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telo118 [61]
3 years ago
12

Find the value of x. If necessary, you may learn with the markings on a figure indicate.

Mathematics
1 answer:
love history [14]3 years ago
6 0

Answer:

112

Step-by-step explanation:

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The vertical height v, in feet, of a snowboarder jumping off of an overhang can be modeled by the function h(t)=15-10t-16t^2, wh
olga55 [171]
I don't know for sure, but I think there might be an error in the way you copied your function. In all of my dealings with these types of problems, I have learned the formula to be h(t) = 15 + 10t - 16t^2. Notice the plus in front of the "10t". This is due to the fact that if he pushes off of the overhang he would have an upward force of 10 feet per second as soon as his feet left the ground. The only thing pulling him back to Earth is gravity, modeled by the "-16t^2". This is derived from a bit of slightly advanced physics involving the gravitational constant, but let's work under my formula for a second...

Either way, we will wind up using the Quadratic Formula (or possibly factoring if the numbers are easy enough to work with). So let's start. 

h(t)= 15 +10t - 16t^2

In order to use the QF or factoring I will need to make h(t)=0. Simply done by:

0= 15 +10t -16t^2

Looking at the numbers, I'd prefer to use the QF so here it is:

x= \frac{-b + or -  \sqrt{b^{2}-4ac } }{2a}

I know that my answer will need to be positive since you can't have a negative value when dealing with time, so I will eliminate the positive sign from the "+or-" part leaving me with:

x= \frac{-b -\sqrt{b^{2}-4ac } }{2a}

And I know that a= -16, b= 10, and c=15. So all that's left to do is substitute and solve.

x= \frac{-10 -\sqrt{-16^{2}-4*-16*15 } }{2*-16} 

There's a decent amount of math that would be difficult and sloppy for me to do over the computer, but all you need to do is solve the rest of the equation and you would get your answer.

Exact answer: \frac{5-4 \sqrt{15} }{8} or rounded answer: ≈1.31 seconds.

Hope this helps!
NoThisIsPatrick

7 0
3 years ago
Read 2 more answers
What value of x is in the solution set of 4x - 123 16 + 8x?
Monica [59]

Answer:

the value of x is in the solution set of 4x-12<16=8x

Step-by-step explanation:

multiply the 4x take away from 12= 8x

4 0
3 years ago
Find the values of m and b that make the following function differentiable.
dimaraw [331]
Now, bearing in mind that, for a graph, to be "differentiable", means a "smooth transition", not an abrupt edge or a "cusp", the first subfunction of the piece-wise is just a quadratic, the second subfunction is a linear, well, so the linear needs to hit the quadratic "smoothly", not make an abrupt edge, for that, the linear must continue the quadratic from 2 onwards, since 2 is the range edge.

now, what is the piece-wise when x = 2? well, f(2) = x² or (2)² or 4

that means, the linear needs to hit it at that point, to make it so, let's make it the slope of the linear, the same as the quadratic's.

what's the quadratic's slope? well, simple enough

\bf \left. \cfrac{dy}{dx}=2x \right|_{x=2}\implies 4\impliedby \textit{this means }&#10;\begin{array}{llll}&#10;mx+b\\&#10;\uparrow \\&#10;4&#10;\end{array}

so we have y = 4x + b

now, recall, for the quadratic, when x =2, y = 4, so for the linear, when x = 2, y = 4 as well, this means

\bf 4 = 4(2) + b\implies 4=8+b\implies 4-8=b\implies \boxed{-4=b}&#10;\\\\\\&#10;mx+b\implies 4x-4\\\\&#10;-------------------------------\\\\&#10;f(x)=&#10;\begin{cases}&#10;x^2&x\le 2\\&#10;4x-4&x\ \textgreater \ 2&#10;\end{cases}

check the picture below.

4 0
3 years ago
Find the slope of the line that passes through the two points. (0, 0), (3, 2)
Anit [1.1K]

Answer:

the slope is 2/3 bcoz u do 2-0/3-0

4 0
3 years ago
the length of a rectangular yard is 50ft and it's perimeter is less than 170ft. Describe the width of the yard.
Rufina [12.5K]
The width of yard is 120 ft
4 0
3 years ago
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