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Solve the inequalities. Give your answer in interval notation, and indicate the answer
geometrically on the real-number line.
a. t + 6 ≤ 2 + 3t
b. 3(2 – 3x) > 4(1 – 4x)
In the following problems, perform the operations and simplify as much as possible.
a. (x2 + 2x)/(3x2 – 18x + 24) ÷ (x2 – x – 6)/(x
2 – 4x + 4)
b. (x2 + 6x + 9)/x/(x + 3)
c. 1/(3x – 1) + x/(x2 – 9)
Let the function f : R → R and g : R → R be defined by f(x) 2x + 3 and g(x) = -3x + 5.
a. Show that f is one-to-one and onto.
b. Show that g is one-to-one and onto.
c. Determine the composition function g o f
d. Determine the inverse functions f -1 and g -1 .
e. Determine the inverse function (g o f) -1 of g o f and the composite f -1 o g -1 .
A ship is 20km west of another ship B. If a sails at 10km/hr. and at the same time B sails north 30km/hr. Find the rate of change of distance between them at the end of half hour.
What happens to the mass of water in a
pot when it cools, assuming no
molecules escape or are added? Is this
observable in practice? Explain.
Use three functionsto perform the following tasks:
modify should modifythe values of fnum and snum as stated.
-Modify the contents by multiplying the original values by 10. The function
-Display the new value to the user. The function displayshould print to the
local variables fnumand snum.
-Accept two integers from user. A functioncaptureshould do this using its
user the new values of fnum and snum variables
Determine the effective capacitance if two capacitors, C1 = 10F and C2 = 5F, are
connected in parallel.
Determine the effective capacitance if two capacitors, C1 = 10F and C2 = 5F, are
connected in series.
How far must a 1.00x10-7C test charge (q) be from a 5.00x10-6C point
charge (Q) for it to experience a push of about 1.25 N?
An electric field with a strength of 1.25x104N/C exerted 2.50 N on a
certain test charge, q. Determine the charge on q.
#339914 on Dec 2023