Find the equation of the line parallel to x=1 that contains the point (-2,-1)
answer : x= -2
bc the graph of x=1 is just a straight vertical line across the x-axis, so any lines parallel have to go vertically across the x-axis as well. The graph of line that goes through the point (-2,-1) is x=-2
A certain city's population is 120,000 and decreases 1.4% per year for 15 years.Is this exponential growth or decay? Growth What is the rate of growth or decay? What was the initial amount? 120000 What is the function? What is the population after 10 years? Round to the nearest whole number.
Decay rate, r = 0.014
Initial Amount =120,000
The exponential function for growth/decay is given as:
In this problem:
The city's initial population is 120,000 and it decreases by 1.4% per year.
Since the population decreases, it is a Decay Problem.
Decay rate, r=1.4% =0.014
Initial Amount =120,000
Therefore, the function is:
When t=10 years
Jenny has 50 square tiles she arranges the tiles into a rectangular array of 4 rows how many tiles will be left over
50/4=12 2/4 Therefore, there will be 2 tiles left over.
Although still a sophomore at college, John O'Hagan's son Billy-Sean has already created several commercial video games and is currently working on his most ambitious project to date: a game called K that purports to be a "simulation of the world." John O'Hagan has decided to set aside some office space for Billy-Sean against the northern wall in the headquarters penthouse. The construction of the partition will cost $8 per foot for the south wall and $12 per foot for the east and west walls.What are the dimensions of the office space with the largest area that can be provided for Billy-Sean with a budget of $432?south wall length ft -east and west wall length -What is its area?
27 feet for the south wall and 18 feet for the east/west walls
This is a simple case where an objective function must be minimized or maximized, given some restrictions coming in the form of equations.
The first derivative method will be used to find the values of the parameters that control the objective function and the maximum value of that function.
The office space for Billy-Sean will have the form of a rectangle of dimensions x and y, being x the number of feet for the south wall and y the number of feet for the west wall. The total cost of the space is
The budget to build the office space is $432, thus
Solving for y
The area of the office space is
Replacing the value found above
This is the objective function and must be maximized. Taking its first derivative and equating to 0:
Compute the second derivative to ensure it's a maximum
Since it's negative for x positive, the values found are a maximum for the area of the office space, which area is
A sample of 8 new models of automobiles provides the following data on highway miles per gallon. Highway Miles Model Per Gallon 1 33.6 2 26.8 3 20.2 4 38.7 5 35.1 6 28.0 7 26.2 8 27.6 a. What is the point estimate for the average highway miles per gallon for all new models of autos? b. Determine the point estimate for the standard deviation of the population.
The point estimate for the mean is 29.5 miles per gallon and the standard deviation is 5.9
The formula por the point estimate of the mean is: