Cross-sectional Area The cross-sectional area of a beam cutfrom a log with radius 1 foot is given by the functionA1x2 = 4x21 - x2, where x represents the length, in feet,of half the base of the beam. See the figure. Determine thecross-sectional area of the beam if the length of half the baseof the beam is as follows:(a) One-third of a foot(b) One-half of a foot(c) Two-thirds of a foot

Q: Sunlight is absorbed in water, and as a result the light intensity in oceans, lakes, and ponds…

A:

Q: Graph the exponential function g(x)= -(-) +2. To do this, plot two points on the graph of the…

A: given exponential function g(x)=-14x+2 we know graph of parent function g(x)=14x

Q: Graph the exponential function g (x)=2" + 2. To do this, plot two points on the graph of the…

A:

Q: The value of a home y  (in thousands of dollars) can be approximated by the model, y= 192 (0.96)^t…

A:

Q: In 2012, the population of a city was 6.82 million. The exponential growth rate was 3.36% per year.…

A: Concept: Formula for the exponentia growth: P=P0ert Where e is expoential growth P0 is initial…

Q: f1x2 = log3 1x + 52 and g1x2 = log3 1x - 12.(a) Solve f1x2 = 2. What point is on the graph of f?(b)…

A: Note:- Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the…

Q: In 2012, the population of a city was 5.77 million. The exponential growth rate was 1.23% per year.…

A: Proceed as shown below

Q: b. log₂(x 3) = log₂ 9

A:

Q: Lions were introduced in the park in 2010. In 2012, the park has a population of 32 lions. A year…

A: We have to first assume an exponential function.

Q: In 2012, the population of a city was 5.77 million. The exponential growth rate was 1.23% per year.…

A: Given:- In 2012, the population of a city was 5.77 million. The exponential growth rate was 1.23%…

Q: In 2012 the population of a city was 5.59 million the exponential group rate was route rate was…

A:

Q: Soon after taking an aspirin, a patient has absorbed 320 milligrams of the drug. After 2 hours, only…

A: Given information: A patient has absorbed 320 milligrams of the drug. After 2 hours, only 80…

Q: log4(x2 − 64) − log4(x − 8)

A:

Q: 1) Suppose you are a biochemist studying a type of mold. The growth of this type of mold can be…

A:

Q: Log(2x-1)=8

A:

Q: In 2012, the population of a city was 6.34 million. The exponential growth rate was 3.37% per year.…

A:

Q: x+3 aph the exponential function g (x) =| do this, plot two points on the graph of the function, and…

A: In the given question we need to graph the exponential function- g(x)=13x+1First we will find the…

Q: Graph the exponential function g(x) =4* +2. To do this, plot two points on the graph of the…

A:

Q: person invests $4080 in stocks​ today, and their value doubles every 5years. Let f​ (t) be the…

A:

Q: In 2012, the population of a city was 5.32 million. The exponential growth rate was 3.82% per year.…

A: According to the guidelines issued by the company We are supposed to answer only first three…

Q: Vlog2(x - 8) + log2(x + 8) = 64 %3D

A:

Q: Graph the exponential function. 3 f (x) = – () Plot five points on the graph of the function, and…

A: Given: -The exponential function is, f(x)=-32x To Plot: - The five points on the graph of the given…

Q: logg (x – 2) +  logg (x) = 1

A:

Q: Each year the local country club sponsors a tennis tournament. Play starts with 128 participants.…

A: Exponential function is given as  y = ar^t  a = initial number of items  r = part which got consume…

Q: Log3 3x=log3 600-log3 20

A: Use log property

Q: Jack plants a magic beanstalk that is 3 feet tall. The height of the magic beanstalk increases…

A: Jack plants a magic beanstalk that is 3 feet tall. The height of the magic beanstalk increases…

Q: In 2012, the population of a city was 5.99 million. The exponential growth rate was 2.51% per year.…

A:

Q: Find the solution: log4 x-log4(x-1)=1/2

A: Properties to know to solve this question:

Q: Graph the exponential function g (x)=2- 1. To do this, plot two points on the graph of the function,…

A:

Q: All changes saved 8. The population, P, of a small town experiencing exponential population growth…

A: To find the correct expression

Q: logaM/x=logaM1/x Is it true or false?

A: logaM/x=logaM1/x

Q: The number of bacteriaN ina culture group exponentially. It begins with 250 bacteria in the culhere.…

A:

Q: Find the equation of the exponential function represented in the table below. Be careful with the…

A: General form of an exponential function is,                 y = abx Here we have several points…

Q: What is the domain of this exponential function? y = 2* + 6 {x | x 2 -6} {x | x > -6} {x | x > 6}…

A:

Q: log (4x-2)=2

A: Given, log (4x-2)=2

Q: Il in the table for the exponential function y = 3* 1 -2 -1 3. y

A: y=3x We put the value of x in above equation and get value of y .

Q: Español -()* X +3 1 Graph the exponential function g (x) = 3 To do this, plot two points on the…

A: To plot two points on the graph of the function also give the domain and range.

Q: The graph of an exponential function has a y-intercept of 9 and contains the point (2,144).…

A:

Q: In 2012, the population of a city was 5.55 million. The exponential growth rate was 3.55% per year.…

A: GIVEN DATA : Population of the city in 2012 was 5.55 million.                         Exponential…

Q: This table illustrates the growth of a population, which is assumed to be exponential growth. Note x…

A: The year is the independent variable (x) and the population is the dependent variable (y).

Q: In a wildlife refuge, scientists have released six rabbits. They return one year later and have…

A: To find exponential function for growth , we will use formulaA = A0ektwhere A= Growth or population…

Q: Graph the exponential function. f(x)=2^x Plot five points on the graph of the function. Then click…

A: To graph the exponential function. f(x)=2xAlso, to plot five points on the graph of the function

Q: Graph the exponential function. g (x) = Plot five points on the graph of the function. Then click on…

A:

Q: log12 (x ^ 2 + 35) = log12 (- 12x - 1) Please use one of the property and please specify which…

A: We can use logarithmic property in order to solve the given problem.

Q: log2(x+2)+log2x=3

A:

Q: log -2 -2)+ 6x 2 log6= log ニ

A: Given log(x2-2)+2log6 = log 6x There is always 10 in the base of a log  log10(x2-2)+2.log106 =…

Q: In 2012, the population of a city was 5.96 million. The exponential growth rate was 3.54% per year.…

A:

Q: A new strain of bacteria is studied in a lab. The lab begins with 10,000 bacteria and observes a 20%…

A:

Q: Solve logg (x – 2) +  logg (x) = 1

A:

Q: In 2012, the population of a city was 6.89 million. The exponential growth rate was 2.29% per year.…

A: Given value  In 2012 population of a city = 6.89 million  Growth rate = 2.29% per year = 0.0229 per…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.