Which of the following represents the graph of f(x) = 4x − 2? graph of exponential rising up to the right, through the point 0, negative 3
graph of exponential rising up to the right, through the point 0, 1
graph of exponential rising up to the right, through the point 0, 3
graph of exponential rising up to the right, through the point 0, negative 1

Answer:

-5/3 ft/sec

Step-by-step explanation:

In this question, we are asked to calculate the rate at which the height of the top of a ladder is changing given that the lower end is being dragged at a particular rate.

Please check attachment for complete solution and step by step explanation.

Answer:

The rate of change of height,  dy / dt = -1.667 ft/s  

Step-by-step explanation:

Solution:-

- The length of the ladder, L = 39 ft

- The foot of the ladder is moved away from wall at a rate, dx/dt = 4ft/s

Find:-

how fast is the height of the top changing​ (this will be a negative​ rate) when the lower end is 15 feet from the​ wall?

Solution:-

- We will first draw a right angle triangle, with vertical height of the ladder to be"y" and distance of the foot of the ladder and the wall to be "x".

- Then express the length "L" in terms of x and y using pythagorean theorem:

                        L^2 = x^2 + y^2

                        y^2 = 39^2 - x^2  

- Taking height of the ladder as the dependent variable and distance of the foot of the ladder from wall as independent variable.

- Formulate a differential equation from the given expression above in terms of "dy/dt" and "dx/dt". Perform implicit differential of the computed expression "d/dt":

                        2y*dy/dt = -2x*dx/dt

                        dy / dt = -(x/y)*dx/dt

- Where, dy / dt : The change in height of the ladder.

- The height of the ladder at x = 15 ft is:

- Then evaluate dy/dt:

                        dy / dt = -(15/36)*4

                        dy / dt = -1.667 ft/s      

Answer:

Step-by-step explanation:

To determine the exact value of the covariance expression Cov(2m, em), we need more information about the variables involved. The covariance between two random variables, X and Y, is calculated as the expected value of the product of the differences between each variable and their respective means. Without the means or additional information, we cannot calculate the exact value of the covariance.

For the simulation method, we can generate random samples for 2m and em, calculate their covariance, and repeat the process multiple times to estimate an approximate value for Cov(2m, em). The simulated value will depend on the specific values generated for 2m and em in each iteration.

b) To compute the exact value of the integral η = ∫1^5 y^2 e^y dy, we can use integration techniques such as integration by parts or substitution. However, without further information or specific instructions, it is not possible to determine the exact value of this integral.

To estimate the integral using the Monte Carlo (MC) integration method, we can generate random points within the interval [1, 5] and evaluate the function y^2 e^y at those points. The estimate is then obtained by taking the average of these function values and multiplying it by the interval length (5 - 1). Using a sample size of n = 1000 means generating 1000 random points.

To calculate the approximate percentage error (ϵ) between the exact value and the MC value, you would need to know the exact value of the integral, which is not provided in the question.

c) The given code represents a pseudorandom number generation (PNG) method. It generates pseudorandom numbers using a linear congruential generator (LCG) algorithm. The LCG algorithm is a simple and widely used method for generating pseudorandom numbers based on a linear recurrence relation.

The LCG algorithm is defined by the recurrence relation:

X(n+1) = (a * X(n) + c) mod m

In the code, the values a = 11, c = 56, x0 = 13, and m = 15 are used as parameters for the LCG algorithm. It generates 30 pseudorandom numbers by iterating the recurrence relation.

To test the hypothesis that the generated numbers are uniformly distributed, you can perform a statistical test, such as the chi-square test or the Kolmogorov-Smirnov test. These tests compare the distribution of the generated numbers to a uniform distribution.

Answer:

315 red flowers

420 white flowers

315 yellow flowers​

Step-by-step explanation:

1050 flowers

3/10 of them are red=> 3/10 *1050=3*105=315 red flowers

2/5, (or 4/10),  are white =>4/10 * 1050=4*105=420 white flowers

=> 1050-(315+420)=1050-735=315 yellow flowers​