Melody

0.4^log0.4(10).

\(x^{log_xy} =y\)

 so      \(0.4^{log_{0.4}(10)}=10\)

There is no question here. :/

Yes, unless you are told you have to use a particular method you are free to choose :)

y= -2x^2 + 5

It is a parabola because of the x^2   (The degree of trhe polynomial is 2)

And it is concave down because the number in front of the x^2 ( the leading coefficient) is negative.

The vertex is (0,5)

2x^2+16x+26=0

Just use the quadratic formula

Find sin t and cos t for the given value of t.

t = 945°

945-360-360=225

225-180=45

so  

945 is equivalent to 225 degrees which is in the 3rd quadrant and the equivalent acute angle is 45 degrees.

Sin and cos are both negative in  the 3rd quadrant.

\(sin(945)=cos(945)= - cos(45) =-sin(45)=\frac{-1}{\sqrt2}\)

log3(x) = 5

\(If\;\;log_3(x) = 5\\ then\\ x=3^5\\ x=243\\~\\or\\~\\ log_3(x) = 5\\ 3^{log_3(x)} =3^ 5\\ x=243\)

A light house is located on a small island 3 km away from the nearest point P on a straight shoreline and the light makes 4 revolutions per minute. How fast is the beam of light moving along the shoreline when it is 1 km away from P?

Distance of light house to new point is  sqrt(9+1)=sqrt10

Circumference of circle with radius of sqrt(10) = 2pi* sqrt(10) 

The light is travelling at 4 rvs per minute which is equal to  1 rev per  (1/4) minute

so

speed = distance / time

\(speed = 2\pi\sqrt{10}\div \frac{1}{4}\;\;km/min\\ speed = 2\pi\sqrt{10}\times 4\;\;km/min\\ speed = 4\pi\sqrt{10}\;\;km/min\\ speed = 4\pi\sqrt{10}\;\;km/min\\ speed \approx 39.73835\;\;km/min\\ speed \approx 39.73835*60\;\;km/hour\\ speed \approx 2384\;\;km/hour\\ \)

Thanks DS.

I like seeing your sketches. You are very talented. :)

Bruce has $5.15 in dimes and quarters. He has 8 more quarters than dimes. How many quarters does he have?

We have done 2 of these for you already.  I want you to show me how you would start the problem.

Let D be the number of dimes (10c) and Q be the number of quarters (25c)

He has 8 more quarters than dimes.  Turn that into a number sentence please