Answer:
The maximum acceleration over that interval is [tex]A(6) = 28[/tex].
Step-by-step explanation:
The acceleration of this car is modelled as a function of the variable [tex]t[/tex].
Notice that the interval of interest [tex]0 \le t \le 6[/tex] is closed on both ends. In other words, this interval includes both endpoints: [tex]t = 0[/tex] and [tex]t= 6[/tex]. Over this interval, the value of [tex]A(t)[/tex] might be maximized when [tex]t[/tex] is at the following:
One of the two endpoints of this interval, where [tex]t = 0[/tex] or [tex]t = 6[/tex].A local maximum of [tex]A(t)[/tex], where [tex]A^\prime(t) = 0[/tex] (first derivative of [tex]A(t)\![/tex] is zero) and [tex]A^{\prime\prime}(t) <0[/tex] (second derivative of [tex]\! A(t)[/tex] is smaller than zero.)Start by calculating the value of [tex]A(t)[/tex] at the two endpoints:
[tex]A(0) = 10[/tex].[tex]A(6) = 28[/tex].Apply the power rule to find the first and second derivatives of [tex]A(t)[/tex]:
[tex]\begin{aligned} A^{\prime}(t) &= 3\, t^{2} - 15\, t + 12 \\ &= 3\, (t - 1) \, (t + 4)\end{aligned}[/tex].
[tex]\displaystyle A^{\prime\prime}(t) = 6\, t - 15[/tex].
Notice that both [tex]t = 1[/tex] and [tex]t = 4[/tex] are first derivatives of [tex]A^{\prime}(t)[/tex] over the interval [tex]0 \le t \le 6[/tex].
However, among these two zeros, only [tex]t = 1\![/tex] ensures that the second derivative [tex]A^{\prime\prime}(t)[/tex] is smaller than zero (that is: [tex]A^{\prime\prime}(1) < 0[/tex].) If the second derivative [tex]A^{\prime\prime}(t)\![/tex] is non-negative, that zero of [tex]A^{\prime}(t)[/tex] would either be an inflection point (if[tex]A^{\prime\prime}(t) = 0[/tex]) or a local minimum (if [tex]A^{\prime\prime}(t) > 0[/tex].)
Therefore [tex]\! t = 1[/tex] would be the only local maximum over the interval [tex]0 \le t \le 6\![/tex].
Calculate the value of [tex]A(t)[/tex] at this local maximum:
[tex]A(1) = 15.5[/tex].Compare these three possible maximum values of [tex]A(t)[/tex] over the interval [tex]0 \le t \le 6[/tex]. Apparently, [tex]t = 6[/tex] would maximize the value of [tex]A(t)\![/tex]. That is: [tex]A(6) = 28[/tex] gives the maximum value of [tex]\! A(t)[/tex] over the interval [tex]0 \le t \le 6\![/tex].
However, note that the maximum over this interval exists because [tex]t = 6\![/tex] is indeed part of the [tex]0 \le t \le 6[/tex] interval. For example, the same [tex]A(t)[/tex] would have no maximum over the interval [tex]0 \le t < 6[/tex] (which does not include [tex]t = 6[/tex].)
Please someone help me with this question...
Answer:
(❁´◡`❁)
Step-by-step explanation:
Solve the system by graphing.
y - X= 17
y = 4x + 2
The solution is?
pleae help me.!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
3/5
Step-by-step explanation:
I believe I'm right lol
Please help me, time sensitive
Answer:
1) Irrational
2) Rational
3) Irrational
4) Rational
5) Rational
Step-by-step explanation:
A rational number is one that can be expressed as a ratio of 2 integers while an irrational number is one that can not be expressed like that. Another difference is that rational numbers can have finite or recurring decimals while irrational numbers have infinite and non - recurring decimals.
1) -20π is an irrational number because π contains infinite decimal digits
2) -26.23 is a rational number because it can be expressed as a ratio of 2 integers
3) -2√3 is an irrational number because √3 contains infinite decimal digits
4) -√1 is a rational number because √1 is a perfect square root and as such it can be expressed as a ratio of 2 integers.
5) 95.60 is a rational number because it can be expressed as a ratio of 2 integers
>
The value of the expression 6x when x = 2 is
Answer:
12
Step-by-step explanation:
Answer:
12
Step-by-step explanation:
6x means 6 times x so when you replace x with 2 you get 6×2= 12
Which graph below best represents y = -2x +3?
Answer:
A.
Step-by-step explanation:
It's a little blurry to see the answers but I can assure you that A is the best answer because C has a y-intercept of 2 while A is higher in which it is placed at 3.
I GIVEEE BRAINLILSTTT
Answer:
T 9,9
U 0,9
V 8,10
because it's a reflection over y axis, everything negative will be positive
Answer:
Below
Step-by-step explanation:
The x's will be the opposite (y's will stay the same):
T=(9,9)
U=(0,9)
V=(8,10)
A company spent 35% of its annual budget building a new machine. How much of the
companies budget was spent on the machine if annual budget is $25,000?
divide -3x^3-4x^2+4x+3 by x-2
Answer: -3x^2-10x-16
Step-by-step explanation:
Zoey read 2 books in 12 months. What was her rate of reading in books per month?
