The economic dimension (diameter and height) of a cylindrical overhead storage tank for a capacity of 125,000 gallons (use 1ft^3 = 7.842 gallons) are nearly. 1. 15 ft and 7.5 ft 2. 45 ft and 22.5 ft 3. 35 ft and 17.5 ft 4. 20.5 ft and 10.25 ft

Q: The total daily cost (in dollars) of producing x park benches is given by C(x) = 2250 + 10x +0.1x²…

A: I have explained everything with in the solution .please go through that.

Q: 5. Determine the measures of angles a, b, and c. Indicate the properties that you used to solve…

A: Definition of Alternate angles-: Two angles ,formed on opposite sides of a line that crosses two…

Q: Select the negation for each of the following statements. The dog is sleeping and the dog is…

A:

Q: 2. Let T: M2,2 (R) → R be defined by T(A) = det(A). Show that T is not a linear transformation.

A:

Q: Sketch the region bounded by the surfaces z = √√x² + y² and x² + y² = 1 for 1 ≤ z ≤ 2.

A: 43Our region is bounded by the surface                  z=x2+y2                  x2+y2=1;…

Q: B C D The graph of the function f, shown above, consists of two line segments. If h is the function…

A: We are given the relation that          h(x) =  ∫0x f(t)dt    for 0 ≤ x ≤ 6  Then, differentiating…

Q: Find the equation of the straight line that (1).makes equal intercepts on the axes and passes…

A: (1) Let the equation of the line bexa+yb=1Since it makes equal intercepts on the coordinates axes,we…

Q: Find the general solution of the given higher-order differential equation. y" - 6y" - 7y' = 0 y(x)

A: This question is about ordinary differential equation.

Q: A deposit is made at the EOY 2021. Five equal withdrawals are to be made, starting at the EOY 2025,…

A: Sol:- To solve this problem, we need to use the formula for the future value of an annuity. First,…

Q: Let F be the function whose graph is shown below. Evaluate each of the following. Note: Input DNE,…

A: I have explained everything with in the solution .please go through that.

Q: Sketch the graph of a function that satisfies all of the given conditions. • f'(2) = f'(-2) = 0…

A: We have to draw the graph of the function which satisfied all the conditions given below. i.…

Q: Select all statements below which are true for all invertible n x n matrices A and B DA. AB is…

A:

Q: Compute the volume occupied by revolving a circle of radius 3 m from the axis about 10 m radius away…

A: Sol:- To find the volume of the solid generated by revolving a circle of radius 3 m about an axis 10…

Q: Suppose f(x) = ∞ 2.9 5" n! (x − 3) n To determine f(2.9) to within 0.0001, it will be necessary to…

A: Given Data: Let us consider the given data, fx=∑n=0∞5nn!x-3n

Q: 37. Asymptote Behavior How close to -3 do we have to take x so that > 10,000 (x + 3)?

A: We can solve this inequality by isolating x and finding the values of x that make the inequality…

Q: Find two solutions to equation: w2 = ( -1 -i )

A: let , w2=-1-i⇒w=-1-i12          .......in general w=x+iy12 so x=-1 and y=-1  Now polar form of w is…

Q: Solve the given initial-value problem. y(x) = y" + 36y = 0, y(0) = 4, y'(0) = −4

A: Given initial value problem  y'' +36 y = 0 , y(0) = 4 , y'(0)= -4 .  The general solution of linear…

Q: The tangents to x\power{2}+y\power{2}=a\power{2} inclinations a and b intersect at P.if cot a+cot…

A: Let the coordinates of P be (h,k).Let the equation of a tangent from P(h,k) to the circle x2+y2=a2…

Q: 5. T:R² R2 is a vertical shear transformation that maps e₁ into e, -2e2 but leaves the vector e₂…

A:

Q: 2. Given the differential equation: solution. 3. Solve this differential equation: Variables. y"-6y'…

A:

Q: aluate the line integral F. dr, where - (x, y, z) = 3x i − yj - zk and C is given by the vector…

A: Given problem is from vector analysis. I have explained everything below.

