A ball is thrown directly upward from a height of 3 ft with an initial velocity of 20 ft/sec. The function s(t)=−16t2+20t+3 gives the height of the ball, in feet, t seconds after it has been thrown. Determine the time at which the ball reaches its maximum height and find the maximum height.
Answers
Answer:
[tex]t=\frac{5}{8}s[/tex] and [tex]s(\frac{5}{8})=\frac{37}{4}ft[/tex]
Step-by-step explanation:
There are different approaches you can take to solve this problem. You can look at it from the geometric approach or the calculus approach. I will us the geometric approach.
When we analyze the given function for the height of the ball:
[tex]s(t)=-16t^2+20t+3[/tex]
we can see that we are dealing with a quadratic function. This means that the graph will be an inverted parabola, just like the one in the attached picture.
so the idea is to find the vertex of the parabola to find the highest the ball gets to be and the time it gets to be at that height.
In order to do so, we can use the vertex formula, which looks like this:
[tex]t=-\frac{b}{2a}[/tex]
this is use when you have a function with the form:
[tex]f(x)=ax^2+bx+c[/tex]
in this case:
a=-16, b=20 and c=3, so the formula then turns to:
[tex]t=-\frac{20}{2(-16)}[/tex]
which yields:
[tex]t=\frac{5}{8} s[/tex]
which is our first answer. So we can then use this to find the maximum height of the ball, just by substituting t into the original function:
[tex]s(\frac{5}{8})=-16(\frac{5}{8})^2+20(\frac{5}{8})+3[/tex]
which yields:
[tex]s(\frac{5}{8})=\frac{37}{4} ft[/tex]
which is our second answer.
Related Questions
HURRY UP NEED HELP
7. Find the equation of a line that fits the data shown in the graph below.
Answers
Answer:
y=-x+3/2, I hope that I hoped, and by the way, it is NEGATIVE x. It's a little hard to see :P
Answer:
y=2x + (-1)
Slope is m=2 and the y-intercept is b= -1
A truck used 6.3 gallons of gasoline to travel 105 miles. How many gallons of gasoline would it need to travel 250 miles? A 15 gallons B 4,166.7 gallons С 150 gallons D 16.7 gallons
Answers
Answer:
a
Step-by-step explanation:
got it right in my test
slope of one dotted lines:
slope of the reflection line:
Answers
Answer:
Slope of dotted lines: 1
Slope of reflection line: -1
Step-by-step explanation:
For the dotted lines, the rise up by one unit and run for one unit, thus their slopes are 1.
For the reflection line, it does the same thing as the dotted line, but instead of rising one unit, it goes down for one unit and runs for one unit, making its slope -1.
3. 100x2-36y2 ??
ito pa guys pleasedddd!!
Answers
Answer:
4(5x - 3y)(5x + 3y)
Step-by-step explanation:
Assuming you require the expression factored.
Given
100x² - 36y² ← factor out 4 from each term
= 4(25x² - 9y²) ← is a difference of squares and factors in general as
a² - b² = (a - b)(a + b) , thus
25x² - 9y²
= (5x)² - (3y)² ← with a = 5x and b = 3y
= (5x - 3y)(5x + 3y)
Thus
100x² - 36y² = 4(5x - 3y)(5x + 3y) ← in factored form
Marsha gave the cashier 20 to pay for 3 pairs or socks.
Answers
First, you must subtract.
$20 - $5.03 = $14.97This is because he recieved $5.03 in exchange.
Next, you must divide by 3.
$14.97 / 3 = $4.99
Therefore each pair of socks costs $4.99.
Hope this helps!
I already know that the answer is 190 but why
Answers
Answer:
You know that the total number of persons is 20 , so every person shakes hands with 19 persons.. It then mean that, there are 20×19=380 handshakes. But by every handshake two persons are involved. Therefore, 380 is the result of double-counting, which gives 190 handshakes.Step-by-step explanation:
Hope this helpsIf BC measures 8 inches, the approximate area of circle B is
square inches.
Answers
The area of the circle radius as 8 inches will be 201.062 inches².
What is a circle?A circle is a geometrical figure which becomes by plotting a point around a fixed point by keeping a constant distance.
In our daily life, we always see circular objects for example our bike wheel.
The longest line which can be drawn inside the circle will be the diameter.
Area of circle = πr² and the perimeter of circle = 2πr where r is the radius of the circle.
