An archers arrow follows a parabolic path. The height of the f(x) is given by f(x) =-16x^2+200x+4 in feet. Find the maximum height of the arrow

QUESTION POSTED AT 03/12/2019 - 04:20 AM

Answered by admin AT 03/12/2019 - 04:20 AM

Maximum of function f(x)=ax^2+bx+c where a \neq 0 you can find by using this formula: y_{\max}=  - \dfrac{\Delta}{4a}=-\dfrac{b^2-4ac}{4a}=\dfrac{4ac-b^2}{4a}=c-\dfrac{b^2}{4a}

In height function you've got:

a= -16
b= 200
c= 4

Just substitute! You'll get

y_{\max} = 4 - \dfrac{200^2}{4 \cdot (-16)}=4-\dfrac{40 \ 000}{-64}=4+\dfrac{40 \ 000}{64}=4+625=629

Maximum height is  629  [units]
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Related questions

In 2004, there were approximately 275 students in the Delaware high school band. In 2010, that number increased to 305. Find the annual rate of change in the number of students in the band.

Annual rate of change in the number of students in the band is 5 students per year.

Step-by-step explanation:

In 2004, there were approximately 275 students in the Delaware high school band.

Number of students in band on 2004 = 275

In 2010, that number increased to 305

Number of students in band on 2010 = 305

Duration of years = 2010 - 2004 = 6 years

Increase in number of students in band = 305 - 275 = 30

\\\\\texttt{Annual rate of change in the number of students in the band = }\frac{30}{6}\\\\\texttt{Annual rate of change in the number of students in the band = }5

Annual rate of change in the number of students in the band is 5 students per year.

ANSWERED AT 09/12/2019 - 05:13 AM


QUESTION POSTED AT 09/12/2019 - 05:13 AM

Use compatible number to find two estimate 2,242÷33

Compatible numbers are also considered as estimates numbers.
Now the given equation is 2 242 / 33
=> Let’s find the compatible number to find the estimate quotient
=> 2 242 – 2 = 2 240
=> 33 + 2 = 35
=> 2 240 / 35
=> 62, this is the estimated quotient
The correct answer is:
=> 2 242 / 33
=> 67.94, the exact answer.
62 and 67.94 is not exactly the same but close. That’s how estimation works.



ANSWERED AT 09/12/2019 - 05:09 AM


QUESTION POSTED AT 09/12/2019 - 05:09 AM

How do you find the total angle measurement of an octagon and a decagon

Use this equation (n-2)*180 n being the number of sides a shape has.

ANSWERED AT 09/12/2019 - 05:06 AM


QUESTION POSTED AT 09/12/2019 - 05:06 AM

Two students participated in a fund-raiser. Each sold a combination of pencils and notebooks. The first student sold 2 pencils and 8 notebooks for a total of $17. The second student sold 10 pencils and 3 notebooks for a total of $11. Find the price of each item. Write a system of equations (two equations), and define the variables also. x= y= 1) 2)9 POINTS! Please help!

2x + 8y = 17
10x + 3y = 11

We need to solve the system of equations.

x = pencils
y = notebooks

If we solve by graphing, we get the answer:

One pencil costs 0.50 dollars
One notebook costs 2.00 dollars

ANSWERED AT 09/12/2019 - 05:05 AM


QUESTION POSTED AT 09/12/2019 - 05:05 AM

Explain how knowing 1+7 helps you find the sum for 7+1

Knowing 1+7 helps you find the sum of 7+1 because 1+7 and 7+1 is communitive property of addition. Also because 1+7 is the same answer as 7+1. 
Ex:
      1+7=8 
        And
       7+1=8
its the same result.

ANSWERED AT 09/12/2019 - 04:58 AM


QUESTION POSTED AT 09/12/2019 - 04:58 AM

A ribbon is 3 2/3 yards long mae needs to cut the ribbon into pieces that are 2/3 yard long use the model to find the number of pieces she can cut

 \frac{2}{3} = 11/3 yards long. 11/2= 5.5... Mae can cut 5 pieces.

ANSWERED AT 09/12/2019 - 04:57 AM


QUESTION POSTED AT 09/12/2019 - 04:57 AM

Explain how you can find 4 times 754 using two different methods.

Method 1:

4(754)

=4(700+50+4)

=2800 + 200 + 16

=3000+16

=3016

-----------------

Method 2:

4(754)

=4(250+250+250+4)

=1000+1000+1000+16

=3016

ANSWERED AT 09/12/2019 - 04:51 AM


QUESTION POSTED AT 09/12/2019 - 04:51 AM

Find the number of meters each record holder ran in one second of 200 meters, 19.30 seconds

Mostly when a math problem says the word OF it means to multiply most of the time and I you multiply this I is 3860.

ANSWERED AT 09/12/2019 - 04:47 AM


QUESTION POSTED AT 09/12/2019 - 04:47 AM

A pile of 34 coins consists of nickels and dimes. the total value of the coins is $3.30. find the number of each type of coin.

