Calculus question and answers for July 01, 2023
- Q Express the following expression in the form of a + bi: (14+ 5i) - ((2 - 3i) + (4 - 8i)).5+4i8+16i4-2i4+5i
- Q The distance between 3(2+ 4i) and 2(1 + 2i) is4?3 units2?7 units3?5 units4?5 units
- Q Determine the area of the region bounded between the two curves y = x and y = x - 2x from x = -1 to x = 1. Use a...
- Q Find a unit vector that has the same direction as the given vector.-3i + 2j - k
- Q Vector b [Xb, Yb, Zb] has a magnitude of 6 and the same direction as the vector [2, 3, -1]. The value of Yb is:a) 1.60b) 3.20c) 3.74d) 4.81
- Q The scalar equation of the plane passes through (-1, 3, -2), (-1, 2, -1) and (4, 1, -2) is:2x - 5y + 5z + 3 = 02x - 5y5z +...
- Q Let P(E)=0.75, P(F) = 0.37, and P(EUF) = 0.91. Find (a) P(EIF) and (b) P(FIE).(a) P(EIF) =(Type an integer or decimal rounded to two decimal places as needed.)(b) P(FIE)=(Type an...
- Q For the vectors a = (1, 4) and b = (2, 3), find orth ab.orth ab =
- Q Solve using elementary row operations:x - y - 3z = -14x + y + z = 4-x + y + z = 6
- Q Subtract 6 + 2i from 14 + i.8-1i8+1i-8+1i84 + 2i
- Q A card is drawn from a deck of 52 playing cards.a) Find the odds in favor of drawing a face card or a diamond.b) Find the odds against drawing a...
- Q Assume A and B are independent events with P(A) = 0.3 and P(B) = 0.6. Find (a) P(An B), (b) P(A U B), (c) P (An B'), (d) P (A'n...
- Q Which of the following vectors is coplanar to [1, 1, 1] and [1, 2, 3]?a) [1, 4, 8]b) [7, 5, 3]c) [4, 2, -2]d) (5, 7, 6]
- Q Find the vector that has the same direction as (3, 2, -6) but has length 2.
- Q A baseball player's batting average is 0.337, which can be interpreted as the probability that he got a hit each time at bat. Thus, the probability that he did not...
- Q Use vectors to calculate the area of the parallelogram formed by the points A(-1, 1, -1), B(2, -1, 3) and C(5, 3, 4).
- Q Find the acute angle between the lines. Round your answer to the nearest degree.5x - y = 4, 8x + y = 7
- Q The distance between (-3 + 10i) and (-6 + 14i) is ?x. What is the value of x?101525
- Q Find the intersection of the following planes by letting z = t.5x - 4y + z- 1 = 0x - z + 3 = 0
- Q Which of the following is not an equation for the line passing through the points P(1,4,-3) and Q(3,2,1)?a. r = (1,4,-3) + s(2,-2,4), s?Rb. x-3/2 = y-2/-2 = z+1/4c. x...
- Q Three different forces act on an object. They are:F? = <2, -3>F? = <-2, 5>F? = <-8, -5>Find the net force Fnet on the object (the sum of the forces)Fnet...
- Q Sample space S is partitioned into E?, E?, E?, and E? such that P(E?)=0.11, P(E?)=0.02, and P(E?) = 0.38.a. Find P(E?).b. Find the odds in favor of and the odds...
- Q Graph the parabola.y=x +6x+4Plot five points on the parabola: the vertex, two points to the left of the vertex, and two points to the right of the vertex. Then click...
- Q Determine whether the given information results in one triangle, two triangles, or no triangle at all. Solve the triangle(s) that results. Round any side length to two decimal places and...
- Q What is the solution to the system of equations?x - 0.2y = 2-10x + 2y = 4(4,0)(-4/2,0)(0,-2)(0, 2/2)There are no solutions.
- Q Given the vector field F(x, y) = (y, -x) and the counterclockwise oriented unit circleC: {x = ?os?ty = sin?t, compute ?F. dr.t = [0,2]
- Q 4. (28 points) Given the vector field F(x, y) = (ye^xcos e^x, sin e^x), the clockwise oriented part of the ...
- Q James and Abeer took a backpacking trip together. On the first day, they hiked 9 miles to a campsite. The next day, they took a different route back that was...
- Q The Mosteller formula for approximating the surface area S, in square meters (m), of a humanis given by the function below, where h is the person's height in centimeters and...
- Q Resolve the following vectors into components:(a) The vector i in 2-space of length 5 pointing up at an angle of 3/4 measured from the positive x-axis.(b) The vector u in...
- Q You want to be able to withdraw $20,000 each year for 30 years. Your account earns 5% interest.a) How much do you need in your account at the beginning?b) How...
- Q A 30-ft tree casts a shadow horizontally along the ground. A girl standing at the tip of the shadow is looking at a bird nesting at the top of the...
- Q Suppose a river has a current of 2 miles per hour going south. If a swimmer can swimeast at a rate of 4.5 miles per hour, what is the speed...
- Q The graph of f(x)= 3x+1/8x3 will behave like which function for large values of |x|?y= 3/8y= 3x/8y=3/8xy=3/8 x3
- Q Integrate f(x,y,z) = (x+y+z)/(x + y +z) over the path r(t)=ti + 2t j + 3t k, 0<a?t?b.The integral of f is
- Q Compute the curl of the vector field F=-zi+6yj-3xk.curl(F) =
- Q In Littletown, the probability that a baseball team goes to the city playoffs is 0.20. The probability that the team goes to the state playoffs given that the team goes...
- Q Solve the system of equations.2x+3y + 2z = 86x +9y+6z=12x-2y+3z = 4
- Q Given the region R enclosed by y = x and x + (y + 5) = 10.a) Sketch the region R.b) Set up the double integral that represents the area...
