Learn more about our help with Assignments: Math
Search & Filtering
The depth (D metres) of water in a harbour at a time (t hours) after midnight on a particular day can be modelled by the function
D = 2 times sin times ( 0.51 times t minus 0.4 ) + 5 , em space times t less-than-or-equal 15 ,
where radians have been used.
Select the two options which are correct statements about the predictions based on this model.
Select one or more:
The largest depth is 7 metres.
At midnight the depth is approximately 4.2 metres.
The depth of water in the harbour falls after midnight.
The model can be used to predict the tide for up to 15 days.
The time between the two high tides is exactly 12 hours.
At midday the depth is approximately 7 metres.
The smallest depth is 5 metres.
D = 2 times sin times ( 0.51 times t minus 0.4 ) + 5 , em space times t less-than-or-equal 15 ,
where radians have been used.
Select the two options which are correct statements about the predictions based on this model.
Select one or more:
The largest depth is 7 metres.
At midnight the depth is approximately 4.2 metres.
The depth of water in the harbour falls after midnight.
The model can be used to predict the tide for up to 15 days.
The time between the two high tides is exactly 12 hours.
At midday the depth is approximately 7 metres.
The smallest depth is 5 metres.
In a supermarket cans of beans are on display. There is one can in the front row, 2 in the second, 3 in the
third, 4 in the forth and so on.
(a) Find how many rows are needed to have at least 24 cans in total on display.
(b) Show that there are no more than 12 cans in the first 4 rows.
third, 4 in the forth and so on.
(a) Find how many rows are needed to have at least 24 cans in total on display.
(b) Show that there are no more than 12 cans in the first 4 rows.
56 people go to a party. 24 take food, 12 take drink and 8 take both food and drink. Find the probability of
someone from the party going without food or drink.
someone from the party going without food or drink.
) Bob has 4 different coins in his pocket. They add to 28p. He takes two coins out of his pocket and puts one
different coin in. What is the maximum amount he can now have in his pocket?
different coin in. What is the maximum amount he can now have in his pocket?
) Given 2p – 3q = 10, write an expression for the number (a) 100 (b) 30 and (c) -10
The nth derivative of the function t(x) where t(x)=5x^6 - 9x^5 +3x^3 - 0.5 is a cubic function.
(a)State the value of n.
(b)Find the ratio of coefficient in x^3 to the coefficient in x^2 of the cubic function giving your answer in the form 1:k(1 is to k)where k is a fraction in its simplest form.
(a)State the value of n.
(b)Find the ratio of coefficient in x^3 to the coefficient in x^2 of the cubic function giving your answer in the form 1:k(1 is to k)where k is a fraction in its simplest form.
A cube is cut into 216 identical smaller cubes. In how many different ways can the smaller cubes be arranged to form cuboids of different surface areas if no two cubes are to be placed one above another?
(1) 6
(2) 8
(3) 14
(4) 16
(1) 6
(2) 8
(3) 14
(4) 16
The position vectors of the points A and B are (1,5,3) and (3,6,6). Find the vector equation of the line AB and the points where the line intersects the coordinate planes.
For the three vectors a=(1,1,1), b=(5,2,-6) and c=(3,-7,5) show that a∙b=a∙c and interpret the results.
A ship travels 84 km on a bearing of 17°, and then travels on a bearing of 107° for 135 km. Find the distance of the end of the trip from the starting point, to the nearest kilometer