Q: QUESTION 3 Let f(x) = ³1. (a) Find the average rate of change over [1,2]. (b) Find the average rate…

A:

Q: 22. f (x) = 4 sin ( (x − 3)) - + 7

A: Given: The sine function is given as fx=4sinπ2x-3+7. To find: Amplitude. Period. Mid-line. Minimum…

Q: A variable circle which always touches the line x+y-2=0 at (1,1) cuts the circle…

A: Any circle which touches the line x+y-2=0 at (1,1) will be of the form…

Q: The graph to the right shows a region of feasible solutions. Use this region to find and minimum…

A: Given: (a) z=6x+8y. We have to find the maximum value of the function in the feasible region.

Q: Archaeologists used pieces of burned wood, or charcoal, found at the site to date prehistoric…

A:

Q: Note: you can add as many rows or columns to the data presented below as you find necessary. 2011…

A: We will use the following formulas: The rate of change of assets each year is calculated using the…

Q: If a function f(x) is continuous on (a, b) and differentiable on (a, b), then the Mean Value Theorem…

A:

Q: Find the following. (Round your answers to the nearest cent.) Finance Number of Charge Payments…

A: a)Unearned finance charge = (m * (m+1)) / (n * (n+1)) * F = (6 * (6+1)) / (12 * (12+1)) * $9.20 = (6…

Q: Consider the function f(x) = (a) The domain of f(x) is √3x² +96-12 x-4 (b) The only potential…

A:

Q: A family wants to have a $150,000 college fund for their children at the end of 20 years. What…

A: Given that future value  FV=$ 150,000 Interest rate r=7.6%=7.6100=0.076Compounded quarterly m=4…

Q: The indicated function y₁(x) is a solution of the given differential equation. Use reduction of…

A: The given differential equation is y''-10y'+25y=0; y1=e5x We have to find second solution y2.

Q: Find the volume V (S) of the solid S generated by revolving the given region R where R is bounded by…

A: To find the volume of the solid generated by revolving the region R bounded by y = 2x + 3, y = -1…

Q: essian matrix for f is:  H = [5 2]        [2 3]  Which one of these options best describes the…

A:

Q: Find a formula for det(rA) when A is an n x n matrix and r is a real number

A:

Q: Show the derivation of temperature conversion using the linear interpolation method.

A: Sol:- The linear interpolation method is a way to convert temperatures between two different scales.…

Q: For each of the following statements, if the statement is true, then give a proof, and if the…

A:

Q: The Cauchy problem 2ux + 3uy = 5 u = 1 on the line 3x - 2y = 0) Has (a) Exactly one solution (b)…

A: The given Cauchy problem is ,               2ux+3uy = 5 u=1 on the line  3x-2y = 0 (.)  Consider the…

Q: The given family of functions is the general solution of the differential equation on the indicated…

A:

Q: 8-1) T:R³ R², T(e)=(1, 3). T(ez)=(4, 2), and T(es) = (-5, 4), where e₁, ez, es are the columns of…

A: Given: In this question, the given details are, T:ℝ3→ℝ2, T(e1)=(1,3), T(e2)=(4,2), and T(e3)=(-5,…

Q: Find the size of the matrix. Identify a square, column, or row matrix. Give the additive inverse of…

A:

Q: A product is introduced to the market. The weekly profit (in dollars) of that product decays…

A:

Q: (f) y" - y' + 2y = 3e + 4 cos 2x

A: Consider the differential equation y''-y'+2y=3ex+4cos2x. To find the general solution of given…

Q: Problem #3: Solve for the matrix A in the following equation. - [¹4] (4¹+31)-¹ 18 -46 •[*]] •[3]«[3*…

A:

Q: 8-3) show that T is a linear transformation by finding a matrix that implements the mapping. Note…

A: (a) The given linear transformation is  Tx1,x2=2x2-3x1,x1-4x2,0,x2 (b) The given linear…

Q: Give small examples of equivalence relations R and P such that RUP is not an equivalence relation.

A:

Q: Maximize Z = 100x₁ + 100x2 10x1 +5x380 6x1+6x2 ≥ 66 subject to 4x1 + 8x2 ≥24 5x1 +6x290 x1, x₂ > 0

A:

Q: Use the graph of f'(x) to discuss the graph of y = f(x). Organize your conclusions in a table and…

A: We know that graph of f(x) increasing if f'(x) >0 and graph of decreasing if f'(x) <0 .

Q: Find the reference angle 'of 0 = −635°. Then, sketch in standard position and label 0'.

A:

Q: Show that the application of L'hopital's rule is relevant for lim (+). X-1

A: