So since, they are the same distance from zero, they should be the oppposite of each other so in other words, k=-h and h=-k

so k+h=(subisute)k-k=-h+h=0 because they cancel

4 0

3 years ago

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A street light is mounted at the top of a 15-ft-tall pole. A man 6 ft tall walks away from the pole with a speed of 4 ft/s along

mina [271]

Answer:

The tip of the man shadow moves at the rate of $\frac{20}{3} ft.sec$

Step-by-step explanation:

Let's draw a figure that describes the given situation.

Let "x" be the distance between the man and the pole and "y" be distance between the pole and man's shadows tip point.

Here it forms two similar triangles.

Let's find the distance "y" using proportion.

From the figure, we can form a proportion.

$\frac{y - x}{y} = \frac{6}{15}$

Cross multiplying, we get

15(y -x) = 6y

15y - 15x = 6y

15y - 6y = 15x

9y = 15x

y = $\frac{15x}{9\\} y = \frac{5x}{3}$

We need to find rate of change of the shadow. So we need to differentiate y with respect to the time (t).

$\frac{dy}{t} = \frac{5}{3} \frac{dx}{dt}$ ----(1)

We are given $\frac{dx}{dt} = 4 ft/sec$ . Plug in the equation (1), we get

$\frac{dy}{dt} = \frac{5}{3} *4 ft/sect\\= \frac{20}{3} ft/sec$

Here the distance between the man and the pole 45 ft does not need because we asked to find the how fast the shadow of the man moves.

7 0

3 years ago

Tshepo needs R5 000 urgently. He goes to the bank and borrows the money at an interest rate of 28% per annum, compounded monthly

12345 [234]

Answer:

<u>R8000</u>.

Step-by-step explanation:

First, let's calculate the amount they are going to have to pay the bank after 1 year. It is given by the following expression:

R5 000 * 1.28= R6400

Therefore, they have to pay R6400/12 monthly.

Now, in fifteen months the total amount to pay should be (R6400/12) * 15= <u>R8000</u>.

8 0

2 years ago