30 Points! A soccer ball hit from the ground into the air and is modeled by the function
h(t)=-16t^2+48t+2 (see attachment)
Answers
Answer:
A)
At t = 3/2
B)
36 feet
Step-by-step explanation:
The soccer ball is modeled by the function:
[tex]h(t)=-16t^2+48t[/tex]
Where h(t) represents the height in feet of the ball over time t.
Note that this is a quadratic equation.
Part A)
Since this is a quadratic, the maximum height will be reached when the ball reaches its vertex.
So, we will find the x-coordinate of the vertex.
The vertex is given by:
[tex]\displaystyle \Big (-\frac{b}{2a} , h( -\frac{b}{2a} ) \Big)[/tex]
In this case, a = -16 and b = 48. Thus, the t-coordinate is:
[tex]\displaystyle t=-\frac{48}{2(-16)}=-\frac{48}{-32}=\frac{3}{2}[/tex]
The ball will reach is maximum height at t = 3/2.
Part B)
To find the maximum height, we can simply substitute the value back into the function and evaluated. Therefore:
[tex]\displaystyle\begin{aligned} h(\frac{3}{2})&=-16\Big(\frac{3}{2}\Big)^2+48\Big(\frac{3}{2}\Big)\\\\ &=-16\Big(\frac{9}{4}\Big)+24(3)\\ \\ &=-36+72\\\\ &= 36 \end{aligned}[/tex]
The maximum height of the ball is 36 feet.
Related Questions
-3x = 12
i really need to know this for my math exam
Answers
Answer:
x = -4
Step-by-step explanation:
[tex] - 3x = 12[/tex]
Lets divide both the sides by -3.
[tex] = > \frac{ - 3x}{ - 3} = \frac{12}{ - 3} [/tex]
[tex] = > x = - 4[/tex]
x= -4
-3x=12
divide x by -3 and do the same on the other side
12÷(-3)= -4
hence, x= -4
if you want to check if something is right, substitute your answer into the question
hope this helped
I need some help with this problem
Answers
Answer:
B
Step-by-step explanation:
15x + 3x + 19 = -17
18x + 19 = -17
18x = -36
x = -2
sarah says the two expressions 3(2+x) and 6+3x are equivalent is she right ?
Answers
Answer:
Yes
Step-by-step explanation:
She just distributed the 3 to the (2+x). If you multiple each by 3, you'll get 6+3x.
Answer:
Yes
Step-by-step explanation:
3 and 6 are multiples so yes they are equivalent
I need 3-5 ASAP PLEASE
Answers
What number is equivalent to 7/15
Answers
Answer:
0.5385
-or-
7/13, 14/26, 21/39, 28/52, 35/65, 42/78, 49/91, 56/104, 63/117, 70/130, 77/143, 84/156
Answer:
14/30
Step-by-step explanation:
You just have to multiply the denominator (bottom number) and the numerator (top number) by the same number or dived both numbers.
1. Are the polygons similar?
A. Similar
B. Not similar
2. Because...
A. The corresponding sides are congruent, and corresponding pairs of angles all have the same ratio
B. The sides are not the same length as their corresponding sides
C. The corresponding pairs of sides do NOT have the same ratio
Answers
The polygons are similar.
This is because dividing the corresponding sides forms the same ratio, as shown by the three equations below
35/28 = 1.25
25/20 = 1.25
(15.5)/(12.4) = 1.25
So the larger figure on the right has side lengths that are 1.25 times larger compared to the corresponding sides of the figure on the left.
You'll need to flip the figure on the left so that the side labeled "20" is along the top, and the "28" is along the bottom.
After this flip happens, also note that the angle arc markings match up. The bottom pairs of angles of each figure are shown with a single arc, while the top angles are shown as double arcs. This helps visually show which angles pair up and are congruent to one another.
Because we have similar proportions as discussed earlier, and congruent pairs of angles like this, this shows the two figures are similar quadrilaterals. The one on the right is simply an enlarged scaled up copy of the figure on the left.
the product of a number y and 3 is 6
Answers
Answer:
y=2
Step-by-step explanation:
Answer:
y×3=6
y=6/3
y=2............
What is the areas of triangle
Answers
135 is the answer hope this helps
What is the answer for this question 5 + (x^2 - xy) - 4
Answers
Answer: x^2−xy+1
Step-by-step explanation:
simplify:
5+x^2−xy−4
5+x^2+−xy+−4
Combine Like Terms:
5+x^2+−xy+−4
(x^2)+(−xy)+(5+−4)
x^2+−xy+1
Expand.If necessary, combine like terms (2x-3)(2x-3)
Answers
The expression (2x-3)(2x-3) can be written as (2x-3)² or 4x² - 12x + 9 after expanding by using the identity (a - b)² = a² -2ab + b²
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
We have given an expression:
= (2x-3)(2x-3)
After multiplication:
= (2x-3)²
We can also expand the above expression by using the identity:
(a - b)² = a² -2ab + b²
= 4x² - 12x + 9
Thus, the expression (2x-3)(2x-3) can be written as (2x-3)² or 4x² - 12x + 9 after expanding by using the identity (a - b)² = a² -2ab + b²
Learn more about the expression here:
brainly.com/question/14083225
#SPJ1
how do you solve this problem?
