A drug is eliminated from the body through urine. Suppose that for a dose of 10 milligrams, the amount A(t) remaining in the body t hours later is given by A(t) = 10(0.9)t and that in order for the drug to be effective, at least 2 milligrams must be in the body. (a) Determine when 2 milligrams are left in the body. (Round your answer to two decimal places.)(b) What is the half-life of the drug? (Round your answer to two decimal places.)

Q: Solve the following exponential equation. Express the solution set in terms of natural logarithms or...

A: Given,

Q: Practice 5.8 Question #8

A: Given inequality:

Q: Solve the following exponential equation. Express the solution set in terms of natural logarithms or...

A: Given exponential equation is,

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

A: Given the logarithmic equation

Q: Determine the equation of the line that contains the point (2, -3) and is perpendicular to the line ...

A: Given:

Q: The number of books in a small library increases according to the function B= 3700e0.05t, where t is...

A: Given,The number of books in a small library increases according to the function B= 3700e0.05t, wher...

Q: Find a polynomial function with the zeros - 5, 0, 3, 1 whose graph passes through the point f(x) = (...

A: Given,           A polynomial function with the zeros - 5, 0, 3, 1 whose graph passes through the po...

Q: Find the interest. Round to the nearest cent. John borrowed $4800 from his aunt to buy a car. He rep...

A: Formula:

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 given exponential equation. Express the solution set in terms of natural logarithms or com...

A: The given exponential equation is,

Q: Use the square root property to determine all real solutions for each of the following equations. 2h...

A: Given:

Q: A rectangle is drawn so the width is 7 inches longer than the height. If the rectangle's diagonal me...

A: A width of  rectangle is 7 inches longer than the height and its diagonal measurement is 37 inches.

Q: Question 19: Solve for x in the following equation (show steps to get to the answer): log2(x? + 2x) ...

A: Solve x.

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

A: Given,

Q: Find the required annual interest rate, to the nearest tenth of a percent, for $5200 to grow to $650...

A: Consider the given information

Q: Solve for x Preview

A: Consider the given equation

Q: Problem: A college bookstore charges $60 for a semester membership. The first book is free withthe m...

A: Given:The college bookstore membership charge be 60 dollars.The book cost after one free book be 27....

Q: The amount of coffee sold depends on the price of coffee. The following table gives the amount of co...

A: a) From the given information, 13 million pounds of coffee is sold at $4 per pound and 8.2 million p...

Q: Solve the rational inequality. Write the solution set in interval notation. x+11/x+4<3

A: Subtract 3 from both sides.

Q: Please show in detailed steps how to factor as well as use the quadratic formula: 4.9t2+3.1t-5.0=0 T...

A:

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

A: Get rid of ln using exponential form of logarithm.

Q: determine the intervals where H(x) = ( x+2)(x-4)3>0

A: Set H(x)=0 and find x. 

Q: Solve the equation. Write the solution set with the exact solutions. 4Log6 (5y - 4) + 20 = 28 If the...

A: The given equation is

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

A: Given series can be written as,

Q: ln4x+ln3x=ln13 solve and express in exact form

A: Given:

Q: 16. Write in logarithmic form =343 %3D

A: First of all, consider the given equation.

Q: In 1980, the population of blue whales in the southern hemisphere was thought to number 4500. The po...

A: First of all, find the value of t for the year 2021.

Q: 9. State the domain and range of the following graph. foivsd bro 8. 9. -10 86 -4 -2 10 -6 ps to snoe...

A: Consider the given graph.It is known that the domain of the function refers to the set of possible i...

Q: given zeros: -2( multiplicity 1 ); 3( multiplicity 2); 4(multiplicity 1); degree of f is 4 and the g...

A:

Q: A metal wire of length 80 cm is cut into two parts such that one part is 4k cm long. Each part of th...

A:

Q: 21. A house remodeling costs $35.000, You decide to pay a 15% down payment and amortize the rest wit...

A: Formula used:

Q: Find an exponential function of the form f(x) = bax that has the given y-intercept and passes throug...

A: Given:

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: F(x)=x2(x+3) Determine the end behavior of the graph of the function Find the x- and y- intercepts ...

A:  The given function is

Q: Find the slope of the line passing through the points (-9,3) and (-2, 3)

A: Given:points (-9,3) and (-2, 3)

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

A:

Q: A one–to–one function is given. Write an equation for the inverse function. V (x) = x - 2/ x + 9

A: The given function is,

Q: Samy took 3/4 hour to travel from home to the zoo. He took 1 1/4 hours to return home. How much long...

A: Given information

Q: Question 15: For each function, 6. x+2 8. ()** + 5 g(x) 1. 3*+5 + 2 f (x) 2. (a) write out the trans...

A: The given function is g(x) = 8(1/3)x+2 + 5.(a)Obtain the transformation of the function as follows.C...

Q: 1. At a price of $4 per slice, the supply of pizzas is 800 slices and the demand is 580 slices. At t...

A: a) Since price-supply equation is linear , so we can use two-point form of equation by taking points...

Q: Find the compound amount for the deposit. Round to the nearest cent. $15,000 at 3% compounded annual...

A: From the given information, it is observed that,

Q: If g(5) = 0, what point is on the graph of g? What is the corresponding x-intercept of the graph of ...

A: Given: -

Q: perform the indicated  11/x+10 - 10x/x^2-100

A: Given,

Q: Find the equation of the circle with center at (−2, 1) and that passes through the point whose coord...

A: The center of the circle and a point through which the circle passes is given as follows.

Q: Please see attachment and answer all questions

A: Given,The area of a rectangular wall of a barn is 154 square feet and the length is 8 feet longer th...

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

A: The given function is,

Q: Solve: 6 3 5 If there is more than one solution, enter the solutions separated with commas. If there...

A: Given equation 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: Write the equation in logarithmic form. (1/2)-8 = 256

A: Given:

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.