Answer:
484feet
Step-by-step explanation:
If the height as a function of time could be modeled by the function h(t)=−16t^2 +16t+480, where t is the time in seconds and h is the height in feet.
The maximum height of Jason occurs when dh/dt = 0 (velocity is zero)
dh/dt = -32t + 16
0 = -32t + 16
32t = 16
t = 16/32
t = 1/2
t = 0.5secs
Get the maximum height
Recall that h(t)=−16t^2 +16t+480
Substitute t = 0.5
h(0.5)=−16(0.5)^2 +16(0.5)+480
h(0.5) = -4 + 8 + 480
h(0.5) = 4 + 480
h(0.5) = 484
Hence the maximum height reached by Jason is 484feet
The maximum height that Jason reaches is h = 484 feet and it will be reached at t = 0.5 sec.
How to find the maximum of a polynomial function?Let the function be denoted by [tex]y = f(x)[/tex]
If it is twice differentiable, then, firstly, we differentiate it with respect to x and equate with 0 to find the critical values.
Let the obtained critical values be [tex]x_1, x_2, ... x_n[/tex]
The second derivative of that function is then evaluated on those critical values.
The [tex]i^{th}[/tex] critical value has got the maximum if [tex]f''(x_i) < 0[/tex]
That means, if at [tex]x = x_i[/tex] , we get
[tex]f'(x-i) = 0\\and\\f''(x_i) < 0[/tex]
Then that point is where function will have maximum.
If [tex]f''(x_i) > 0[/tex], then the point where the function will have minimum
If value of second rate at point [tex]x_i[/tex] is 0, then we go for third rate of function and check the same facts so on for upper rate(if they exist).
For the given case, we're given the height function as:
[tex]h(t) = - 16t^2 + 16t + 480[/tex]
The function is infinitely differentiable as its polynomial(by a theorem).
Its first and second rate with respect to 't', we get;
[tex]h(t) = - 16t^2 + 16t + 480\\h'(t) = -32t + 16\\h''(t) = -32 < 0[/tex]
Thus, all critical points will be maximum points.
The critical points are evaluated by [tex]h'(t) = 0[/tex]
They are calculated as:
[tex]h'(t) = 0\\-32t + 16 = 0\\t = 0.5 \: \rm sec[/tex]
The height at t = 0.5 s is evaluated as:
[tex]h(0.5) = - 16(0.5)^2 + 16(0.5) + 480 = 484 \: \rm feet[/tex]
Thus, at time 0.5, the height function will be at its maximum value(484 feet). That means, the height of Jason will be maximum when time will be 0.5 seconds from initial time.
Learn more about maximum and minimum values here:
https://brainly.com/question/13333267
The lenght of a turtles shell z, in millimeters, is related to the turtles age in years a , as described by the equation below.
s=55a+37
Which statements about the turtle are true?
Select 3
Answer:
B, C , F
Step-by-step explanation:
The age multiplied 55, so the shell grows at rate of 55mm per year
in fact if the age is 2 we have (55 x 2) = 55 + 55
if 3 = (55 x 3) = 55 + 55 + 55
and so on
When the turtle is hatched the shell is 37 mm in lenght.
In fact, if we substitute 0 to a, we have
s = (55 x 0) + 37
s = 37
when the turtle is 1 year old, the shell is 92 mm in length.
in fact if we substitu a with 1, we have
s = (55 x 1) + 37
s = 55 + 37
s = 92
ASAP!!! and no links please 25 points!!!!!
The radius of a can of soda is 0.75 inches. Find the area of the top of the can. Round to the nearest hundredth.
(Values only! No units!)
Answer:
2.36
Step-by-step explanation:
Multiply the radius (0.75) with the value of pi (3.14.....)
0.75 x pi = area
area = 2.35619449019
ROUNDED TO HUNDREDTHS = 2.36
hope this helps :)
PLEASE HELP THANK YOU
Answer:
thanks you too for having us
How many more brooms must each earn in order to have enough credit to get a month off with pay?
Answer:
5
Step-by-step explanation:
Eric carved this solid out of wood.
