Trigonometry & Vectors
Dylan and Lucas are standing 50m apart looking at a blimp. Dylan's angle of elevation is 58°, Lucas' is 41°. How far are they from the blimp?
Dylan is 33.6m from the blimp and Lucas is 42.8m from the blimp.
a circle has a radius of 12 in. The central angle of a sector of the circle is 52°. Calculate the area of the sector.y
A = 65.3 in²
On July 26, 1896, an earthquake with magnitude 5.5 hit California, the next day, a second earthquake with magnitude 6.2 hit the same region. how many times as intense as the first earthquake was the second one?
the second earthquake was approximately 5 times as intense as the first
list the end behaviors, leading coefficient, zeroes, y-intercept, degree, and type of polynomial of:
y = x³ - 9x² -9x + 81
EB: Q3 to Q1
LC: positive 1
zeroes: 9, 3, -3
y-int: 81
degree: 3
type: cubic
Write an equation for y = 1.5sin(x-105°)+3 as a cosine function
y = 1.5cos(x-15°)+3
Given angle A = 40°, side a = 22 cm, and side b = 27 determine all possible values for side c in triangle ABC
side c can either be 34.2 cm or 7.1 cm
what is the surface area of the figure below?
(diagram on paper)
SA = 12401.4 mm²
if an 8 hour exposure to 90 dB of sound is considered acceptable, and for every 5 dB increase in loudness, the acceptable exposure is reduced by one half, what is the acceptable exposure to 140 dB?
the acceptable exposure time to 140 dB of sound is 28 seconds
determine the equation of:
A quartic function with zeroes of -3, -1, 1 and 2 and passes through (-2, -12)
y = (x + 3) (x + 1) (x - 1) (x - 2)
list all transformations from y = sin(x) to y= -2sin1/2(x - 30°)-3
reflection in the x axis, vertical stretch by a factor of 2, horizontal stretch by a factor of 2, phase shift right 30°, vertical shift down 3
what is the resultant of two vectors with magnitudes of 5 km and 7 km that act 15° from one another
the resultant is 11.9 km at 9° counter clockwise from the 5km vector
given the figure below, what is the distance from point E to F, from F around the arc to G, and from G to H
(diagram on paper)
The distance is 18.6 km
Ed got sick one day and decided to go to the doctor, Dr. B. Better told him that he had a bacterial infection and put him on penicillin. Ed had 10000 bacteria in his body, and the medication results in a net population decrease of bacteria by 5% per hour.
determine an equation in the form of y = abₓ to represent the number of bacteria, N, after t hours and use that equation to determine the number of bacteria present after 3 days.
N = 10000(1 - 0.05)ₜ
approximately 249 bacteria remain after 3 days
Computer programs are being sold for $25 each, 300 people are willing to buy them at that price, for every $10 increase in price, 30 fewer people are willing to buy the software.
represent the revenue function as a function of the number of $10 increases, draw and the function using a graphing calculator and determine what price range will generate a revenue of $8000 or higher
R(x) = (300 - 30x) (25 + 10x)
(graph on answer sheet)
Price range: $27.30 - $97.70
The height, h, in meters of a basket on a water wheel at time t, in seconds, is given by h(t) = sin(6t)
When will the basket first be 0.5m under water? When will it be at that same height again?
the basket will first be 0.5 m under water after 35 s, and again after 55 s