The population of the United States from 1790 to 1860 is given by the following formula, where t is years since 1790 and N is the population, in millions. N = 3.93 x 1.03t(a) What was the population in 1790? million(b) Express the population in 1815 using functional notation.N(       )(c) Calculate the value of the population in 1815. (Round your answer to two decimal places.) million

Q: you ave $5000 to place in a CD for 10 years. the CD pays 2.9% annual interest, compounded quarterly....

A: Given,

Q: Please see attachment

A: Given,The number of incarcerated adults N (measured in thousands) in a certain country can be approx...

Q: Bob owns a watch repair shop. He has found that the cost of operating his shop is given by c(x) = 4x...

A: The equation for the cost of operating the watch shop is given as follows.

Q: Use the compound interest formula to determine how long it will take for a sum of money to double if...

A: Formula for compound interest:

Q: Solve the linear programming problem by the method of corners.Find the minimum and maximum of P = 7x...

A: The given linear programming problem is,

Q: If f={(1,−3),(−3,2),(4,34),(π,2)}f={(1,-3),(-3,2),(4,34),(π,2)} and g={(1,1),(−3,2),(34,0)}g={(1,1),...

A: Given f and g.

Q: A company finds that it can make a profit of P dollars each month by selling x patterns, according t...

A: Given,

Q: A drug is eliminated from the body through urine. Suppose that for a dose of 10 milligrams, the amou...

A:

Q: Find the equation of the circle that has a diameter with endpoints (−8, 7) and (8, −3).

A: Given information:The diameter with endpoints is shown below:(−8, 7) and (8, −3)

Q: The function f(x) = is one-to-one. (a) Find its inverse and check your answer. (b) Find the domain a...

A: F(x)= 8/(3+x)For the given functionFind the inverse and check your answerFind the domain and range o...

Q: solve for x to the nearest hundredth 3x=22

A: The given equation to be solved is,

Q: For f(x) = x and g(x) =x +7, find the following composite functions and state the domain of each. %3...

A: Find the  composite functions and state the domain of eachF(x)= x2G(x)= x2+7FogGofFofGog

Q: Graph the linear equation x=-6

A: Graph the linear equation:

Q: Find the length of the missing side x in this right triangle. 84 85 х Preview

A: Given informationRight angle triangle, length of hypotenuse = 85, length of one side of right angle ...

Q: solve 3(x--4)=12x please go step by step

A: The equation is given by,

Q: Solve:  16x = 1/4-8/x a.) -2  b.) 2  c.) 0  d.) -4  e.) 4

A: Given equation

Q: Use a formula to express y as a function of t if  y = 3x2 + 9x and x = t − 1.   y =

A: First of all, both equations i.e. y in terms of x and x in terms of t.

Q: Solve for a by completing the square. - 4a? – 8a + 32 = 0 Preview

A:

Q: Solve the following equations by the most convenient method. Please show all work. 5/x-4 - 8/x+1 = 3...

A: Use cross multiplication to simplify the given expression as.

Q: Find the equation of the axis of symmetry and the coordinates of the vertex of the parabola given by...

A:

Q: Find the sum of the geometric series, if possible. n 6) n=1 :/-

A: Given series can be written as,

Q: write the domain of the following using interval notation f(x)= radical 35-5x

A:

Q: For f(x)=x^2 and g(x)=x^2+8, find the following composite functions and state the domain of each (a)...

A: Find the  composite functions and state the domain of eachF(x)= x2G(x)= x2+8FogGofFofGog

Q: Solve the following logarithmic equation. Be sure to reject any value of x that is not in the domain...

A: Consider the given equation.

Q: square root of x+7 =x+1

A: Consider the provided equation,

Q: What is the doubling time of the bacteria population given that it quadruples every 92 minutes?

A: Given,Bacteria population quadruples every 92 minutes.

Q: The long leg of a right triangle is 17 feet longer than the short leg. The hypotenuse is 25 feet lon...

A: Let x be the length of one leg in feet.Then, the length of other leg will be x +17.We have given the...

Q: Consider the functions f(x)= 2x+5 and g(x)= x-4 Find (f+g)(3)

A: Given functions are

Q: The amount remaining of a certain radioactive substance after t days is A(t)=A0e^-0.025t , where A0 ...

A: Given,

Q: solve by completeing the sqaure  9y^2+30y-32=0

A: Given:

Q: Evaluate v-4 Enter DNE if not a real number.

A: Evaluate

Q: Use the Pythagorean theorem to find the missing side. c= 9, b = 4a; find a and b (Simplify your answ...

A: Plug b=4a and c=9 in Pythagorean theorem.

Q: Number 29 on my test review I don't undertand.

A: The given functions are

Q: domain of 3x^4-7x^2+x-3

A: The given function is,

Q: A strain of bacteria is placed into a nutrient broth at 30° Time (hr), t Population (g), P C and all...

A: The average rate of change between

Q: In business, the total profit P is the difference between the revenue R and the cost C. For x 43. an...

A: Given:

Q: Plotting mix fraction -1 1/6 and 4/3 on a number line

A: The given mixed fractions are,

Q: x^2+5x+6/ x^2 +10x+21divided by x^2+2x/x^24x-21

A:

Q: Find the equation of the circle with radius 1 and center (5, −3). Find the equation of the circle wi...

A: The general equation of the circle with center (a, b) and radius r is,

Q: Solve the logarithmic equation. Be sure to reject any value of x that is not in the domain of the or...

A: Solve the logarithmic equation

Q: Give the solution to the system of equations.  x=2y x=y2-2y

A: Given:

Q: Question 20: What is the inverse f-1(x) of the logarithmic function f(x) = log2(x)?

A: Given function logarithmic is,

Q: If f(x)=x^4-3x^3+2x^2+x-3 find the value f(-1) f(2) f(-2)

A: Given information

Q: Find the quotient. Write the answer in standard form. 4+2i/7-9i

A: Given,

Q: (x - 1)4 - 5(x - 1)2 + 4 = 0

A: We need to find the values of x which satisfies the given equation

Q: Fcator by grouping x3-6x2+5x-30

A: From the given statement, the polynomial expression is,

Q: Solve the following logarithmic equation. Be sure to reject any value of x that is not in the domain...

A: The given logarithmic function is,

Q: Please see attahcment

A:

Q: Given f(x) = 6/x and g(x) = 6x, find the following expressions. (b) (go f)(2) (c) (fo f)(1) (d) (g •...

A: Since we are entitled to answer up to 3 sub-parts, we’ll answer the first 3 as you have not mentione...

Q: Log2 (1/64) =

A: Given is the following exponential equation:

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.