Find the volume of the solid
Answer:
3,456
Step-by-step explanation:
Just did the question and got it correct.
Hope this helps ;)
2/5 of the flowers in Veronica's garden are marigolds. If there are 55 flower plants in her garden, how many marigold plants does she have?
Answer:Veronica has 22 marigold plants
Step-by-step explanation:
Total Number of flower plants in her garden=55
fraction of flower plants which are marigolds=2/5
Number of flower plants which are marigolds=2/5 x Total Number of flower plants in her garden
=2/5 x 55
=22
Observa las siguientes imágenes formadas por círculos:
Figura 1 (un circulo) Figura 2 (5 círculos)
-¿Cuántos círculos tendrá la Imagen 10?
-¿Cuántos círculos más tendrá la imagen 12 respecto de la imagen 7? ¿Puedes saberlo sin necesidad de encontrar la cantidad de círculos de cada imagen? ¿Cómo?
Veremos que en la imagen 10 hay 37 circulos, y la diferencia entre las imagenes 12 y 7 es de 20 circulos.
¿Como encontrar el patrón?
Primero, debemos contar la cantidad de circulos que tenemos en las imagenes mostradas.
En la primera, tenemos 1 circulo.En la segunda, hay 5 circulos.En la tercera, hay 9 circulos.En la cuarta, hay 13 circulos.Entonces podemos ver que en cada imagen se agregan 4 circulos, es decir tenemos una secuencia aritmetica, de tal forma que la imagen número N tendremos:
[tex]C_N = 1 + (N - 1)*4[/tex]
Entonces, cuantos circulos hay en la imagen 10? para ver eso reemplazamos N por 10.
[tex]C_{10} = 1 + (10 - 1)*4 = 37[/tex]
¿Cuántos círculos más tendrá la imagen 12 respecto de la imagen 7?
Para ver esto calculamos:
[tex]C_12 - C_7 = (1 + (12 - 1)*4) - (1 + (7 - 1)*4) = 11*4 - 6*4 = 20[/tex]
Es decir, la image 12 tiene 20 circulos más que la imagen 7.
Sí quieres aprender más sobre secuencias, puedes leer:
https://brainly.com/question/7882626
A woman is rowing a boat across a 60 wide river from west to east. She can row at 2 mph in still water, but the river's current is 5 mph from north to south. To the nearest foot, how far downstream on the east bank will she land?
Answer:
S, and the other day. I have been a while. I have a great drea the most important things. The may have to pay a fee of the most popular and I will not 66 the most of the most of my life. I was a bit of the best, but the 15th. I have been a while. I am your what is happening in the next couple days 6 the most of the most of the most
Step-by-step explanation:
popular and I will not be hurt by a friend of the day, and the other side, I think I have a great drea, I think I have been a while. I have been in touch. Thanks for the next day delivery. We have a great drea the same time. I was just the right place for the use of the most of the most popular and I am a beautiful person. The comments for your email.
The woman will land on the east bank of the river at a downstream of 37.5 miles.
What is meant by relative velocity ?Relative velocity of an object in motion is defined as the velocity of the object with respect to another object.
Here,
Width of the river, W = 60 miles
Velocity of the boat in still water, Vb = 2 mph
Velocity of river, Vr = 5 mph
Relative velocity of the boat with respect to river in downstream,
Vbr = Vb + Vr
Vbr = 8 mph
Drift of the boat, d = Vr W/Vbr
d = 5 x 60/8
d = 37.5 miles downstream
Hence,
The woman will land on the east bank of the river at a downstream of 37.5 miles.
To learn more about relative velocity, click:
https://brainly.com/question/19260269
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(HALP ILL GIVE BRAINLY AND IS A MULTIPLE CHOICE) no links or I will report
Answer: the correct answer is answer (4) (2,4)
Step-by-step explanation:
I hope you get it right :)
based on the table, what is the slope,m, and y-intercept , b , on the line that models this relationship?
Answer: slope: 180 y intercept: -360
I hope this helps!
Arthur went to dinner. The meal cost $157 and
he wants to leave an 18% tip. How much money
should he leave for the tip?
