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a)  There are no zeros:  the vertex of the parablola is (0,24) and this parabola rises from there.

Another way:  setting the equation equal to zero:  0.005x² + 24  =  0

                                                      --->                            0.005x²  =  - 24

                                                      --->                                      x²  =  - 24/0.005                      

                                                      --->                                      x²  =  - 4800  (there is no real solution)

b)  24 meters because this is the minimum value of the quadratic.

Bonus:  Setting the equation equal to 30:  0.005x² + 24  =  30

                                               --->                      0.005x²  = 6

                                               --->                               x²  =  6/0.005

                                              --->                                 x  =  sqrt(1200)  =  34.64

Total distance:  34.64 ·2  =  69.3 meters.

Find positive integers m and n such that 5m + 7n = 46.  

m = 5  &  n = 3  will work.  

_.

Thank you!

can you please do the one with the square

With 4 black socks and 6 red socks, he can end without two red socks in these ways:

1) grabbing two black socks:                             (4/10)·(3/9)  =  12/90

2) grabbing a red sock and then a black sock:  (6/10)·(4/9)  =   24/90

3) grabbing a black sock and then a red sock:  (4/10)·(6/9)  =  24/90

Since these are independent:  12/90 + 24/90 + 24/90  =  60/90  =  1/3

The probability that he will not have a pair of red socks:  1/3

Adding on to Alan's answer; 4n=28 so n must equal...

The sum of four consecutive integers is 34.  What is their product?

Let the smallest be n.

n + (n+1) + (n+2) + (n+3) = 34  or

4n + 6 = 34

Can you take it from here? 

If 3a + 7b + c = 315 and 4a + 10b + c = 420, what is a + b + c?

If 3x + 1/(2x) = 3, find 8x^3 + 1/(27x^3).

Oh, thank you so much!

Do you mean something like:

12*143+6*214 = 6*2*143 + 6*214   

6*2*143 + 6*214  = 6*(2*143 + 214)

6*(2*143 + 214) = 6*(286 + 214)

6*(286 + 214) = 6* 500  = 3000

|x-5| >=0 for all values of x, so

| |x-5| + 5| >= 5 for all values of x, so

| | |x-5| + 5| - 5| >= 0 for all values of x. so

| | |x-5| + 5| - 5| + 5 >= 5 for all values of x, so minimum value = 5, when x = 5.

As follows:

1 US ton = 2000 lb

1 UK ton = 2240 lb

1 metric ton (tonne) = 2204 lb

An athlete runs four times around a 400m track in 5.00 min. Determine the athlete’s speed in meters per second. 

Hello Guest!

\(v=\frac{s}{t}\)

\(v=\frac{4\cdot 400m}{5min}\times \frac{1min}{60sec}\)

\(v=5.\overline{3}\ \frac{m}{sec}=5\frac{1}{3}\frac{m}{sec}\)

D. 5.33 m/s

In the figure shown, a circle is enclosed in trapezium ABCD touching all of its 4 sides, where AD = BC, AB = 10, CD = 16, find BC.

Hello Guest!

The contact radius at \(\overline{BC}\) divides \(\overline{BC}\) into \(\frac{\overline{DC}}{2}\) and \(\frac{\overline{AB}}{2}\).

\(\overline{BC}= \frac{\overline{CD}}{2}+ \frac{\overline{AB}}{2}\)

\(\overline{BC}= \frac{16}{2}+ \frac{10}{2}\)

\(\overline{BC}=13\)

  !

Are x and n in degrees or radians?

Here is a graph that might help.

Please put your answers on the forum loki where they can be viewed by all.