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, where 15 is the initial height (in feet) of the overhang, -10 is the initial vertical velocity (in feet per second), and t is the time (in seconds). How long does it take the snowboarder to land after jumping off the overhang?"

Answers

Answer 1

Answer:

Step-by-step explanation:

It is given that, the vertical height v, in feet, of a snowboarder jumping off of an overhang can be modeled by the function as :

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

Where

15 is the initial height of the overhang

-10 is the initial vertical velocity

t is in second

We need to find the time taken by the snowboarder to land after jumping off the overhang. At this condition,

h(t) = 0

So, $15-10t-16t^2=0$

On solving above equation using online calculator, we get the value of t = 0.705 seconds. So, the time taken by the snowboarder to land after jumping off the overhang is 0.705 seconds.

Answer 2

Answer: 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: $(5-4 √(15) )/(8)$ or rounded answer: ≈1.31 seconds.

Hope this helps!
NoThisIsPatrick

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The sum of 6 consecutive even numbers is 126.what is the fourth number in this sequence

Answers

This can be put into a formula like so:

Since they are 6 consecutive even numbers, they will alternate odd/even/odd/even.

x, x+2, x+4, x+6, x+8, x+10 = 126

Simplify

6x + 30 = 126

6x = 96

x = 16

And you want the fourth number, so plug the x value back into the equation of 'x+6' and you will get 16+6 which = 22.

Answer:

Step-by-step explanation:

x+x+2+x+4+x+6+x+10

126

x=16

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A plant can either have a smooth seed (p) or a rough seed (q). Rough seeds are recessive and smooth seeds are dominant. In a population of 100 plants, 32 of them have rough seeds.p^2 + 2pq + q^2 = 1

a) What is q^2?

b) What is q?

c) What is p?

d) If there are 19 plants with rough seeds in a population of 100, what is the allele frequency for smooth seeds?

Answers

To calculate this, the Hardy-Weinberg principle can be used:

p² + 2pq + q² = 1 and p + q = 1

where p and q are the frequencies of the alleles (p - dominant, q - recessive), and p², q² and 2pq are the frequencies of the genotypes.

a) Since 32 plants have rough seed (recessive genotype: q²) out of 100 plants in total, then

q² = 32/100 = 0.32

b) q = √q² = √0.32 = 0.56

c) Since p + q = 1, then

p = 1 - q = 1 - 0.56 = 0.44

d) 19 plants with rough seeds (recessive genotype: q²) in a population of 100 means that q² = 19/100 = 0.19

We need to calculate p (the allele frequency for smooth seeds).
We can find q because we know q²:

q = √q² = √0.19 = 0.44

Since p + q = 1, then

p = 1 - q = 1 - 0.4 = 0.56

I followed what the other user said and I think it's correct!

a) 0.32

b) 0.56

c) 0.44

d) 0.56

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Answers

Answer:

Step-by-step explanation:

First, divide 32 by 4 to see how many times larger the numbers in the second ratio are than in the first ratio. 32/4=8 This means that the numbers in the second ratio are 8 times larger than in the first

Then, since the second ratio’s numbers are 8 times bigger than those of the first ratio, you can multiply both numbers in the first ratio by 8. The problem already multiplied 4 by 8 for us, which is 32, so all we have to do now is multiply 9 by 8. 9*8=72, which means that 4:9 is equivalent to 32:72

2/3 of the pizza was left over from last night. Then, Marcy ate another 2/9 of it. Which of the following statements is true?A.Very little of the pizza is left.
B.About half of the pizza is left.
C.Most of the pizza is left.

Answers

About half of the Pizza is left

Explanation
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