- Q What is the area of ?ABC such that b = 26 centimeters, c = 16 centimeters, and m?A = 25?203.013 centimeters189.333 centimeters87.905 centimeters29.647 centimeters
- Q Modular cassettes are often used in long-term care settings for all of the following, except:A. to simplify record keepingB. to minimize wasteC. to decrease chances of medication errorsD. to decrease...
- Q Given that the transformation C: R ? R is the composite of counterclockwise rotation R about the point (-1,3) by 270 followed by a projection P onto the y-axis, use...
- Q The produce manager at a market orders 50 lb of tomatoes, 10 lb of zucchini, and 20 lb of onions from a local farmer one week.a) Write a 1x3 matrix...
- Q Decompose the function y = 2+ into u(v(x)). If we assume v(x) = -x, what is u(x)?
- Q Write the equations in cylindrical coordinates.(a) 3x - 9x + 3y + z = 7(b) z = 6x - 6y
- Q Plot the point whose cylindrical coordinates are given. Then find the rectangular coordinates of the point.(a) (4, ?/2, 3)(x, y, z) = ( )(b) (4, -?/4, -3)(x,y,z) =...
- Q What are the magnitude and direction of w = (-5, -14)? Round your answer to the thousandths place.
- Q Change from rectangular to spherical coordinates. (Lt p ? 0, 0 ? ? ? 2?, and 0 ? ?? ?.)(a) (0, 3, -3)(p, ?, ?) =(b) (-7,7,7?6)(p, ?, ?) =
- Q Solve the system of equations.x-3y - z=-9-x+8y-4z=242x-15y+7z=-45Select the correct choice below and fill in any answer boxes within your choice.A. There is one solution. The solution is ( , ,...
- Q Vector v has an initial point at (8, 8) and a terminal point at (16, 11). Which of the following represents the linear form of v?v=-3i-8jv=3i+ 8jv=-8i-3jv = 8i +...
- Q Given u = -3i+5j and v= -24i + 40j, are u and v parallel or orthogonal? Explain.The vectors are orthogonal because cos ? = 1.The vectors are orthogonal because u...
- Q Determine the measure of angle in standard position, and the diagram:Show all your work to receive full marks.a) Sin = -0.7502, if is in the 3rd quadrantb) Sin = 0.9122,...
- Q Determine the solution set for the equation.(x-6)+(y+9) = -9The solution set is
- Q An object is suspended by two cables attached at a single point. The force applied on one cable has a magnitude of 125 pounds and acts at an angle of...
- Q Consider the system of equationsdx dt = x(1-x 2-y)dy dt = y(1-y 3-x),taking (x, y) > 0.(a) Write an equation for the (non-zero) vertical (x-)nullcline of this system:(Enter your equation,...
- Q The Coffee Counter charges $9 per pound for Kenyan French Roast coffee and $8 per pound for Sumatran coffee.How much of each type should be used to make a 20...
- Q The functions f, g, and h are defined as follows.f(x) = ?11+|6x| g(x) = x 1 +x2 h(x) = ?-2x+15Find f(-3 2), g (-2), and h (3).Simplify your answers as...
- Q Given u = 4i +2j and v = ?7+ 5j, find the dot product u . v.
- Q The point A(-6, 6) is reflected over the point (0,7) and its image is point B. What are the coordinates of point B?
- Q To verify the identity, start with the more complicated side and transform it to look like the other side. Choose the correct transformations and transform the expression at each step.csc...
- Q Use the log properties to rewrite the expression. Simplify as much as possible. Enter the final result without any blank spaces.In ()
- Q Create each of the following during your work: Det A, Det Ax, and Det Ay.4x + y = 5x - ky = 2Complete the ordered pair: (x,y) where
- Q On our moon, the acceleration of gravity is 1.6 m/sec. If a rock is dropped into a crevasse, how fast will it be going just before it hits bottom 45...
- Q Find the inflection points (if any) on the graph of the function and the coordinates of the points on the graph whe function has a local maximum or local minimum...
- Q Explain why the following four statements ask for the same information.(i) Find the roots of f(x) = 3x3 - 3x - 1(ii) Find the x-coordinates of the intersections of the...
- Q At noon, ship A was 12 nautical miles due north of ship B. Ship A was sailing south at 12 knots (nautical miles per hour; a nautical mile is 2000...
- Q One 8-oz serving each of coffee, energy drink, and soda contains 201 mg of caffeine. One serving of coffee has 7 mg more caffeine than two servings of soda. One...
- Q For the real-valued functions g(x)=x + 1 and h(x)=?x-4, find the composition goh and specify its domain using interval notation.
- Q Use mathematical induction to prove that the alternating sum of n numbers isfor odd n andfor even n.1-2+3+.........+n=n+1/21-2+3-..........-n= -n/2
- Q Tutorial ExerciseSolve for x accurate to three decimal places.In(?x + 6) = 3Step 1The given function is In (?x + 6) = 3. Take the natural antilog of each side...
- Q To measure the height of the Eiffel Tower in Paris, a person stands away from the base and measures the angle of elevation to the top of the tower to...
- Q (1 point) Consider the two points (3,-1) and (6, 10). The distance between them is:The x co-ordinate of the midpoint of the line segment that joins them is:The y co-ordinate...
- Q What is the shortest possible length of the line segment that is cut off by the first quadrant and is tangent to the curve y = 5 x at some...
- Q Draw a vector representing the course of a ship that travels6 miles on a course with bearing 225
- Q The figure shows a 800 foot tower on the side of a hill that forms a 8 angle with the horizontal. Find the length of each of the two guy...
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