Melody

Welcome back Aziz, I have missed you as well.  

This is worth a watch.

$$\frac{299}{3\frac{1}{4}}\\\\
=\frac{299}{\frac{13}{4}}\\\\
=299\div \frac{13}{4}}\\\\
=299\times \frac{4}{13}}\\\\
=\frac{299*4}{13}}\\\\
=\frac{23*4}{1}}\\\\
=92$$

$$\\4y^2 + 12x^2 y + 9x^4\\\\
(2y+3x^2)^2$$

Thanks Chris,

It is the easiest way of doing it.

Just multiply by 10^n  where n is the number of digits that are repeating.  do the subtraction and simplify.   

J=5B (1)

J-64=B+64   (2a)

add 64 to both sides

J=B+128       (2b)

(1)=(2b)

5B=B+128

4B=128

b=128/4

b=$32

J = 5*32 = $160

All the numbers are multiplied by 4 so the scale factor is  4 new:1old    The scale factor is 4.

The centre of the dilation is the origin.   [ also, I assume you meant B' to be (-8,24) ]

always draw the picture when you do these types of questions.

This is the boat in the water.  The red line is the water.

Can you work it out now?

d(t) = 3/2 sin (5πt/31) + 23

The average depth of the water, over time, is 23 feet.

The amplitue of the tide is 1.5 feet

So the maximum depth of the water is 24.5m

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You do not need this but the period is 2pi divided by 5pi/31 = 2pi*31/5pi = 62/5 = 12.4

I think it fair to assume that we are talking tides and time is in hours.

You are wonderful Ghost of Web2.0calc.   You write your lay so beautifully.  

Kitty is one fortunate Princess to have such attention lavished upon her.  

Our magical realm is truly blessed.

Queen Guinevere.