It just means to multiply or divide

ANSWERED AT 09/12/2019 - 04:46 AM


QUESTION POSTED AT 09/12/2019 - 04:46 AM

A girraffe can run up to 46.93 feet per second.How far could a giraffe run in 1.8 seconds justify your answer

 4693 <----- I think this is how you solve it.
x   18

ANSWERED AT 09/12/2019 - 04:44 AM


QUESTION POSTED AT 09/12/2019 - 04:44 AM

Sandra is putting up a fence around her garden which is in the shape of a square.each foot of fencing costs $9.if each side of the fence will be 8feet long how many feet of fencing will Sandra need?

Its a square so all the side will be the same.
so thats just 8x4 and that equals 32
If your trying to find the price then just do 9x32 
and that gets you $288
Hope I helped :)

ANSWERED AT 09/12/2019 - 04:30 AM


QUESTION POSTED AT 09/12/2019 - 04:30 AM

A 91 square foot bathroom has a length of 13 feet. what is the width of the bathroom

The answer is 7 ft. The bathroom has rectangular shape. The area (A) of a rectangle is the product of the width (w) and length (l): A = w * h. The bathroom is rectangular. We know that A = 91 ft^2 and l = 13 ft. Let's substitute them in the formula for the area: 91 ft^2 = w * 13 ft. w = 91 ft^2 : 13 ft. w = 7 ft. The width of the bathroom is 7 ft.Hope this helps. Let me know if you need additional help!

ANSWERED AT 09/12/2019 - 04:30 AM


QUESTION POSTED AT 09/12/2019 - 04:30 AM

Find two integers whose sum is -7 ans whose product is 12. Explain how you found the numbers.

-3 + -4 = -7
add the numbers and keep the common sign.
-3 * -4 = 12
since the factors are both negative, the product is positive, when multiplying and/or dividing. 

ANSWERED AT 09/12/2019 - 04:26 AM


QUESTION POSTED AT 09/12/2019 - 04:26 AM

Explain two different waysto find the difference for 12-3

One way: subtract 12-3 =9 
the other way sub in and make equations

ANSWERED AT 09/12/2019 - 04:25 AM


QUESTION POSTED AT 09/12/2019 - 04:25 AM

Mei is writing 4.28 as a mixed number. Find her mistake and correct it.

4.28 is a decimal and not a mixed number. To write it as a mixed number you keep the 4 and put 28 over 100 then simplify.

4.28= 4 28/100 (simplify)
4 28/100= 4 14/50= 4 7/25

4.28 as a mixed number would be 4 7/25

ANSWERED AT 09/12/2019 - 04:22 AM


QUESTION POSTED AT 09/12/2019 - 04:22 AM

I just need to find y explain please :p

Rewrite in slope intercept from y=mx+b  y=1-3x+11/3

ANSWERED AT 09/12/2019 - 04:22 AM


QUESTION POSTED AT 09/12/2019 - 04:22 AM

How can you find 3 times 584 using expanded form

we know that

 584 in expanded form is equal to

 584=5*100+8*10+4*1

so

 3*584 is equal to

 3*(5*100+8*10+4*1)=15*100+24*10+12*1\\ =1,500+240+12\\ =1,752

therefore

the answer is

 1,752

ANSWERED AT 09/12/2019 - 03:59 AM


QUESTION POSTED AT 09/12/2019 - 03:59 AM

If 18 is added to a certain number and the sum is divided by 6, the result is 1 more than 14 of the original number. Find the original number.

The original number is 72 


(18+x)/6 = 1+14 
1/6x + 3 = 1 + 14 (Distribute)
1/6x + 3 = (1+14) (Combine Like Terms)
1/6x + 3 = 15 
        - 3 = -3          (Subtract 3 From Both Sides)
1/6x = 12 
(1/6x)*6 = 12 * 6  (Multiply Both Sides By 6)
x = 72


ANSWERED AT 09/12/2019 - 03:58 AM


QUESTION POSTED AT 09/12/2019 - 03:58 AM

Suppose you bought a pizza for $8.00. You also bought a salad but you can not remember how much you paid and you can not find the receipt.You know the total amount you spent was $10.00. Which equation would best to answer to find the cost to the salad A:8.00+$=10.00 B:8.00+10.00=$ C:8.00 x $=10.00 D.10.00 x $ = 8.00

The best equation would be A.

with A you get to calculate what is the value of $. 

