The exponential function N = 500 × 0.74t, where t is measured in years, shows the amount, in grams, of a certain radioactive substance present. (a) Calculate N(3). (Round your answer to one decimal place.) N(3) = Explain what your answer means. After years there are grams of the radioactive substance present. (b) What is the yearly percentage decay rate? (Round your answer to one decimal place.) % (c) What is the monthly decay factor rounded to three decimal places? What is the monthly percentage decay rate? (Round your answer to one decimal place.) % (d) What is the percentage decay rate per second? (Note: For this calculation, you will need to use all the decimal places that your calculator can show. Round your answer to eight decimal places.)

Q: Use expansion by cofactors to find the determinant of the matrix.

A: Given:  A=24603100-5 we know that for matrix A=a1b1c1a2b2c2a3b3c3 determinant by using cofactors can...

Q: Given f(x)=10x+8 Find f–1(f(2)). Step 1: Find f–1(x)= x10​−45​   Step 2: Find f(2)= 28   Step 3:...

A:

Q: Solve the system. Give answer as (x, y, z) - læ – 4y + 4z - 8 - 5x – 8y – 4z = 8 - 6x – 16y + 4z - 8...

A:

Q: Identify the graph of the given equation. x2 - y - 1 = 0

A: The given equation is x2-y-1=0. To identify the graph of the given equation, write y as a function x...

Q: Let A be a nonsingular n × n matrix. Use mathematical induction to prove that Am is nonsingular and ...

A: Method used: Induction method. Let A be a non-singular matrix of order n. It is known that A is a no...

Q: Write the interval notation corresponding to the set notation {x | x < 8}

A: To write the interval notation corresponding to the set notation  x|x<8

Q: a) Assume that people can go to work from home either by SkyTrain or by car. Driving takes 10 min if...

A: (a) Calculate the cost for travelling per traveler "x" by sky train. Fixed cost for the travelling b...

Q: Solve the system. Give your answer as (x, y, z) 5а + 5у — 2х 3D 13 2x + 3y – 4z = - 14 5х + 3у — 52 ...

A: The given system of equations are 5x+5y-2z=13                    ...(1)2x+3y-4z=-14                ....

Q: Let A be an m × n matrix. Show that ATA and AAT are both symmetric.

A: Given A be an m×n matrix. we have to show that ATA and AAT are both symmetric.we will make use of al...

Q: Answer the questions about the following polynomial. 1 3 - The expression represents a polynomial wi...

A: The given polynomial is 19x3-3 Here, the given expression is cubic polynomial as its degree is three...

Q: Prove that a finite group is the union of proper subgroups if andonly if the group is not cyclic

A: union of proper subgroups  proof: Let G be a finite group. In the first place, we are going the show...

Q: Solve the following linear programming problem. Restrict  x ≥ 0  and  y ≥ 0. Minimize  g = 8x + 6y  ...

A: Given inequalities are 5x+2y≥16,3x+7y≥27,x≥0,y≥0. Draw the graph for the above inequalities as shown...

Q: evalute 3x -4y when x=2 and y = -2

A: From the data: The equation is:  3x-4y

Q: Find the roots for each of the following using the quadratic formula. Also, describe the number and ...

A:

Q: Draw a slope triangle and use it to write the the line shown in the graph at right.

A:

Q: determine the dimension of the subspace of R3 spanned by the given vectors.

A: Determine the dimension of the subspace of ℝ3 spanned by the given vectors.    

Q: Solve the linear system x + y-2z = 4 x + 3y-z = 7 2x + y-5z = 7

A: the linear equations given are: x+y-2z=4x+3y-z=72x+y-5z=7

Q: Answer please

A: We have to given rectangles and triangles. We have to decide scale factor from one to another is gre...

Q: Bill and Ted earned a total of $65 babysitting during the month of November. Bill earned $5 more tha...

A: Given:Bill and Ted earned =$65Bill earned $5 more than 1/2  of Ted

Q: 68. Newspaper Ad Revenue The table lists U.S. print news- paper advertising revenue (in billions of ...

A: The line passes through two points (2009,25)  and (2014, 16) first we find out the slope m slope m=y...

Q: In 1993, the moose population in a park was measured to be 3250. By 1996, the population was measure...