4^x=3x/2+5
Answers
Answer: [tex]{ x = 3.33}{}\\\\\end{array}\right] }[/tex]
Explanation: Hello , Solve for x by simplifying both sides of the equation, then isolating the variable.
I hope this helps!
Find the measure of the missing angle.
Answers
Answer: 35 degrees
Step-by-step explanation:
A triangle always adds up to 180 degrees
? + 125 + 20 = 180
? + 145 = 180
? = 35
HELP ME ASAP PLEASE!
In right triangle ABC, altitude CD is drawn to its hypotenuse. Select all triangles which must be similar to triangle ABC.
(Select all that apply.)
ABC
ACD
BCD
BDC
CAD
CBD
Answers
Answer:
I would say ACD and BCD.
Step-by-step explanation:
Sorry if I am wrong.
A shelf measures 720 mm long.
a) How many centimetres long is the shelf?
b) How many metres long is the shelf?
Answers
b) 0.72 m
10mm = 1cm
100cm = 1m
a) The length of shelf in centimeters is 72 cm
b) The length of shelf in metres is 0.72 m.
What is Unit Conversion?The same attribute is expressed using a unit conversion, but in a different unit of measurement. For instance, time can be expressed in minutes rather than hours, and distance can be expressed in kilometres, feet, or any other measurement unit instead of miles.
Given:
A shelf measures 720 mm long.
a) As 1 cm = 10 mm
So, the length of shelf in centimeters
= 720 /10
= 72 cm
b) As 1 m = 1000 mm
So, the length of shelf in meters
= 720 /1000
= 0.72 m
Learn more about Unit Conversion here:
https://brainly.com/question/19420601
#SPJ2
What variable do you eliminate?
4x + 8y = 20
-4x + 2y = -30
x because they have opposite signs
O
O
y because they don't have opposite signs
x but you have to multiply the top equation by 2, and the bottom equation by -2
O y but you
y but you have to multiply the bottom equation by 4
Answers
Hope this helps :3
You run 1/12 mile in 1/2 minute. How many miles per hour do you run?
Answers
Answer:
10
Step-by-step explanation:
1/12 times 2 would be 1/6 miles per minute, so times that by 6 and it takes 6 minutes to run 1 mile. 60 minutes divided by 6 equals 10 miles per hour. Sorry if thats confusing
Pls help
Solve 3in= ft
Answers
Answer:
3in= 1/4 ft
Step-by-step explanation:
1 foot equals 12 inches so a quarter of 12 inches is 3. PLEASE MARK BRAINLIEST
Answer:
3 inches = 1/4 of a foot
Step-by-step explanation:
There are 12 inches in one foot, so we can create a quick proportion:
1 foot/12 inches = x feet/ 3 inches
x = 1/4 of a foot
Hope this helps!!
answer quick please !!
Answers
Answer:
8
Step-by-step explanation:
Answer:
36 units²
Step-by-step explanation:
I used the triangles' area to find the area of the quadrilateral. The area of a triangle is 1/2 x base x height. The top triangle is 1/2 x 5 x 10 or 25. The bottom triangle is 1/2 x 2 x 11 or 11. Add 25 + 11 to get the total area.
Hope it helps!
The answer to the problem
Answers
================================================
Apply the slope formula
m = (y2-y1)/(x2-x1)
m = (8-6)/(2-5)
m = (2)/(-3)
m = -2/3
As you can see, we subtract the y coordinates together. We also subtract the x values together in the same order. If the order is mixed up, then you'll get the wrong sign for the final answer.
