Trigonometry
Nimo has constructed a deck in the shape of an equilateral triangle with each side length equal to 2 m. If she enlarges her deck to a similar shape whose side lengths are doubled, what will the area of the new deck be?
6.92
The area of a rectangle is represented by the equation A = 6x^2 + 5x − 4.
a) Factor the right side of the equation fully to find expressions for the length and width of the rectangle.
b) Find an expression for the perimeter.
c) If x represents 7 cm, find the area and the perimeter of the rectangle
a) l=2x -1 & w=3x+4
b) P =10x+6
c) A=325cm^2 & P=76cm
Explain how to determine the value(s) of k that would make
x^2 + kx + 100
a perfect square trinomial.
+20 or -20
Petr has $5000 invested in two plans. One plan pays 5% simple interest per year and the other pays 8%.
At the end of the year, Petr receives a total of $340 in interest. How much did he invest in each plan?
$2000 at 5% and $3000 at 8%
From a point on the ground 47 feet from the foot of a tree, the angle of elevation of the top of the tree is 35º. Find the height of the tree to the nearest foot.
33 feet
If part of a photograph is used to fill an available space in a book or magazine, the photograph is said to be cropped.
A photograph that was originally 15 cm by 10 cm is cropped by removing the same width from the top and the left side.
Cropping reduces the area of the photograph by 46 cm2. What are the dimensions of the cropped photograph?
13 x 8 cm
A stone is thrown straight down off a cliff.
The relation h = 150 − 5t − 5t^2 approximates its path, with h in metres and t in seconds.
a) How tall is the cliff?
b) Factor the right side of the equation fully.
c) When does the stone hit the ground
a) 150m
b) -5(t+6)(t-5)
c) 5s
White vinegar is a solution of acetic acid in water. There are two strengths of white vinegar— a 5% solution and a 10% solution. How many millilitres of each solution must be mixed to make 50 mL of a 9% vinegar solution?
10ml of 5% and 40ml of 10%
The Carziz Tunnel cuts through Mount Mainet.
At the start of the tunnel, the angle of elevation of the top of Mount Mainet is 38°. At the end of the tunnel, the angle of elevation of the top of Mount Mainet is 42°. The height of Mount Mainet above the tunnel passage is 584 m.
How long is the Carziz tunnel through Mount Mainet? Round your answer to the nearest metre.
1396 m
A rectangular prism has a volume of
V = 4x^3 + 12x^2 + 9x.
Determine algebraic expressions for the dimensions of the prism.
Determine the volume if x = 3 cm.
Determine the surface area if x = 3 cm
V=243cm^3
SA=270cm^2
The path of a jet plane in training manoeuvres is given by the relation
h = −5(t + 20)(t − 100),
where h represents the height, in metres, above the ground and t is time, in seconds.
What is the maximum height? At what time does the plane reach its maximum height?
After 40s it is 18000m in the air
Lawrence is 12 years older than Patrick. Last year, he was twice as old as Patrick.
How old is each person now?
Patrick is 12 and Larry is 24
Three trees are in the yard at the back of Aly’s house. The oak tree is 10 m from the ash tree and 15 m from the maple tree. The line from the oak tree to the ash tree and the line from the ash tree to the maple tree form an angle of 78°. How far apart are the ash tree and the maple tree? Round your answer to the nearest tenth of a metre.
13.4 m
Need-a-Ride is a car rental agency that rents 400 cars a week at $80 per car. Industry research has shown that for every $2 increase in rental price, an agency will rent eight fewer cars.
a) Total revenue is the product of the price per rental and the number of vehicles rented. Write an expression to represent the revenue for the rental agency.
b) Find the maximum revenue.
c) For this revenue, how many cars are rented and how much is the rental price per car?
a) R=(400-8x)(80+2x)
b) $32400
c) 360 cars at $90
The path of a basketball can be modelled by the equation h = −0.06d^2 + 0.6d + 3, where h represents the height, in metres, of the ball above the ground and d represents the horizontal distance, in metres, that the ball travels.
a) What is the maximum height reached by the ball?
b) What horizontal distance has the ball travelled when it reaches this maximum height?
4.5 m
5 m
A container has 30 bolts in it and has a mass of 635 g.
When an additional 15 bolts are placed in the container, the mass is 935 g.
Find the mass of a bolt and the mass of the container.
Bolt is 20g and the container is 35g
Two drivers leave home and travel on straight roads that diverge at 70 degrees.
If one driver travels at an average speed of 83.0 km/h and the other travels at an average speed of 95.0 km/h, how far apart will they be after 45 min?
76.9 km
If the product of two consecutive even numbers is 8648, what are the two numbers?
92, 94 AND -92,-94
Susan throws a rock off a cliff that is 210 m tall. The height, h, in metres, of the rock above the ground can be related to the time, t, in seconds by the equation h = −5t^2 + 10t + 210.
What is the maximum height of the rock? When does it reach its maximum height?
1 second, 215m
The difference between two numbers is 22.
Twice the smaller number exceeds the larger number by 17.
What are the two numbers?