A:

Q: Find the equation of the line that contains the given point and is perpendicular to the given line. ...

A:

Q: Write an equation in point-slope form and slope-intercept form. L is parallel to y=2x.

A: Given Data: Line 1: y=2x Point of line L: x0, y0=2, 2   The line L is parallel to line y=2x. The poi...

Q: For every prime p, show that Х-1 — 1 %3 (х — 1)(х — 2) : .. [x — (р — 1)] in Zp[x].

A: Fermat's Little Theorem: Let p be a prime and let a∈N , 0<a<p. Let Ap={1a,2a,....(p-1)a} No tw...

Q: Rewrite quadratic in vertex for f(x) = 3x^_ 15x  find f(x) and the vertex

A: To rewrite the quadratic equation in vertex form and to find vertex fx=3x2-15x

Q: The graph of the quation appear to be parallel. Solve the system of equations algebraically. Explain...

A: The equation is  21x − 20y = 0                    .......(1)13x − 12y = 120                 ......(2...

Q: A plumber and his assistant work together to replace the pipes in an old house. The plumber charges ...

A:

Q: Exercise 1.2.16 Find the circle x²+y² +ax+by+c=0 passing through the following points. а. (-2, 1), (...

A: a) The given equation of the circle x2+y2+ax+by+c=0 Since the points (-2, 1), (5, 0) and (4, 1) pass...

Q: a specific radioacitve substance follows a continuous exponential decay model. It has a half life of...

A: Given  Amount of radioactive substance is present at the start of experiment =581.8g Half life=11 ho...

Q: Sarah can run 8 miles in 36 minutes. How long will it take him to run two miles?

A: Consider the formula for speed is, Speed=distancetime Since, "S" can run 8 miles in 16 minutes and i...

Q: Plz answer to 2 for me. Fill in the blanks

A: 2.(a) Given function is f(x)=-x-4-5 We, know that for every x x-4≥0 -x-4≤0 -x-4-5≤0 -5f(x)≤-5  There...

Q: Factor the expression. If prime, then enter "prime". 125y+ 27. (If the expression is prime, then ent...

A: Prime expression: expression which can not be factored.  a3 + b3 = (a + b)(a2 - ab + b2)

Q: Let G be a finite group and let H be a normal subgroup of G. Provethat the order of the element gH i...

A: Given: G be a finite group and H be a normal subgroup of G. 

Q: Chris has $100 in his savings account and he adds $20 a month to the account. The total amount can b...

A: Given: Chris has 100$ in his Savings account; Every month he adds 20$ Now, the linear function :    ...

Q: If f) = 2x-land g(x) - x', Find 8*/

A:

Q: Is (d) true or false. If true, explain why. If false, give a counterexample

A: We have to determine whether part (d) is True or False. (d) If A=a00b then AB=BA for any 2×2 matrix ...

Q: Solve the systems of linear equations over the indicated Zp 3x + 2y = 1 x + 4y = 1 over Zs

A: Given: 3x+2y=1                          ....1x+4y=1                          ....2 for solving this ...

Q: American Dollars and British Pounds Assume that at the current exchange rate, the British pound is w...

A: Let p and d be the number of pounds and dollars respectively. Given that the British pound is worth ...

Q: Solve the following using the principle of the matrix inverse, using any of the appropriate methods....

A: Hi there !! Thank you for the question. Since you have asked multiple questions and did not specify ...

Q: Test the sets of matrices for linear indepen­dence in M22. For those that are linearly dependent, ex...

A: Given: -11-22,3011,02-31,-10-17 To check: Linear independence in M22.

Q: let A = { 2,3, 4, 5, 6,7,8} and B={1,2,4,6,7,8,9} find A-B, B-A

A:

Q: A cell phone company charges a monthly fee of $20 for the first 1000 text messages and 10 cents for ...

A:

Q: How do I solve

A: We have to draw the graph of function: fx=12x-22-4 First we will draw the graph of fx=12x-22 by usin...

Q: The Special Product Formula for the "product of the sum and difference of terms" is (A + B)(A – B) =...

A: We know that A+BA-B=A2-B2

Q: I need help with these

A: y varies directly as x. Therefore y = kx ( where k is constant) Given that y = 3 when x= 15. Therefo...

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.