Determine the dimensions of the maximum strength beam that can be cut from a log. Consider that the strength of the beam is proportional to the product of its width times the square of its height.

Q: Complete the following table so that f(x) represents a linear function and g(x) represents an…

A: for the linear function, two points are (x1,y1)=(-2,6) (x2,y2)=(0,14)...............y-intercept is…

Q: Find a logistic function that satisfies the given conditions: y = 33 20 (0, 11) -20 (-2, 1) 20 40 2

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Q: Expand : logs VZ 125 y?

A:

Q: Express x in term of y if: log,xy =2 +2log,x -3log,y

A: Given that:  log4xy=2+2log4x-3log4y We have to express x in the form of y.

Q: The stiffness of a rectangular beanm is proportional to the breadth and the cube of the depth. Find…

A: Let the diagonal of a given rectangular beam is h . breadth and depth are b and d respectively.…

Q: Find the exponential function f(x)=a^x that passes through the point (−3,1/27) and has a y-intercept…

A:

Q: The cubic function that is the best fit for the data, with y equal to the number of millions of…

A: Given,            The cubic function that is the best fit for the data, with y equal to the number…

Q: Assume that the population of the greater roadrunner in the Guadelope Desert was 250 per hectare at…

A:

Q: Find the exponential function y = Cekt that passes through the two given points. (0,1/2),(3,1)

A: We have to find exponentially function

Q: The function defined by y= x3 (is/is not) an exponential function, whereas the function defined by y…

A: Definition of exponential function – A mathematical function of the form f(x) =ax, where a is the…

Q: What is the greatest constant of variation

A: I am attaching image so that you understand each and every step.

Q: An engineer creates a model to predict the electric consumption of a household in summer in a day…

A: # consider a linear regression model  y=b0+b1*X  b0=23 hr  & b1=1.55 hr  then to find y at x=17…

Q: form is gi = = log x- %3D

A:

Q: Use the linear approximation to estimate the value. Compare with the value given by a calculator.…

A: Think of 4.19.9 as a value of fx,y=xy f4.1, 7.9=4.17.9 Then it makes sense to use the linear…

Q: A landscaping company charges $49 per cubic yard of mulch plus a delivery charge of $27. Find a…

A: Given A landscaping company charges  per cubic yard= $49 delivery charge =$27

Q: Approximately how many seconds does it take for the object to return to its minimum height? seconds

A: From the graph, the minimum height of the graph can be noticed:

Q: Find the exponential function f(x) = Cbx whose graph is given. f(x) = y WebAssign Plot (3, 32)

A:

Q: Hamed own a local gold market that currently has 1159129 subscriber in Instagram at a quarterly…

A: Let the number of subscribers is denoted by x and the price of a commodity be denoted by y. Then we…

Q: The population of a country will quadruple in  4 years. If its current population is  15000, what…

A:

Q: 1. Create the equation where life expectancy of a person is positively affected by the number of…

A: Endogenous variable: The variable which can be affected with the changes in independent variable is…

Q: Use the linear approximation to estimate the value. Compare with the value given by a calculator.…

A: The given number is (2.01)3(1.02)2

Q: Model the data using an exponential function f (x) = Ab" 1 2 fx) 40 80 160 Select the correct…

A:

Q: If dairy cows eat hay containing  too much iodine 131, their milk will be unfit to drink. Iodine 131…

A: Given:- If dairy cows eat hay containing  too much iodine 131, their milk will be unfit to drink.…

Q: Show that log, (x + Vx² – 1) + log,(x – Vx – 1) = 0.

A: Logarithm is inverse of exponentiations. A logarithm is easy method to express large number and to…

Q: Which graph represents f (x) = log, r?

A: The given function is f(x)=log6x

Q: The gross profit for Exxon Mobil Corporation for various years is given here. Gross Profit Year (in…

A: From the previous part. The model is given by, P=1447t+54

Q: Graph the function. g(x) = log, (r)

A: graph the function

Q: Assume that it costs Sony approximately C(x)=800,000+340x+0.0005x2 to manufacture x PlayStation 4's…

A: We have given the cost function C(x) = 800,000 + 340x + 0.0005x2

Q: Use the equation and type the ordered-pairs. y = log, z %3D ((1/2, ), (1, ), (2, ). (4, ), (8, ).…

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Q: If a (small) weight w is suspended from a spring, the length L of the stretched spring is a linear…

A:

Q: Determine a formula for the logistic function who graph is shown in the *y = 60 40 (8, 30) 20 (0,…

A: NOTE: Refresh your page if you can't see any equations. . the logistic function is in the form of…

Q: | (1 – a*)dæ (1 — а?) а

A:

Q: A landscaping company charges $46 per cubic yard of mulch plus a delivery charge of $28. Find a…

A:

Q: The nonlinear part is 4x' and the linear part is 2x-2. g(x)-4x'-2x+2 h(x)=-2' +3x-4 K(x)=…

A: In g(x) = 4x3 - 2x + 2  The nonlinear part is 4x3 And the linear part is  - 2x+ 2. Similarly, h(x) =…

Q: Find the linearization of the natural logarithm f(x)=lnx at x=1.

A:

Q: . Find the exponential functions of the form f(x) = ab* that pass through 1) (-2, 32) and (1, –)

A: An exponential function is in the general form f(x) = abx We know the points (-2,32) and (1,1/2) ,…

Q: at the one-dimensional and n are constants.

A:

Q: In the electric currect​ flow, it is found that the resistance​ (measured in the units called​ ohms)…

A: Given: Resistance R1=0.422 ohm Diameter D1=0.01 inches Given resistance offered by a fixed length…

Q: Find the exponential function f(x)  =Cax  whosegraph is given.

A: Given graph of exponential function fx=Cax. From the given we can find that it passes through point…

Q: Consider the following model to explain the percentage of students receiving a passing score on a…

A: Given information: The output of multiple linear regression is given.

Q: Let kids denote the number of children ever born to a woman, and let educ denote years of education…

A: kidsi=β0+β1educi+ui where  kids= number of children born to a womaneduc= years of education

Q: How is the slope coefficient interpreted in a log-linear model, where thedependent variable is (i)…

A: The slope coefficient interpreted in a log-linear model of the dependent variable is given below as,…

Q: The amount of heat H (in joules) required to convert one gram of water into vapor is linearly…

A: Given,The amount of heat H(in joules) required to convert one gram of water into vapor is linearly…

Q: An office building worth $1 million when completed in 2000 is being depreciated linearly over 20 yr.…

A:

Q: ion of a city in 2000 was 900,000 while the at demographic studies show that each ye ile 3% of the…

A: Given,   City Suburbs of the city Population in the year 2000 900,000 400,000

Q: . Use the variation of parameters formula together with the exponential from part 3) to find the…

A: As per the question we have the following second order linear non-homogeneous differential equation…

Q: Find the exponential function y = Cet that passes through the two given points. (4, 5 3 1 (3, 1/2) 2…

A: Given function y=Cekt And points on the curve are (3,1/2) and (4,5)

Q: Find the exponential function of the form y=ab^x  that goes through the points (1,2) and (5,250)

A: Consider the function y = abx.The given points are (1, 2) and (5, 250).Substitute 1 for x and 2 for…

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.