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3 years ago

A rock is thrown upward with a velocity of

Mathematics

1 answer:

Amanda [17]3 years ago

3 0

Answer:

5.76 seconds

Step-by-step explanation:

We are given;

Position of rock from ground level; h(t) = 9 m

Height of cliff;h_0 = 45 m

Velocity;v_0 = 22 m/s

To solve for the time, we will use the gravity formula which is;

h(t) = (-1/2)gt² + (v_0)t + h_0

Plugging in the relevant values to get;

9 = (-1/2)(9.81)t² + 22t + 45

Subtract 9 from both sides to get;

-4.905t² + 22t + 45 - 9 = 0

-4.905t² + 22t + 36 = 0

Finding the roots of the equation through quadratic formula gives;

t = 5.76 or -1.27

t cannot be negative, so we will use the positive value to get;

t = 5.76 s

Thus, the rock will be 9m from the ground level after 5.76 seconds

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There is a bag filled with 4 blue and 5 red marbles. A marble is taken at random fròm the bag,the colour is noted and then is re

atroni [7]

Hi there!

Answer:

1/6

Explanation:

The first probability of getting blue is 4 out of the total marbles so 4/9.

The second time there are only 3 blue marbles out of 8 now so 3/8.

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which equals 12/72 or 1/6

Hope this helps!

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3 years ago

The square has a radius of 3 square root 2 what is the apothem?

Mrrafil [7]

The diagram of the square is shown in the first picture below

We have the radius $3 \sqrt{2}$ and the triangle formed is an isosceles triangle

We can start by finding out the length of one side of the square. A square has four sides of equal length and the length of the diagonal is twice the length of the radius. So, by using the Pythagoras theorem we have

$(2r)^{2} = a^{2}+ a^{2}$
$4 r^{2} =2 a^{2}$ , substitute $r=3 \sqrt{2}$
$4 (3 \sqrt{2}) ^{2} = 2 a^{2}$
$4(18) = 2 a^{2}$
$72=2 a^{2}$
$a^{2}= \frac{72}{2}$
$a^{2}=36$
$a=6$

Then we'll use Pythagoras theorem again to find the length of the Apothem

We need to halve the length of one side of the square to obtain the other short side of the right angle triangle, so 6÷2 =3

apothem² = (3√2)² + 3²
apothem² = 18+9
apothem² = 27
apothem = √27 = 3√3

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3 years ago

Let v=-3i and w=2 - 4i. Find v*w

Mice21 [21]

Answer:

v×w = -6i-12

Step-by-step explanation:

hello :

Let v=-3i and w=2 - 4i.

v×w = -3i(2-4i) = -6i+12i² = -6i-12 ... i² = -1

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icang [17]

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4 years ago