ind the equation of a circle with center (4,3) touching the circle x2 +y2 =1. Find the equation of the smaller circle that touches the circles x\power{2}+y\power{2}=1 and passes through the point (4,3).

Q: Let S represent sales of a new product (in thousands of units), let L represent the maximum level of…

A: Introduction : Sales in math deals with rough estimating at times and it gives that big picture view…

Q: The table shows the amount of water that leaks from a pool. Assume the relationship between the two…

A: Rate of change: Let us consider the two points be x1,y1 and x2,y2. The formula to calculate the rate…

Q: find a point-normal form of the equation of the plane passing through P and having n as a normal.…

A: Here we have to find point normal form of the equation.

Q: If the straight line x - 2y + 1 = 0 intersects the circle x² + y² = 25 at points P and Q, then…

A:

Q: Calculate the volume of a solid enclosed by the following equations z=x² +1, x=3, y=5 and the three…

A: Let E be the region bounded by the graphs in space.

Q: How would you modify the method of steepest ascent ifeach variable x1 were constrained to lie in an…

A: If the variables are constrained to lie in an interval, we need to modify the method of steepest…

Q: Assume that a refrigerator is maintained at a constant of 45°F and that an object having a…

A: We have  Temperature of refrigerator Ts = 45°F  Object's initial temperature T0 = 80°F  Object's…

Q: Lu factorization Ax = b Find X. LUZ = b X3 = t₁ tER 10-716 00 -1811 .131 12 017/300 - 322 15 1 6…

A:

Q: 2²u at² ·x 20u = 0, əx² -∞0 0 the equation subject to the initial and boundary conditions: u(x,0) =…

A: Solution:- Given equation is homogeneous wave equation for infinite string

Q: Let f(x) = 3 x 25 x2 for 0 ≤ x ≤ 5 and f(x) = 0 for all other values of x. 125 - (a) Verify that f…

A:

Q: Fill in the blanks with the correct answer. The measure of ABD is 114°. What are the measures of ABC…

A: Given ∠ABD=114°and ∠ABC=x∠CBD=2x∠ABD=∠ABC+∠CBD114°=x+2x3x=114°x=1143=38°

Q: 6. Regard y as the independent variable and x as the dependent variable and use implicit…

A:

Q: Show that the following graph is nonplanar by showing the K3,3 configuration it contains. B E F H…

A:

Q: Exercise 3. Let n E N with n > 2. Prove that there exists a € Zn such that a² = [1] € Zn and a #…

A:

Q: f(x) *[32snx-05 cos x] x €3,4

A: The given function is  fx=e-x32 sinx-5 cosx, x∈3, 4 We have to find the solution using the false…

Q: Let C(x) be the statement that "x has visited California," and let N(x) be the statement that "x has…

A: Given: C(x) be the statement that states "x has California". N(x) be the statement that states "x…

Q: Using the direction fields given as a guide. (a) Are there any constant solutions? Ifso, what are…

A: Without the given direction fields, it is impossible to provide a specific answer to this question.…

Q: If the equation px² + (2 − q)xy + 3y² − 6qx + 30y + 6q = 0 represents a circle then find th values…

A: Sinec the equation of the circel is given by        x2+y2+2fx+2hy+c=0

Q: 1. Given the polynomials p= −5+2x + x² and q = 3+2x - 4x² i. find the standard inner product on P2…

A:

Q: The electrical resistance of a circuit changes depending on whether the resistors are connected in…

A:

Q: Towards the end of the season, a netballer had played 14 matches and had thrown an average of 16.5…

A: The mean value which is equal to the ratio of the sum of the number of the given sets of values to…

Q: Vector A = in rectangular coordinate system at P(18, 18, -6). What is the magnitude of vector A in…

A: To find the magnitude of vector A in the "theta" direction in the spherical coordinate system at P,…

Q: a) Consider the following equations, 0.7x + 2y 7 1.1x + y = 6 i) Rearrange both equations into the…

A:

Q: 7. For the differential equation (12x)y" + 2y' + (2x - 3)y=e=" (a) Write the associated homogeneous…

A:

Q: (a) Please fill out the rest of the table. n(n+1)² n² (n + 1)² -n² -3 -2 TOI231 0 4 5 61490 4 1 0 1…

