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A plane flying with a constant speed of 240 km/h passes over a ground radar station at an altitude of 1 km and climbs at an angle of 30°. At what rate is the distance from the plane to the radar station increasing a minute later?
Let L:R^n -->R^n be a linear operator on R^n. suppose that L(x) = 0 for some x does not equal 0. Let A be the matrix representing L with respect to standard basis. Show that matrix A is singular.
Automorphism of a Group, Let G be a group, T an automorphism of G, N a normal subgroup of G. Prove that (N)T is a normal subgroup of G.
A conducting loop in the shape of a square of edge length 12cm carries a current of 15A. A) calculate the magnitude and direction of the magnetic field at the center of the loop. B) Calculate the magnetic field at the center if the same wire is fo..
The dimensions of a closed rectangular box are measured as 73 cm, 67 cm, and 48 cm, respectively, with a possible error of 0.2 cm in each dimension. Use differentials to estimate the maximum error in calculating the surface area of the box.
Investigate puzzle and explain the solution to the paradox using mathematical reasoning.
One of the best candidates for a black hole is found in the binary system called A0620-0090. The two objects in the binary system are an orange star, V616 Monocerotis, and a compact object believed to be a black hole.
The graph of a quadratic function (a parabola) has x-intercepts -1 and 3 and a range consisting of numbers less than or equal to 4. Determine an expression for the function.
A company makes two soft drinks A and B. Each liter of A requires 4 hours processing and 4 hours distillation while each liter of B requires 5 hours processing and 3 hours distillation.
a plane flies 435 miles with the wind and 375 against the wind in the same length of time. if the speed of the wind is 10 mph. find the speed of the plane in still air?
Bella requires $80,000 in four years to purchase a new home. What amount must be invested today in an investment that earns 6% interest, compounded annually.
Out of 5000 policies for cell phones, a company received 585 claims. The average amount paid on the claims was $80. If the annual cost of the policy was $48, what was a customer's expected value of the cell phone insurance policy?
Describe the two methods to simplify a complex fraction. Which of the two methods for simplifying a complex fraction is simpler? Explain your reasoning.
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