Arthur should leave a $28.26 tip
Consider this right triangle with given measures.
What is the length of the missing leg?
Answer:
The answer is 6 feet.
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
Find the measure of AC
Answer:
7 inch
Step-by-step explanation:
AC= BC+AB
= (BD-CD) + radius of B
= (radius of B-radius of D) + 4.5
=(4.5-2) +4.5
=2.5+ 4.5
=7 inch
I hope this is correct.
A marine biologist measured one fish that was 9/10 of a foot long and a second fish that was 7/10 of a foot long. How much longer was the first fish?
Write your answer as a fraction or as a whole or mixed number.
Answer:
2/10 of a foot long.
Step-by-step explanation:
Answer:
The first fish was 1/3 of a foot longer.
mark me brainlest
Step-by-step explanation:
1/2=3/6
3/6>1/6
3/6-1/6=2/6
2/6 / 2/2
1/3
Can someone please help me with this math problem please:):)
Answer:
y = 126° + 29° = 155°
Step-by-step explanation:
I think this may be a solution:
126°+29°=155°
So, y=155°
the diagram shows a track composed of a rectangle with a semicircle on each end. the area of the rectangle is 4,000 square meters. what is the perimeter of the track?
Answer:14400
160
=
90
Step-by-step explanation: 90
⋅
π
=
90
π
→
If you are using an approximation such as 3.14 for
π
, multiply that by 90
Add
160
⋅
2
to the circumference since the lengths of the rectangle are also part of the perimeter.
160
⋅
2
=
320
90
π
+
320
Which expression shows 3 decreased by the sum of 11 and a number? A. 3-(11+x) B. (11+x)-3 C. 3-11+x D. 3+11x
Answer:A
Step-by-step explanation:
Answer:
The correct answer Its A. 3-(11+x)
PLEASE HELP ME I WANT TO PASS THIS CLASS AND GRADUATE WILL GIVE BRAINLIEST
A recent study of high school students shows the percentage of females and males who have at LEAST one notation in their school record for inappropriate behavior. A simple random sample of high school students was interviewed. The students were asked whether they had a notation for inappropriate behavior in their school record. Of the 100 females, 21 answered yes, as did 145 of the 400 males.
Part A: Construct and interpret a 99% confidence interval for the difference in population proportions of females and males who have at LEAST one notation for inappropriate behavior. Be sure to state the parameter, check conditions, perform calculations, and make conclusion(s). (8 points)
Part B: Does your interval from part A give convincing evidence of a difference between the population proportions? Explain. (2 points)
lol the handwriting hurts
Answer:
other person!
Step-by-step explanation:
give the other person brainliest; hope you pass the class!
Can somebody help me with one of these i literally don’t get it.
Answer:
basically multiply the height and the base (area), using the two numbers shown. Just add for perimeter. Just use a calculator, no one really cares about doing it them selves
Step-by-step explanation:
Answer:
Step-by-step explanation:
log(x+4)=logX + log4
Answer:
log
(
x
+
4
)
=
log
(
x
)
+
log
(
4
)
=
log
(
4
x
)
, so
x
+
4
=
4
x
, hence
x
=
4
3
Step-by-step explanation:
If the diameter is 26 inches, what is the radius
Answer:
13 inches
Step-by-step explanation:
In any circle, the radius is always half of the diameter.
So, the diameter can be found by multiplying the radius by 2, and the radius can be found by dividing the diameter by 2.
Since the diameter is 26 inches, we can divide this by 2 to get the radius
26/2
= 13
The radius is 13 inches
Answer:
[tex] \bf \huge13[/tex]
Step-by-step explanation:
Given that : the diameter is 26 inches.to find :what is radius .formulas used :radius = diameter / 2explanation :we know that,
finding the radius
⟼ diameter = 26 inches
⟼ radius = diameter / 2
⟼ radius = 26 / 2 inches
⟼ radius = 13 / 1 inches
⟼ radius = 13 inches.
∴ radius is 13 inches .
can someone please help me with this?
There are 5 people at a party. They decide to share 3 ice cream sandwiches equally.
Which model shows how much of the ice cream sandwiches each person will get?