Given the circle with a radius BC of 8 inches.
Area of circle = πr² where r is the radius of the circle.
So,
Area = π(8)² = 201.062 inches.
Hence "The area of the circle radius as 8 inches will be 201.062 inches².
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The given question figure is missing the figure has been attached below;
What is an equation of the line that passes through the points
(0,8) and
(−8,−4)? Put your answer in fully reduced form.
Answers
y+4 = 1.5 (x+ 8)
y+4 = 1.5x + 12
1.5x - y = -12+4
1.5x - y = -8
Answer:
Answer given in the photo
Vinnie is 1/2 as old as Julie Julie is 24 how old is vinnie
Answers
Answer:
Vinnie is 12.
Step-by-step explanation:
24 divided by 2 is 12
A fraction is the representation of a decimal number so the fraction of 1/2 of 24 is 12 thus its age of Vinnie is 12 years.
What is a fraction?In such a fraction, the value that appears above the horizontal line is referred to as the numerator.
In another word, the fraction is the division of the two numbers, but the division is not wholly complete.
For example, 1/3 is a fraction and in decimal, it is 0.333. Here 1 will be called a numerator while 3 will be the denominator.
Given that,
Age of Julie = 24 years
Age of Vinnie = 1/2 of 24
The 1/2 fraction of 24 will be
⇒ 24/2 = 12 years.
Hence "The fraction of 1/2 of 24 is 12 thus the age of Vinnie is 12 years".
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PLEASE HELP ASAP!! I'LL GIVE YOU BRAINLIEST!!
Answers
Answer:
-5
Step-by-step explanation:
This is the correct answer, I messed up at first so I edited it. (my bad)
If you can answer this question please do it as soon as you can.
Answers
(3^8 x 2^ -5 x 9^0)^ -2 x (2^-2/3^3)^4 x 3^28
Any non-zero expression raised to the power of equals
Step 2:(3^8 x 2^-5 x 1)^-2 x (2^-2/ 3^3)^4 x 3^28
Step 3: (3^8 x 2^-5 x1)^-2 x 2^-8/ 3^12 x 3^28
Any expression multiplied by remains the same
Step 4 : (3^8 x 2^-5)^-2 x 2^-8/3^12 x 3^28
To raise a product to a power, raise each factor to that power
Step 5 : 3^-16 x 2^10 x 2^-8/ 3^12 x 3^28
Reduce the expression with
Step 6: 3^-16 x 2^10 x 2^-8 x 3^16
Calculate the product
2^2
Evaluate , and then your answer is 4!!!!
What is the value of x?
(5х)
110°
110°
70
14
Answers
Answer:
The answer to your question is :The value of 5× = 110°
What is the missing exponent? and the numerical answer
Answers
Answer:
? = -4
Step-by-step explanation:
Express x in terms of y:
3(x + 2y) = 2x = 5y
Answers
Answer:
-6y=x
Step-by-step explanation:
3x+6y=2x=5y
Subtract 5y from all
3x+y=2x-5y
subtract y and 2x from both sides
x=-6y
ASAP want your guys opinion about this
What do you think of when you hear the word "Math"?
Answers
Answer:
I think of hard work :)
Step-by-step explanation:
Answer:
The perfect answer would be
M-ental
A-buse
T-o
H-uman
Step-by-step explanation:
hehe, pls mark me brainliest if you can:)
please help. i will mark brainleast
Answers
Answer:
9 is the answer.
Both negative signs cancel eachother, so you just have 45/5.
Step-by-step explanation:
Good luck! <3
Help, please. I will give brainliest to anyone that answers first.
Answers
Answer:
5000 I think bc 5 times 1000 is 500
Answer:
Step-by-step explanation:
1000 meter = 1 kilometer
1 km= 1000 meter
constant proportionality
y/x=k
y is km , x is meter
1/1000=k
y=1/1000 x (x is the number of meters)
meter Km
250 0.25
12 12/1000=0.012
1 1/1000
kilometer meter
5 5000
20 20000
0.3 300
Answer for brainliest!!!! YOU CAN DO IT!!!
Answers
what is the question pls.
can you pls tell me
If it took 7 hours to mow 4 lawns, then at that rate how many lawns can be mowed in
35 hours?
