

Elijah has to run 32 more yards

Answer:

The remainder is 4.

Step-by-step explanation:

Note: This question is not correctly stated. It is therefore correctly restated before answering the question as follows:

When 17 is divided by k; where k is a positive integer less than 17, the remainder is 3. What is the remainder when the sum of the possible values of k is divided by 17?

The explanation of the answer is now given as follows:

Since k < 17, it implies that the possible values of k must be from between 1 and 16 inclusive.

Between 1 and 16, only 7 or 14 will give a remainder of 3 when either of them is used to divide 17. Therefore, 7 and 14 are the possible values of k.

Therefore, we have:

Sum of the possible values of k = 7 + 14 = 21

Also, we have:

Sum of the possible values of k divided by 17 = 21 / 17 = 1 with a remainder of 4.

Therefore, the remainder is 4 when the sum of the possible values of k is divided by 17.

Option D, The next step in constructing an angle bisector of angle ABC is to use a straightedge to connect point C to the point where the angle bisector intersects side AB.

To construct an angle bisector of angle ABC, the next step is to use a straightedge to draw a line from vertex C to the point where the angle bisector intersects side AB.

Learn more about the angle bisector at

https://brainly.com/question/2478436

#SPJ4

Answer:

3240°

Step-by-step explanation:

The sum of the interior angles of a polygon is found by (n-2)(180) where n is the number of sides so (20-2)(180) = (18)(180) = 3240°

Step-by-step explanation:

To find an equation of a line in point slope form when given the slope and a point we use the formula

\(y - y_1 = m(x - x_1)\)

where

m is the slope

( x1 , y1) is the point

From the question

the point is (3,-2) and slope - 4/5

The equation of the line is

Hope this helps you

The point-slope equation of the line is given by:

\(y + 2 = -\frac{4}{5}(x - 3)\)

It is given by:

\(y - y_0 = m(x - x_0)\).

In which:

The line that passes through (3,-2) with a slope of -4/5, hence the parameters are given by:

\(x_0 = 3, y_0 = -2, m = -\frac{4}{5}\)

Thus, the equation of the line is:

\(y - y_0 = m(x - x_0)\).

\(y - (-2) = -\frac{4}{5}(x - 3)\).

\(y + 2 = -\frac{4}{5}(x - 3)\)

More can be learned about linear functions at https://brainly.com/question/24808124