5. f(x)=x² + 8x - 64, what's the minimum point of f(x)?

Q: Let h = f o g where ƒ : R² → R and g : R² → R² is defined by g(x, y) = (–3x²y, y − 2x). Find the…

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Q: Find an equation for the plane consisting of all points that are equidistant from the points  (−7,…

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Q: In three-space there are four possibilities for the intersection of two lines. True False

A: We have to find whether the given statement is true or false. In three-space there are four…

Q: Find the antiderivatives. Show any substitutions. [(7x+3) dx

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Q: A tumor is injected with 0.82 grams of Iodine-125. After 1 day, the amount of lodine-125 has…

A: Law of Decay is given as  P = P0e-kt where P is the amount after time t  P0 is the initial amount  k…

Q: Given the function f and the point Q, find all points P on the graph of f such that the line tangent…

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Q: r(t) = ti+t²j+ + 1 {/f²k 2

A: Solving the problem

Q: Evaluate the integral. (Use C for the constant of integration.) [70 7 tan(x) sec³(x) dx

A: The integration given is, ∫7tan(x)sec3(x)dx

Q: Let f(x)= - (2.-17). a. Use the following definition of the slope of the tangent line at x = a to…

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Q: J 3x ex dx

A: The given integral, ∫3xexdx. We have to solve this integral.

Q: MATCHING LIST Match each pair of vectors with their dot product. v = 6i + 7j and w = -8i + 9j v=3i -…

A: (a) given v=6i+7j and w=-8i+9j

Q: What is the compound interest if $110,000 is invested for 6 years at 8% compounded continuously. If…

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Q: Given one form a line, match it with its equivalent equation in another form. [x, y, z] [3, 2, 1] +…

A: a. x,y,z=3,2,1+t1,2,3b. x,y,z=-1,0,1+t0,1,0c. x,y,z=1,2,3+t3,2,1d. x=0y=1z=te.x=-ty=1z=1+t

Q: 1 cotx ln sinx|dx x In [ x Ja 2 1 2

A: To find, ∫ cotx2lnsinx2dx Let I=∫ cotx2lnsinx2dx We know that cot(x2) = cos(x2)sin(x2). Therefore…

Q: Question 2 Match each trigonometric function with the quadrant where it is positive. sine cosine…

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Q: 4. Graph f(x)=-2log, (x-5)+3 Show your work.Write Domain and range.

A: According to  question,given function,fx= -2 log3x-5+3

Q: A bucket begins holding 15 kgs of sand. The bucket is to be lifted to the top of a 20 meter tall…

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Q: -5 y 30 20 10 f 5 (5,2) 10 15 20 X

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Q: -5x-2y 2x + y x 2z = -2) = 5 +z = 5 =

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Q: 6. Write out the series and find the sum: Σ= 2(k − 1)(2k – 1)

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Q: For the sequence an = its first term is -18 its second term is its third term is its fourth term is…

A: an = (-1)n18/n2

Q: 2^32cos2x is not a correct solution for the equation submitted

A: We will find first few derivative directly and then use that pattern to find solution.

Q: Find the equation of the plane determined by the intersecting lines: (x-2)/3=(y+5)/-2=(z+1)/4 and…

A: We have to find the equation of plane determined by the intersection lines.

Q: 1a Differentiate the following functions with respect to t and simplify your answer as far as…

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Q: What is the product of 5 and 1.0\sqrt(72) in simplest radical form? Please explain, correct answer…

A: 172 = 136*2           = 1(36)*2          =  162 now we rationalize it         = 162* 22         =…

Q: 1. convergent (a) Determine whether each integral is convergent or divergent. Evaluate those are (b)…

A: ∫0∞e5-2xdx

Q: 3 Given that y = ³x solves -2xy"+(6x+2)y-6y=0, find the second solution of the above differential…

A: -2xy''+6x+2y'-6y=0

Q: Let f(x, y) = x+y+xy. d First, find g(x, y) = f(x,y). Then, calculate g(2, 3). (Enter the exact…

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Q: In three-space, find the intersection point of the two lines: [x, y, z] = [-2, 3, −3] + t[1, x = 3-t…

A: We have given that Two lines  [x, y, z] =[-2,3,-3]+t[1,-1, 2]  ----(1) and   x=3-t y=-5+ 2t…

Q: olve the problem. Suppose that g is continuous and that g(x) dx. A) 6 B) 26 -26 g(x) dx-10 and Lås…

A: g(x) = is contionus function

Q: Given the function f and the point Q, find all points P on the graph of f such that the line tangent…

A: Given : f(x)=1x+2 ; Q(2,-2)   To find : All points P such that the line is tangent to f & passes…

Q: Kelly and Stuart bought potato chips for a party at the same store. Kelly spent $14.15 for 3 large…

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Q: Use cylindrical shells to find the volume of the solid obtained by rotating the region bounded on…

A: The volume of the solid obtained by revolving the region bounded on the right by the graph of g(y)…

Q: Sketch a graph of the function f(x) = 3sin x. Please state the range.

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Q: Find the future value if $15,000 is invested for 7 years at 10% compounded continuously. If needed,…

A: Find the future value if $15,000 is invested for 7 years at 10% compounded continuously. If needed,…

Q: 15, Suppose a company has fixed costs of $1200 and variable costs per unit of 16x + 1620 dollars,…

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Q: f(3) = lim f(x)= x-3 f(5) lim f(x)= x-5 lim f(x)= lim f(x)= x-3° lim f(x) = x-5 lim f(x)= 1-5 M lim…

A: When function continuous at x=1⇒limx→afx=faOR⇒limx→a-fx=limx→a+fx=fx

Q: The Candy Factory sells candy by the pound, charging $1.60 per pound for quantities up to and…

A: Given, px = 1.60x for  x ≤ 301.30x+k  for  x > 30  We have to find the value of  k such that…

Q: The region R in the first quadrant is bounded by the coordinate axes, the curve y=e -5x The (exact)…

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Q: Loan Duration 1 day 14 days 30 days Interest Owed $2.72 $37.88 $75.26 (a) Using the interest owed on…

A: Pri copal Amount P =$500 Loan duration t = 1 day Interest I = $2.72

Q: IV. Use the properties of the dot product to evaluate the expression, assuming that u v = 2, ||u|| =…

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Q: A line has slope -3 and y-intercept 5. Find a vector equation of the line. OA) [x, y] = [5, 0] +…

A: A  line has slope -3 and y-intercept 5. To find the vector equation of the line.

Q: How many petals does the graph of the rose curve r=4sin(3θ) have? Enter your answer in the box

A: For the function, r=asinnθ    or    r=acosnθ If n is odd then there are n number of petals. If n is…

Q: PART III: Solve the following problems. 2. The sum of two positive numbers is 2. Find the smallest…

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Q: 5. Evaluate 3x 4e³x -dx 3x e³x +1 S-

A: given integration ∫ 4e3xe3x+1dx

Q: A bucket is filled with sand so that the total mass (sand and bucket) is 20 kgs. The bucket is to be…

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Q: S x cos(x) dx?

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Q: Evaluate the integral. TT/2 [*¹²7 cos²(0) do de

A: NOTE: Refresh your page if you can't see any equations. . use the formula: cos2x=1+cos2x2

Q: Solve for the unknown quantities, if possible, in Exer- cises 5-16. 5. (1, 2) + (0, y) = (1, 3)

A: Note:- Since you asked multiple questions, according to our policy we can solve only first question…

Q: If you want to earn 15% annual simple interest on an investment, how much should you pay for a note…

A: It is given that the annual simple interest on the investment is 15%.  also the amount after 3…