The slope is equal to rise over run. Think of "rise" as "change in y", which explains the difference in y values. The run is equal to the change in x, which is the difference in x values.
if Nandi and thabo share R15,00 in the ratio 1:2 how many rands does each get
Answers
Answer:
[tex]\boxed{\textsf{ The amount shared by Nandi is \textbf{ Rs 500. }.}}[/tex]
[tex]\boxed{\textsf{ The amount shared by Thabo is \textbf{ Rs 1,000. }.}}[/tex]
Step-by-step explanation:
Given that Nandini and Thabo share Rs 1500 in the ratio 1:2 . And we need to find how much each gets . So lets take the given ratio be 1x :2x . Now here we can find the share of both as ,
[tex]\qquad\boxed{\boxed{\sf Share =\dfrac{ Ratio \ number }{Sum \ of\ ratio\ nos. }\times Amount }}[/tex]
Hence here the sum of ratio numbers would be 1+2 = 3 . Here the ratio number of Nandi is 1 and that of Thaboo is 2 . So ,
Share of Nandi :-
[tex]\sf\implies Share =\dfrac{ Ratio \ number }{Sum\ of\ ratio\ nos. }\times Amount \\\\\sf\implies Share_{(Nandi)}= \dfrac{1}{1+2}\times Rs\ 1,500 \\\\\sf\implies Share_{(Nandi)}= \dfrac{1}{3}\times Rs\ 1,500 \\\\\sf\implies \boxed{\pink{\frak{ Share_{(Nandi)}= Rs\ 500 }}}[/tex]
[tex]\rule{200}2[/tex]
Share of Thabo :-
[tex]\sf\implies Share =\dfrac{ Ratio \ number }{Sum\ of\ ratio\ nos. }\times Amount \\\\\sf\implies Share_{(Thabo)}= \dfrac{2}{1+2}\times Rs\ 1,500 \\\\\sf\implies Share_{(Thabo)}= \dfrac{2}{3}\times Rs\ 1,500 \\\\\sf\implies \boxed{\pink{\frak{ Share_{(Thabo)}= Rs\ 1,000 }}}[/tex]
A prize is divided in the ratio 2:5
If the smaller share is £50 what is
the larger share?
Answers
Answer:
125
Step-by-step explanation:
2:5
50: ?
50 divided by 2 = 25
25 times 5 is = ?
50:125
di sure kung tama ^^
how many dogs were household pets in the U.S in 2012, in scientific notation
Answers
Answer:
A
Step-by-step explanation:
how to solve (3x+2) (4x-9)
Answers
Answer:
=12x2−19x−18
Step-by-step explanation:
hope this helps :)
If you are looking for the values of X, they are 2/3, 9/4
3x+2=0
3x=2
X=2/3
4x-9=0
4x=9
X=9/4
If you are looking for the multiplication, it is on this picture:
1.)What is 74% of 44?
2.)105 is 42% of what number
3.)37% of what number is 19
4.)what is 8% of 83
5.)what % of 369 is 29
Answers
Answer:
Step-by-step explanation:
1.)What is 74% of 44? : 32.56
2.)105 is 42% of what number : 250
3.)37% of what number is 19 : 51
4.)what is 8% of 83 : 6.64
5.)what % of 369 is 29: 0.07%
Bacteria A has a growth rate of 0.68% per minute. Bacteria B has a growth rate of 0.012% per second. Determine which bacterium has a faster growth rate. Explain.
can someone help me with this
Answers
Answer:
bacteria A
Step-by-step explanation:it is growing at a faster rate
Answer: Bacteria A
Step-by-step explanation:
becasue the growth rate of bacteria a is growing faster than b
find the missing angle
Answers
Answer:
The missing angle is 109°
if chloe has 19 pets and 18 ran away and she got 198 new pets how much pets dose she have
Answers
Answer:
199
Step-by-step explanation:
please help and show work
Answers
Step-by-step explanation:
sides opposite to equal angles are equal in length :
angle45 = angle 45
r = s
by Pythagoras theorem :
r² + s² = (9√2 )²
s²+s²= 9 × 9 × 2
2s²= 9× 9×2
s²= 9 × 9
s= √9× 9
s = 9
r= s = 9 units .
plz mark my answer as brainlist plzzzz hope this will be helpful to you.
A babysitting job pays $4 per hour.
Which table shows the relationship between the number of hours worked and the total amount of money earned babysitting?
$4
O A
Hours Total Money
Worked Earned
1
$4
2
$4
3
$4
4
$4
C.
Hours Total Money
Worked Earned
1
2
$8
3
$12
4
$16
Hours Total Money
Worked Earned
Hours Total Money
Worked Earned
1
$4
2
$16
1
B.
D.
2
$4
$6
$8
3
3
$64
$256
4
4
$10
4
Answers
Answer:
1
2
$8
3
$12
4
$16
Step-by-step explanation:
Owen follows the rule divide by 2 to write the patteren below. He will write two more numbers to complete the pattern. which statement is true
800,400,200,100
A Every number in the pattern will have a 0 in its 10 place
B Every number in the patteren will have a 0 in its ones place
C Every number in the pattern will have a 0 or a 5 in its tens place
D Every number in the pattern will have a 0 or a 5 in its ones place
Answers
Answer:
None of these sound correct but I would say D
Step-by-step explanation: