In the first half of the journey a bus travelled with an average speed of 20 km/hr. If the given average speed for the complete trip made by the bus is 24 km/hr, then calculate the average speed covered by the bus in the second half of the trip.

In the given figure ABCD is a rectangle. It consists of a circle and two semi circles each of which are of radius 5 cm. Find the area of the shaded region. Give your answer correct to three significant figures.

Find the missing values

The diameters of the two circular ends of the bucket are 44 cm and 24 cm. The height of the bucket is 35 cm. Find the capacity of the bucket.

The front row of an auditorium has 10 seats. There are 50 rows in total. If each row has 2 more seats than the row before it, which expression gives the total number of seats in the last row?

Find the missing values

The table above shows selected values for the function h . In the x y -plane, the graph of y = h(x) h is a line. What is the value of (8) ?

Note:
After finding the equation y = 2x + 3 , we can verify it by putting the third point in the equation and check if it lies on the line, that is, the third point which is $left parenthesis 4 comma 11 right parenthesis$ lies on $y equals h left parenthesis x right parenthesis$
$11 equals 2.4 plus 3$
So, the equation $h left parenthesis x right parenthesis equals 2 x plus 3$ is the graph of $y equals h left parenthesis x right parenthesis$ .

The table above shows selected values for the function h . In the x y -plane, the graph of y = h(x) h is a line. What is the value of (8) ?

A man reaches a spot from his home in 6 hrs by walking, but he can reach the same spot from his home within 2 hrs by cycle. If the given average cycling speed is 7km/hr faster than his average walking speed, then find the average cycling and walking speeds.

Find the area of the following figure:

Given a rectangular room whose width is 4/7 of its length y and perimeter z. Write down an equation connecting y and z. Calculate the length of the rectangular room when the given perimeter is 4400 cm.

A drainage tile is a cylindrical shell 21 cm long. The inside and outside diameters are 4.5 cm and 5.1 cm respectively. What is the volume of the clay required for the tile?

Find the area of the given figure.

Four years back in time, a father was 3 times as old as his son then was. 8 years later father will be 2 times as old as his son will then be. Find the ages of son and father.

A number which is formed by two digits is 3 times the sum of the digits. While interchanging the digits it is 45 more than the actual number. Find the number.

The gas mileage M (s), in miles per gallon, of a car traveling s miles per hour is modeled by the function below, where $20 less or equal than s less or equal than 75$ .
$M left parenthesis s right parenthesis equals negative 1 over 24 s squared plus 4 s minus 50$
According to the model, at what speed, in miles per hour, does the car obtain its greatest gas mileage?

Note:
We could have also used the first derivative test to find the local
maxima. We need to find critical points and then check whether the
function is increasing or decreasing on either side of the critical
point. If the function is increasing , i. e $M to the power of straight prime left parenthesis S right parenthesis greater than 0$ ., on the left side
and the function is decreasing, i. e $M to the power of straight prime left parenthesis s right parenthesis less than 0$ ., on the right hand side, then we say that is a local maxima.

The gas mileage M (s), in miles per gallon, of a car traveling s miles per hour is modeled by the function below, where $20 less or equal than s less or equal than 75$ .
$M left parenthesis s right parenthesis equals negative 1 over 24 s squared plus 4 s minus 50$
According to the model, at what speed, in miles per hour, does the car obtain its greatest gas mileage?