A penny is thrown straight down froma height of 200 feet. At the same time, a
paintbrush is dropped from a height of
100 feet. The polynomials represent the
heights (in feet) of the objects after
t seconds.
-16t²- 40t + 200
-16t² + 100
a. Write a polynomial that represents the distance between the penny and the
paintbrush after 7 seconds.
b. Interpret the coefficients of the polynomial in part (a).

Answers

Answer 1

Answer: Here is your step-by-step answer

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Which is bigger 4/7 or 3/5

Answers

3/5 is bigger because 4/7 = 20/35 and 3/5 = 21/35

3/5 is bigger because if you cross multiply 4/7 with 3/5 3/5 gets 21 and 4/7 gets 20

A projectile is fired straight upward with an initial velocity of 400 feet per second. The height of the projectile, h(t), if represented by the function h(t)=-16t^2+400t, where t is the time in seconds. How long does it take the projectile to reach the maximum height?

Answers

Taking into account the definition of maximum, minimum and vertex of a quadratic function, it takes 12.5 seconds for the projectile to reach maximum height.

A quadratic function is defined in the form:

y= f (x) = ax² + bx + c

Every quadratic function has a maximum or a minimum, which is the vertex of the parabola. If the parabola has an upward concavity, the vertex corresponds to a minimum of the function; whereas if the parabola has concavity downwards, the vertex will be a maximum.

That is, if the coefficient a is positive the parabola is concave and the vertex will be a minimum of the function, while if a is negative the parabola will be convex and the vertex is a maximum.

The maximum or minimum is reached in $xv=(-b)/(2a)$

The maximum or minimum value of y is obtained by evaluating the function at xv, this is, f (xv).

In this case, the function is:

h(t)= -16t² + 400t

where t is the time in seconds

Being a = -16 and b = 400, the value of a is negative, so the vertex will be the maximum.

You want to know the time it takes for the projectile to reach the maximum height, that is, the maximum in t. That is, you must calculate t using the expression: $t=(-b)/(2a)$

So: $t=(-400)/(2x(-16))$

Solving:

$t=(-400)/(-32)$

t= 12.5 seconds

It takes 12.5 seconds for the projectile to reach maximum height.

Learn more about cuadratic function with this examples:

Answer:

You can find the answer by using the formula x=-b/2a

Step-by-step explanation:

Remember the maximum height will be at the vertex. The x value of the vertex is your time, so use x=-b/2a. Then if it had also asked what the height was, you would plug that answer into your equation to find the y value of the vertex. Pretty sure your teacher is just asking you to find the x though:)

A river flows at the rate of 30 feet per minute what is the rate in seconds per foot

Answers

30 ft/ minute=30 ft/ minute*(1 minute / 60 s)=0.5 ft/s
rate in seconds per foot=1 / (0.5 ft/s)=2 s/ ft.

Answer:2 s/ft.

The junior class has 50 students. Twenty-five students take only French, 15 take only Latin, and 10 take both. If a student is chosen at random from the class, what is the probability that the student chosen takes either French only or Latin only? 1/2 4/5 1

Answers

The answer is going to be 4/5

The answer is 4/5 because the combined probability (French only is .5, and Latin only is .3) for French only and Latin only is .8, which is equal to 4/5.

A sequence is defined that the first term is 4 and each term after the first term is found by adding 4 5 to the preceding term. What is the 8th term of the sequence?

Answers

The 8th term of the sequence is 9.6
Hope this helped! :)

There are multiple chickens and rabbits in a cage. There are 72 heads and 200 feet inside of the cage. How many chickens and how many rabbits

Answers

Let the number of chickens be x and that the number of rabbits be y

So, the equation would be
x+y = 72. --Eq.1
4x + 2y = 200 --Eq.2

Eq.1 can also be written as
2x+2y = 144 --Eq.3

Eq.2 - Eq.3

4x -2x+2y -2y = 200-144
2x = 56
x = 28

So, the number of chickens = 28
Number of rabbits = 72-28 = 44

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