Quadratic Function
What is f(x)= -2(x - 3)(x + 4) in standard form and the y-intercept for this quadratic function?
f(x)= -2x2 - 2x +24; y-intercept = 24.
The angle of elevation to the sun is 65 degrees. A building casts a shadow that is 16 metres long. What is the height of the building, to the nearest metre?
The height of the building is 34 metres.
The value of d in y = sin(x - d) refers to...
Phase Shift
What is [(-2)3]2 simplified, in exponential form?
(-2)6
The simple interest earned on $1000 invested at 5.2% per year for 2 years is...
$104.
What is 3a2 + 21a + 36 fully factored?
3(a + 4)(a + 3)
A laser light, placed 16 m from the base of a wall, shines at a point on the wall that is 7 m up from the ground. At what angle of inclination should the light be set? Round to the nearest tenth of a degree.
The lights angle of inclination should be set at 23.6 degrees.
Which of these angles are not coterminal with 150 degree, 510 degree, 870 degree, 1230 degree, or 330 degree?
330 degree is not coterminal with 150 degree.
An antique automobile was found to double in value every 10 years. If the current value is $100 000, what was the value of the vehicles 20 years ago?
The value of the vehicle 20 years ago was $25 000.
The length of time required for $1000 to double at 6% annual interest, compounded monthly, is approximately...
12 years.
What is f(x) = 2x2 - 9x - 18 in factored form and the x-intercept for this quadratic function?
f(x) = (x - 6)(2x + 3); x = -3/2, x = 6
A communication tower is fixed to the top of a building. From a point 10 m from the base of the building, the angle of elevation to the top of the building is 60 degrees, and the top of tower is 68 degrees. What is the height of the communication tower, to the nearest tenth of a metre?
The height of the communication tower is 7.4 m.
What is the equation for this sine function: amplitude = 1/2, reflected in the x-axis?
The equation is f(x) = -1/2 sin x
A cubical tank at an aquarium has a capacity of 64m3. How long are its sides?
The sides of the tank are 4m.
Harry and Ginny just had a baby. They want to invest in the baby's post-secondary education. Assuming an average annual rate of return of 8% with interest compounded semi-annually, how much would they need to invest when the baby was born in order to have $25 000 when the child turns 19? Round answer to the nearest hundred dollars.
Common ratio = 1.015; exponential growth.
A rock is thrown from the top of a cliff on an uncharted planet. The height of a rock above the planet's surface as a quadratic function of time is given by h(t)= -2t2 +12t +32, where t is the time, in seconds, and h(t) is the height of the rock, in metres. Find the zeros of the function and explain their significance.
The rock will land at the bottom of the cliff is t= 8 seconds.
An airplane is 50 km from a tracking station. A second airplane is 70 km away. The angle formed by the airplanes at the tracking station is 47 degree. What is the distance between the two airplanes, to the nearest kilometre?
The distance between the two airplanes is 51 km.
A toy tractor wheel has a radius of 1 cm and rotates counterclockwise. A stone is embedded in the wheel at the rightmost point. Assume that f(x)= sin x describes the height of the stone relative to the center of the wheel based on the angle x. How would the sine graph change if the wheel is 2 cm in radius?
The sine graph would change to f(x) = 2 sin x.
The population growth rate of the Golden Horseshoe area around Lake Ontario is among the fastest in Canada, an estimate of 1.84% per year. The population of the area according to 2001 census was 11.5 million. What is its estimated population for 2011?
The estimated population for 2011 was 13.8 million.
Arthur gave Gwaine $500 for his trip to Montreal. Gwaine offers to pay Arthur $500 in 6 months. One month from the trip, Gwaine gives Arthur $450 saying that he could invest the $450 at 5.5% per year, compounded monthly, which would make up the difference. Is Gwaine correct, what should Arthur consider before agreeing.
Gwaine is incorrect, because the future value of $450 in 5 months at 5.5% compounded monthly is $460.41, resulting in almost $40 of lost income.
An arrow is fired from a raised platform. Its height as a function of time is given by h(t)= -5t2 + 10t + 40, where t is the time in seconds, and h(t) is the height, in metres. Find the length of the time the arrow is in the air.
The length of the arrow is in the air is 4 seconds.
A triangle piece of wood is to be cut with the side lengths of 5 cm, 6 cm, and 7 cm. What angle measurements does the carpenter need to draw? Round answer to the nearest tenth of a degree.
The angle measurements the carpenter needs to draw are 44.4 degrees, 78.5 degrees, 57.1 degrees.
A crank handle is used to extend and retract an awning. The radius of the crank handle is 1 unit and the direction it rotates is counterclockwise starting from a horizontal position. What is the height of the handle after is rotates 60 degrees? Round to the nearest tenth of a unit.
The height of the handle after is rotates 60 degrees is 0.9 units.
Genevieve grew a colony of bacteria as a science project. On Monday morning, she found that the bacteria covered an area of 100 cm2 on the nutrient gelatin. Ten hours later, she found that the area had increased to 200cm. Assume the growth is exponential, what is a function that models the growth?
After 10 days the mass will be 10g, after 20 days the mass will be 5g, and after 30 days the mass will be 2.5g.
Tony wants to have $4000 in 5 years. How much does he need to invest now at 3.8% annual interest, compounded semi-annually? Round your answer to the nearest dollar.
Tony needs to invest $3313.74 to have $4000 in 5 years.