C.
D
Answer:
your answer will be D. I think :)
Answer: d
i have the test
Question 5 (1 point)
Which statement about segregation in Arkansas following Reconstruction is true?
The United States Supreme Court supported segregation.
O Governor Clayton put a stop to segregation.
Only public transportation was segregated
The federal government resisted efforts to segregate.
Answer:
Step-by-step explanation:
The answer is the United states Supreme Court suported segreation
Layna can paint a 350-square foot room in 4 hours. It takes Bebe 7 hours to paint the same room. Which equation can be used to find the time in hours, t, it takes Layna and Bebe to paint the room together?
Answer:
A. 1/4t+1/7t=1
Step-by-step explanation:
The measure of ABD is (0.18x + 67) degrees and the measure of CBD is (0.07 + 48) degrees. Find the value of X
Answer:
See Explanation
Step-by-step explanation:
Given
[tex]ABD = 0.18x +67[/tex]
[tex]CBD = 0.07x + 48[/tex]
Required
Find x
The question is incomplete as the relationship between ABD and CBD is not stated.
Assume ABD = CBD
The solution is:
[tex]0.18x + 67 = 0.07x + 48[/tex]
Collect like terms
[tex]0.18x - 0.07x= - 67 + 48[/tex]
[tex]0.11x= -19[/tex]
Solve for x
[tex]x = -\frac{19}{0.11}[/tex]
[tex]x = -172.72[/tex]
Assume ABD and CBD are supplementary
The solution is:
[tex]ABD + CBD=180[/tex]
[tex]0.18x + 67 + 0.07x + 48 = 180[/tex]
Collect like terms
[tex]0.18x + 0.07x = - 48 - 67 + 180[/tex]
[tex]0.25x = 65[/tex]
Solve for x
[tex]x = \frac{65}{0.25}[/tex]
[tex]x = 260[/tex]
Assume ABD and CBD are complementary
The solution is:
[tex]ABD + CBD=90[/tex]
[tex]0.18x + 67 + 0.07x + 48 = 90[/tex]
Collect like terms
[tex]0.18x + 0.07x = - 48 - 67 + 90[/tex]
[tex]0.25x = -25[/tex]
Solve for x
[tex]x = \frac{-25}{0.25}[/tex]
[tex]x = -100[/tex]
Ryan's take-home pay is $2,500 each month. The amount for gas is $125. Calculate the percentage Ryan uses on gas from his take-home pay. please help!! O^O
Answer: 5%
Step-by-step explanation:
Since Ryan's take-home pay is $2,500 each month and the amount for gas is $125.
The percentage that Ryan uses on gas from his take-home pay will be:
= Amount used on gas / Take home pay × 100
= 125/2500 × 100
= 1/20 × 100
= 5%
He used 5% on gas.
HELP ASAP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
3. Use the information about the m<2 and m
determine the missing information.
m22 = 97°
m26 = 83°
m
2
5
m2 3 =
m2 5 =
3
4
7
8
m210 =
m2 7 =
9
10
13
14
m2 9 =
m216 =
$
11
12
15/16
Answer:
m<3 = 97
m<10 = 97
m<9 = 83
m<5 = 97
m<7 = 83
m<16 = 97
Step-by-step explanation:
m<3 = m<2 because of vertical angles
m<10 = m<2 because of corresponding angles
m<9 + 97 = 180
m<9 = 83
m<5 + 83 = 180
m<5 = 97
m<7 = m<6 because of vertical angles
m<16 = m<5 because of alternate exterior angles.
Find the equation parallel to y = -x - 5 and passing through (-3, -3)
Answer:
y = -x - 6
Step-by-step explanation:
If it's parallel, then it means that the slope will remain the same. The slope is
-1.
To find the y-intercept, you need to plug the coordinates into the equation,
y = -1x + b
-3 = -1(-3) + b
-3 = 3 +b
-6 = b
The equation is y = -x - 6
louise decided to purchase a new mountain bike when he saw the sporting good store was offering 20% off their bike. what is the total cost of the mountain bike if the originally price at $249 and louise must pay 7.5% sales tax