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Find in terms of w, a and b, the magnitude of the reaction at the hinge. Find also the tangent this reaction makes with the horizontal.
Determine the value of sin2x given that tan^2x=81/49 and Pi<x<3pi/2
The population of mice in Canterbury High School fluctuates from a minimum of 80 mice to a maximum of 420 mice. This population can be modelled as a function of time in months from Jan. 1st, by a cosine function. At the beginning of the year (January 1st), the population is at its least (80 mice) . After 3 months the population reaches its maximum (April 1st). On Canada Day (July 1st) the population goes back down to its minimum of 80. Three months later it reaches the maximum again (Oct. 1st). (And so on.)
(a) Draw a detailed graph of this situation for 1 year.
(b) Determine the equation of this function as a cosine function and a sine function that
describes the population of the mice in CAnterbury High School.
(c) Determine the time in months (to 1 decimal place) for one year, when the population is
above 165 mice.
find the domain of the indicated functions.express answers in both interval notation and inequality notation.
f (x)=4-9x+3x2
translate each algebraic definition of the following function into a verbal definition.
f (x)=2x2+5
g (x)=-2x+7
M (x)=5t-2
solve the following equation for 0«x«360
a) 6 cos²x + sin x - 4
b) 9 tan x + tan²x + 5 sec² x - 3
given sin α = 3/5 and cos β = -4/5 , α is an acute angle and β is an obtuse angle find ;
a) cot α + cosec β
b) sin 2α tan 2β
A poster is to have an area of 180 in with 1-inch margins at the bottom and sides and a 2-inch margin at the top. What dimensions will give the largest printed area?
A plane flying with a constant speed of 300 km/h passes over a ground radar station at an altitude of 1 km and climbs at an angle of 300. At what rate is the distance from the plane to the radar station increasing a minute later?
A cone of radius 2 cm and height 5 cm is lowered point first into a tall cylinder of radius 7 cm that is partially filled with water. Determine how fast the depth of the water is changing at the moment when the cone is completely submerged if the cone is moving with a speed of 3 cm/s at that moment.