8 + $ = 10 (10 is the total value of your receipt and 8 is the price of pizza)
$ = 10 - 8 (we transfer the price of pizza on the other side to the total amount of your receipt and calculate the remaining amount)
$ = 2

We see that the remaining amount is 2$, which means the salad cost s2$ :)

ANSWERED AT 09/12/2019 - 03:56 AM


QUESTION POSTED AT 09/12/2019 - 03:56 AM

Find a sum equivalent to the product 6(y + x)

6y+6x
all you do is the distributive property

ANSWERED AT 09/12/2019 - 02:36 AM


QUESTION POSTED AT 09/12/2019 - 02:36 AM

Can you find the slope of y=x-3 and find the x and y interceptes

Y = mx + b

m is the slope
b is the y-intercept

y = x - 3

1 is the slope
-3 is the y-intercept

to find the x-intercept, set y=0

0 = x - 3

So the x-intercept is 3

ANSWERED AT 09/12/2019 - 12:20 AM


QUESTION POSTED AT 09/12/2019 - 12:20 AM

The scale model of a building is 5.4 feet tall if the original building is 810 meters tall, what was the scale used to make the model

It's 150 I think. I'm not sure though 

ANSWERED AT 08/12/2019 - 10:44 PM


QUESTION POSTED AT 08/12/2019 - 10:44 PM

A square is put together by two triangles. the hypotenuse is 11 cm and width of 8 cm. find the height of the triangle.

Just use A¨2+B¨2=C¨2, if it forms a square, it has to be a right triangle

ANSWERED AT 08/12/2019 - 05:03 PM


QUESTION POSTED AT 08/12/2019 - 05:03 PM

The area of a rectangular picture frame is 30 1/3 square inches. The length of the frame is 6 1/2. Find the width of the width

Answer:

\texttt{Width of rectangular picture frame}=4\frac{2}{3}inch

Step-by-step explanation:

The area of a rectangular picture frame is 30 1/3 square inches. The length of the frame is 6 1/2.

\texttt{Length of rectangular picture frame = }6\frac{1}{2}=\frac{6\times 2+1}{2}=\frac{13}{2}inch

\texttt{Area of rectangular picture frame = }30\frac{1}{3}=\frac{30\times 3+1}{3}=\frac{91}{3}inch^2

Area of rectangle = length x width

We have

  \frac{91}{3}=\frac{13}{2}\times \texttt{Width}\\\\\texttt{Width}=\frac{91}{3}\times \frac{2}{13}=\frac{14}{3}=4\frac{2}{3}inch

\texttt{Width of rectangular picture frame}=4\frac{2}{3}inch

ANSWERED AT 08/12/2019 - 04:39 PM


QUESTION POSTED AT 08/12/2019 - 04:39 PM

Luis is finding 8.9 -3.72

The answer to this problem is 5.18.

ANSWERED AT 08/12/2019 - 04:34 PM


QUESTION POSTED AT 08/12/2019 - 04:34 PM

Choose any 3 digit number describe how to find the number that is 10 more

Let's divide this question into two parts:
1. Choosing any 3 digit number.
2. Find the number that is 10 more.

1. Let choose the number 111. As you can see it is the three digit number.
2. Now to find the 10 more to 111, we have to add 10 to 111 as follows:

111
+10
--------
121

Hence, the 10 more to the number 111 is 121.

ANSWERED AT 08/12/2019 - 04:27 PM


QUESTION POSTED AT 08/12/2019 - 04:27 PM

At a basketball game, a vender sold a combined total of 200 sodas and hot dogs. The number of hot dogs sold was 30 less than the number of sodas sold. Find the number of sodas sold and the number of hot dogs sold.

Number of sodas sold = s
s-30=h (number of hot dogs sold)
200/2=100
30/2=15
100-15=85
100+15=115
total hot dogs sold= 85
total sodas sold is =115

ANSWERED AT 08/12/2019 - 04:23 PM


QUESTION POSTED AT 08/12/2019 - 04:23 PM

The height of Gateway Arch shown on Missouri quarter is 630 feet or 7,560 inches.Find how many 4-inch stacks of quarters make up the height of Gateway Arch.If there are 58 quarter in a 4-inch stack, how many quarters high is the arch?

To do this you want to divide 7560 by 4.  This leaves you with 1845.  Therefore, you need 1845 4-inch stacks to build that high.  You are not done though.  You need to multiply 1845 by 58. This gives you 107,010.  It would take 107,010 quarters to get to the top.

ANSWERED AT 08/12/2019 - 04:22 PM


QUESTION POSTED AT 08/12/2019 - 04:22 PM

Shella is participating in a multi-day bike trip. on the first day, she rode 100 miles in 8 hours. use the expression d/t where d is the distance traveled and t is the travel time to find her average rate of travel. include units when evaluating the expression.

To solve this problem, first we have to substitute our integers in for our variables in the equation we are using.

d/t= 100 miles/8 hours

Then, we have to simplify the integer equation.

100 miles/8 hours = 12.5 miles per hour

This means that Shella traveled at an average speed of 12.5 mph on her bike trip.

ANSWERED AT 08/12/2019 - 04:15 PM


QUESTION POSTED AT 08/12/2019 - 04:15 PM

Given the function f(x) = −5x2 − x + 20, find f(3).


f(x) = -5x^2 - x + 20;

f(3) = -5*3^2 - 3 + 20 = -5*9 - 3 + 20 = -45 - 3 + 20 = -28;

ANSWERED AT 08/12/2019 - 04:05 PM


QUESTION POSTED AT 08/12/2019 - 04:05 PM