Answers
Answer: I'm pretty sure they mowed 61 lawns
Step-by-step explanation:
Answer:
20
Step-by-step explanation:
first divide 4 by 7 to see how much lawn ncan be mowed in an hour
4/7=0.5714
multiply by 35 = 19.9999
so almost 20 lawns
The sum of -3/8 and 2 2/3
Answers
Answer:
27/24 or (Decimal: 2.291667)
Step-by-step explanation:
I can’t answer this question
Answers
9514 1404 393
Answer:
3
Step-by-step explanation:
The radicals get in the way a bit, so we can define ...
x = √p
y = √q
Then the equation is ...
(x +y)/(1-x) = (4x+y)/(1-x^2)
Multiplying by (1-x^2), we have ...
(x +y)(1 +x) = 4x +y . . . . . . using 1-x^2 = (1-x)(1+x) the 1-x factor cancels
x^2 +xy +x +y = 4x +y . . . eliminate parentheses
x(x +y) = 3x . . . . . . . subtract (x+y)
x +y = 3 . . . . . . . . . . divide by x
This is the sum we're looking for:
√p +√q = 3
Answer: The answer is 3
Step-by-step explanation:
what type of number is -15
Answers
Answer:
an integer
Step-by-step explanation:
integers are whole number that includes positive number, negative numbers, and zero
Drag the cards to create a number that matches these rules.
The number ends in the tenths place.
8 is the nearest one when rounding
Answers
how to find the square root of 1225
Answers
Hope i helped
Answer:
35
Step-by-step explanation:
The square root is 35 because if you multiply 35 times 35 ([tex]35^{2}[/tex]), it would equal 1225.
Hope this helps and pls do mark me brainliest if you can:)
A clothing business finds there is a linear relationship between the number of shirts n it can sell and the price P it can charge per shirt. In particular historical data shows that 2 thousand shirts can be sold at a price of 80 dollars each, and that 5 thousand shirts can be sold at a price of 65 each
Answers
Answer:
We have two data points:
2000 shirts can be sold for $80 each.
5,000 shirts can be sold for $65 each.
Then we can define the relation:
P(n).
Where P is the price, and n is the number of shirts.
Now, we know that we can model this as a linear relationship that passes through the points (2000, $80) and (5000, $65)
A linear relationship can be written as:
y = a*x + b
where a is the slope and b is the y-axis intercept.
For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:
a = (y2 - y1)/(x2 - x1).
In this case, the slope is:
a = ($65 - $80)/(5000 - 2000) = -$0.005.
Then our equation is:
P(n) = -$0.005*n + b
Now let's find the value of b, we know that:
P(2000) = $80 = -$0.005*2000 + b
$80 = -$10 + b
$80 + $10 = b = $90
Our equation is:
P(n) = -$0.005*n + $90.
i need help plz thank you
Answers
Answer:
8 times blank = 48
Good luck!!!
The sun produces 3.8 * 10 to the 27 power joules of energy per second. How much energy is produced in a year?
Answers
Answer:
1.20 × 10^35
Step-by-step explanation:
There are 60 seconds in 1 min and there are 60 mins in 1 hour. So in an hour there are 60 × 60 = 3600 seconds. There are 24 hours in a day. In a day, there are 3600 × 24 = 86400 seconds. A year is 365 days. So in a year there are 86400 × 365 = 31536000 seconds.
[tex](3.8 \times {10}^{27}) \times 31536000 = 1.20 \times {10}^{35} [/tex]
23.79 divided by 3 estimate
Answers
Answer:
Answer: 7.93
Estimate: 8
Answer: 7.93, or to the nearest tenths, 7.9
What is the remainder when 69,694 is divided by 93?
Answers
Answer:
37
hope this helps :3
37 is the remainder when 69,694 is divided by 93
What is Division?A division is a process of splitting a specific amount into equal parts.
We have to find the remainder when 69,694 is divided by 93
The number which is getting divided here is called the dividend.
69694 is dividend
The number which divides a given number is the divisor.
93 is the divisor.
the number which we get as a result is known as the quotient.
The divisor which does not divide a number completely produces a number, which is referred to as remainder.
69694 can be written as (69657+37)
69657 is divisible completely by 93 and the remainder is 37.
Hence, 37 is the remainder when 69,694 is divided by 93
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Find the quotient 122 and -2.
A. 124
B. 61
C. 61
D. 120
Answers
Answer:
C
Step-by-step explanation:
The true answer is -61
Tip: If you want the correct answer you can not have a typo. Just a heads up.