Plugging In

[Determined]

The height h of a soccer ball that is kicked from the ground with an initial velocity of 40 feet per second can be modeled by the equation h=-16t^2+40t where t is time (in seconds). At what times will the soccer ball's height be less than 10 feet?

A. t > 0.282
B. t < 2.218
C. 0.282 < t < 2.218
D. t < 0.282 or t > 2.218

Solve x^2+2x>3 using this table: x=-5, -4, -3, -2, -1, 0, 1, 2, 3; x^2+2x>3=12, 5, 0, -3, -4, -3, 0, 5, 12

A. x<0 or x>-3
B. x>2
C. x<-3 or x>1
D. -3<x<1

~Again, I need the steps and explanations in solving these EoC review questions

 

[DrPhil]

The height h of a soccer ball that is kicked from the ground with an initial velocity of 40 feet per second can be modeled by the equation h=-16t^2+40t where t is time (in seconds). At what times will the soccer ball's height be less than 10 feet?

A. t > 0.282
B. t < 2.218
C. 0.282 < t < 2.218
D. t < 0.282 or t > 2.218

Set h = 10 ft in the equation. You then have a quadratic to solve for t. At one of those times the ball will be going upward, and at the downward.

Solve x^2+2x>3 using this table:
.............x = -5, -4, -3, -2, -1, 0, 1, 2, 3;
x^2+2x-3 = 12, 5, 0, -3, -4, -3, 0, 5, 12

A. x<0 or x>-3
B. x>2
C. x<-3 or x>1
D. -3<x<1

~Again, I need the steps and explanations in solving these EoC review questions

The second row of the table has "-3" rather than ">3".
If you subtract 3 from both sides of the inequality,
\(\displaystyle x^2 + 2x > 3 \; \longrightarrow \; x^2 + 2x - 3 > 0\)

 

[daon2]

The height h of a soccer ball that is kicked from the ground with an initial velocity of 40 feet per second can be modeled by the equation h=-16t^2+40t where t is time (in seconds). At what times will the soccer ball's height be less than 10 feet?

A. t > 0.282
B. t < 2.218
C. 0.282 < t < 2.218
D. t < 0.282 or t > 2.218

Solve x^2+2x>3 using this table: x=-5, -4, -3, -2, -1, 0, 1, 2, 3; x^2+2x>3=12, 5, 0, -3, -4, -3, 0, 5, 12

A. x<0 or x>-3
B. x>2
C. x<-3 or x>1
D. -3<x<1

~Again, I need the steps and explanations in solving these EoC review questions

Algebraically you want to solve -16t^2+40t < 10, or -16t^2+40t-10 < 0. To solve this you want to first solve for the roots of -16t^2+40t-10. Then you will end up with one or two values of t: a and b. Plot on a number line:

----?---a-----?-----b---?-----

You know h=10 when t=a or t=b. h will either be less than 10 or greater than 10 for values in the question marked areas above. Pick convenient values of t to see which occurs.

Intuitively, you can see that the function f(t) = -16t^2+40t-10 is an upside down parabola, so that it will only be positive when t is between the roots of f(t) and negative otherwise. The roots of f(t) are the values t for which h(t)=10, so after finding the roots, again a and b, this tells you f(t)<0, i.e. h(t)<10, when t<a or t>b.

 

[lookagain]

The height h of a soccer ball that is kicked from the ground with an initial velocity of 40 feet per second can be modeled by the equation h=-16t^2+40t where t is time (in seconds). At what times will the soccer ball's height be less than 10 feet?

A. t > 0.282
B. t < 2.218
C. 0.282 < t < 2.218
D. t < 0.282 or t > 2.218

Solve x^2+2x>3 using this table: x=-5, -4, -3, -2, -1, 0, 1, 2, 3; x^2+2x>3=12, 5, 0, -3, -4, -3, 0, 5, 12

A. x<0 or x>-3
B. x>2
C. x<-3 or x>1
D. -3<x<1

~Again, I need the steps and explanations in solving these EoC review questions

No, you do *not* "need the steps and explanations in solving" those questions. Show your work/attempts and/or pertinent questions here *first* so that you may be helped where you are stuck. I am also sending you a private message, because you're off on the wrong foot with your expectations. Read the suggestions at this link about posting: http://www.freemathhelp.com/forum/threads/41536-Read-Before-Posting!!