**Answer:**

a) 27 m/s

b) 30 m/s

c) i) 3

ii) Deceleration

**Step-by-step explanation:**

The question is not complete, the correct question is given as:

The graph shows information about the speed of a vehicle during the final 50 seconds of a journey. At the start of the 50 seconds the speed is k metres per second. The distance travelled during the 50 seconds is 1.35 kilometres.

(a) Work out the average speed of the vehicle during the 50 seconds

(b) Work out the value of k.

(c) (i) Calculate the gradient of the graph in the final 10 seconds of the journey

(ii) Describe what this gradient represents

**Answer:**

The graph is attached. The total time = 50 seconds, total distance = 1.35 km = 1350 m

a) The average speed is the ratio of the total distance traveled to the total time taken to cover this distance. The average speed is given by the formula:

b) From the graph, the total distance covered is the area of the graph. The graph is made up of a rectangle and triangle, the area of the graph is equal to the sum of area of rectangle and area of triangle.

c) i) The gradient in the last 10 seconds is the ratio of change in speed to change in time

ii) Since the gradient is negative it means it is deceleration. That is in the in the last 10 seconds the vehicle decelerates at a rate of 3 m/s²

**Answer: 13 minutes**

**Step-by-step explanation:**

( 0 + 2 + 10 + 8 + 20 + 12 + 30 + 7 + 40 + 1)/10 = 130/10 = 13

Hope this helps!

**Answer:**

1

+

sec

2

(

x

)

sin

2

(

x

)

=

sec

2

(

x

)

Start on the left side.

1

+

sec

2

(

x

)

sin

2

(

x

)

Convert to sines and cosines.

Tap for more steps...

1

+

1

cos

2

(

x

)

sin

2

(

x

)

Write

sin

2

(

x

)

as a fraction with denominator

1

.

1

+

1

cos

2

(

x

)

⋅

sin

2

(

x

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1

Combine.

1

+

1

sin

2

(

x

)

cos

2

(

x

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⋅

1

Multiply

sin

(

x

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2

by

1

.

1

+

sin

2

(

x

)

cos

2

(

x

)

⋅

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Multiply

cos

(

x

)

2

by

1

.

1

+

sin

2

(

x

)

cos

2

(

x

)

Apply Pythagorean identity in reverse.

1

+

1

−

cos

2

(

x

)

cos

2

(

x

)

Simplify.

Tap for more steps...

1

cos

2

(

x

)

Now consider the right side of the equation.

sec

2

(

x

)

Convert to sines and cosines.

Tap for more steps...

1

2

cos

2

(

x

)

One to any power is one.

1

cos

2

(

x

)

Because the two sides have been shown to be equivalent, the equation is an identity.

1

+

sec

2

(

x

)

sin

2

(

x

)

=

sec

2

(

x

)

is an identity

**Step-by-step explanation:**