A: (a) The complete table will be as follows: n (n+1)² n² (n+1)² - n² -3 4 9 -5 -2 1 4 -3 -1 0…

Q: 7. Assume vectors V₁, V2, V3 are nonzero. Explain why the set S = {V1, V2, V3} is linearly dependent…

A: This question examines the linear dependence of three non-zero vectors v1,v2, and v3, where v3 is…

Q: 10. Consider the polynomial p(x) = 3+x. a) Can p(x) be written as a linear combination of the…

A:

Q: Determine the number of terms necessary to approximate cos x to 8 significant figures using the…

A: Here, we need to determine the number of terms necessary to approximate cos x to 8 significant…

Q: (a) Suppose a bank offered an annuity that pays 6.73% compounded monthly. What is the rate per…

A: a Interest rate r=6.73%=6.73100=0.0673Compounded monthly  m=12i=rm=0.067312=0.0056083333Therefore…

Q: e the system of two linear inequalities graphically. x > -4 ory ≥ 1 p 1 of 3: Graph the solution set…

A: We have solve graphically of given inequality.

Q: Find the monthly interest payment in the situation described below. Assume that the monthly interest…

A:

Q: Find a representation of the vector AB = (4, -14) in R2 by giving appropriate values for the points…

A:

Q: ! Let ECR. Show that E is Lebesgue measurable if and only if there exists a sequence of open sets…

A: We know a theorem that            let E be any set. then given ∈>0, there is an open set S⊃E such…

Q: In each of the statements that follow, answer trueif the statement is always true and false…

A: The statement in question claims that if two matrices A and B are close to each other, then their…

Q: A function (t) satisfies the differential equation da (x - 1)²(x-2)(x - 5)(x-8). dt Compute the…

A:

Q: Let R= {(x, e¹x) : xER, n = Z}. Here e = 2.71828... as usual.) Prove that R is an equivalence…

A: For all real number x,        (x, x) = (x, 1.x) = (x, e0x) ∈ R  [ as 0 ∈ Z ]    Hence, R is…

Q: Plot the Euler's Method approximate solution on [0,1] for the differential equation y' = 1 y² and…

A:

Q: performance of three such funds as of February 27, 2015.†   Year-to-date Loss SHPIX (Short Smallcap…

A:

Q: 122 c. Show that the matrix Chapter 2 Linear Combinations and Linear Independence 25. A = 26. A =…

A:

Q: The 65 students in a classical music lecture class were polled, with the results that 37 like…

A: Given: The total number of students in a classical music lecture that were polled is 65. Number of…

Q: Find the equations of the normals to the circle x\power{2}+y\power{2}-8x-2y+12=c at the points whose…

A: The abscissa of a point is found by substituting the ordinates and solving for abscissa.therefore,…

Q: This equality is called the Parallelogram Law (a) Determine whether the lines a (2) 1+ t. y -2+3t, z…

A:

Q: Compute the total cost per year of the following pair of expenses. Then complete the sentence: On an…

A:

Q: The line 2x-y+1=0 is tangent to yhe circle at the point (2,5) and yhe center of the circle lies on…

A: Center lies on x-2y=4.let the center be C(4+2t,t).nowradius r=distance of from the…

Q: Each machine on Widgetco’s assembly line gets out ofwhack an average of once a minute. Laborers are…

A: a) Widgetco's hourly cost can be expressed as the sum of the cost of labor and the cost of idle…

Q: Prove that there are exactly n! n X n permutation matrices.

A: Given: n×n permutation matrices. To Prove: There are exactly n!, n×n permutation matrices.

Q: Please I need help to solve these questions. Kindly help explain all steps involved. If possible,…

A:

Q: Problem 5 multiplicative and satisfies f(n) = 0 for all n > 4. Justify your answer. Is there a…

A: Sol:- Yes, there exists a multiplicative function f(n) that is not completely multiplicative and…

Q: Given A = 1 3 -2-6 3 9 b = 0 and 6 find parametric equations for all least squares solutions of A =…

A: Given: A=13-2-639 ,b→=101. To Find : A parametric equation for all  least square solutions of Ax→=b→…

Q: In this problem, we use weak duality to prove Lemma 3.a Show that Lemma 3 is equivalent to the…

A: a) We can use the contrapositive of Lemma 3 to prove the equivalence: Contrapositive of Lemma 3: If…