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MArishka [77]
2 years ago
5

A ball is hit vertically upwards from a cliff, which is 80 m above the sea. The displacement

Mathematics
1 answer:
Stels [109]2 years ago
6 0

Answer:

a) 8 seconds

b) 3 seconds

c) 170 meters

Step-by-step explanation:

a) When the ball lands in the sea, s = -80.

-80 = 30t − 5t²

5t² − 30t − 80 = 0

t² − 6t − 16 = 0

(t + 2) (t − 8) = 0

t = -2 or 8

t = 8 seconds

b) The ball reaches its highest point when the velocity is 0 (or at the vertex of the parabola).

t = -b / (2a)

t = -30 / (2 × -5)

t = 3 seconds

c) The highest point is:

s = 30(3) − 5(3)²

s = 45

So the ball rises 45 meters, falls 45 meters, then falls 80 meters.

The total distance traveled is 45 + 45 + 80 = 170 meters.

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Find all the zeroes of the equation. x4 – 6x2 – 7x – 6 = 0
NeX [460]

Answer:

-2, 3,  -0.5 + 0.866i,   -0.5 - 0.866i.

Step-by-step explanation:

As the last term is -6 , +/- 2 , +/- 3 are possible zeroes.

Try 2:-

(2)^4 - 6(2)^2 - 7(2) - 6 = -28 so  2 is not a zero.

3:-

(3)^4 - 6(3)^2 - 7(3) - 6 = 0 so 3 is a zero.

(-2)^4 - 6(-2)^2 - 7(-2) - 6 =  0 so -2 is also a zero.

Divide the function by (x +2)(x - 3),  that is  x^2 - x - 6

gives  x^2 + x + 1

x^2 + x + 1

So we have x^2 + x + 1 = 0

x =  [-1 +/- √(1^1 - 4*1*1)] / 2

= -1 + √(-3) / 2 , - 1 - √(-3)  / 2.

= -0.5 + 0.866i, -0.5 - 0.866i

7 0
2 years ago
joanna went school supply shopping she spent $35.98 on notebooks and pencils notebooks cost $2.30 each and pencils cost $1.42 ea
Mumz [18]

Joanna bought 7 notebooks and 14 pencils

Step-by-step explanation:

Step 1 :

Let x denote the number of notebooks and y denote the number of pencils Joanna bought.

Cost of one notebook = $ 2.30

Cost of one pencil = $1.42

Step 2 :

Total of notebooks and pencils bought  = 21

=> x + y = 21 => y = 21-x

Total cost of notebooks and pencils = $35.98

=> 2.3x + 1.42y = 35.98

Substituting y = 21- x here , we have,

2.3x + 1.42 ( 21-x) = 35.98

2.3x + 29.82 - 1.42x = 35.98

0.88 x = 6.16

=> x = 7

y = 21-x = 21-7 = 14

Step 3 :

Answer :

Joanna bought 7 notebooks and 14 pencils

6 0
3 years ago
The lighthouse was moved 230 feet inland at a rate of 40 feet per hour. How many hours did it take to move the lighthouse? What
Aleks04 [339]

Answer:

5.75

Step-by-step explanation:

4) 230 ÷ 40 = 5.75

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