Answer:
6 months per books it's the answer
Complete each congruence statement by naming the corresponding angle or side (odd questions only)
Answer/Step-by-step explanation:
5. Given that ∆FGH ≅ ∆TSU, all three angles and sides of ∆FGJ are congruent to all corresponding angles and sides of ∆TSU.
Thus:
Since, <HFG in ∆FGH corresponds to <UTS in ∆TSU, therefore:
<HFG ≅ <UTS
7. Given that ∆FGH ≅ ∆FGL, the following are the corresponding sides and angles:
FG ≅ FG
GH ≅ GL
FH ≅ FL
<FGH ≅ <FGL
<FHG ≅ FLG
<GFH ≅ GFL
Jalen says that 60% of his teammates are over 70 inches. Is Jalen's statement correct? 73, 61, 62, 59, 75, 60, 74, 75, 78, 69, 70
A. No, because there are 5 players with a height greater than 70 inches and that's about 45% of the players B. Yes, there are at least 9 players with a height of at least 70 inches and that is 60% of the players C. No, there is one player with a height of 70 inches and that is 9% of his teammates. D. Yes, because the median height of the ponies is 60 and 60% of the ponies would be taller
Answer:
A
Step-by-step explanation:
5/11 X 100% = 45.45%
Find the midpoint of A and B where A has coordinates (-3,-5) and B has coordinates (4,4).
Answer:
([tex]\frac{1}{2}[/tex], [tex]\frac{-1}{2}[/tex])
Step-by-step explanation:
Use the midpoint formula to solve.
1) Given 2 points: ([tex]x_{1}[/tex], [tex]y_1[/tex]) and ([tex]x_2[/tex], [tex]y_2[/tex])
The midpoint formula would be ([tex]\frac{x_1+x_2}{2}[/tex], [tex]\frac{y_1+y_2}{2}[/tex]).
2) Based on this, we can easily find the midpoint of AB.
-3 would be [tex]x_1\\[/tex] -5 would be [tex]y_1[/tex] 4 would be [tex]x_2[/tex] the next 4 would be [tex]y_2[/tex]3) With this information, we can solve for the midpoint.
([tex]\frac{-3+4}{2}[/tex], [tex]\frac{-5+4}{2}[/tex]) --> ([tex]\frac{1}{2}[/tex], [tex]\frac{-1}{2}[/tex]) --> This is your answer.
Question # 5 What is the constant of proportionality in the following equation? b = 1.25c
Answer:
someone will be with you in a moment
Step-by-step explanation:
Find 4/5 of 6/9 in simplest form
9514 1404 393
Answer:
8/15
Step-by-step explanation:
In this context, "of" means "times." The product is ...
[tex]\dfrac{4}{5}\times\dfrac{6}{9}=\dfrac{4\cdot6}{5\cdot9}=\dfrac{3\cdot8}{3\cdot15}=\boxed{\dfrac{8}{15}}[/tex]
Find the mean, median, mode and range of the following data
set:
13, 2, 20, 20, 14, 16, 20, 30, 3, 40
Answer:↓↓
Step-by-step explanation:
2, 3, 13, 14, 16, 20, 20, 20, 30, 40
Mean: the average of a data set.
2 + 3 + 13 + 14 + 16 + 20 + 20 + 20 + 30 + 40 / 10 = 178/10 = 17.8
Median: the middle of the set of numbers.
16 + 20 / 2 = 36/2 = 18
Mode: the most common number in a data set.
20
Range: The difference of the smallest and highest number.
40 - 2 = 38
find the volume of figure B. round your answer to two decimal places
Answer:
468.75 m³Step-by-step explanation:
Figure A has volume of 30 m³
Figure B is similar to figure A and the scale factor is:
5/2 = 2.5Volume is the product of three dimensions, therefore the volume of B will be greater by:
2.5×2.5×2.5= 15.625 times than AThe volume of B is:
30*15.625 = 468.75 m³Geometry i need help now and could you tell me the name of the subject
Answer:
x = 16Step-by-step explanation:
5, 7 and 8 are midsegments of the given triangle.
As per property, midsegment is parallel to one of the sides and is equal to its half by measure.
Midsegment with the length of 8 is parallel to side with the length of x and is half of its size:
x/2 = 8x = 8*2x = 16Plz help brainlest if correct
Quickly
What is the rate of change and initial value for the linear relation that includes the points shown on the table?
X Y
1 20
3 10
5 0
7 -10
A. Initial value: 20, rate of change:10
B. Initial Value: 30, rate of change:10
C. Initial Value: 25, rate of change: -5
D.Initial value: 20, rate of change: -10
Answer:
D.Initial value: 20, rate of change: -10
Step-by-step explanation:
As you see, it starts with x=1, y=20 so the initial value is 20 and as x goes up y changes by -10 so thats ur rate of change
Hope this helps! :)
what is 2 1/4 . 9/5?
Answer:
0.05
Step-by-step explanation:
Kevin has a stack of newspapers. Each one weighs 15 pounds. The entire stack weighs 4
1
2
pounds. How many newspapers are in the stack?
Answer:7
Step-by-step explanation:
does anyone know how to solve this? and if so can you put an explanation? ive been struggling with this question for a while
Answer:
x = 31
Step-by-step explanation:
So, the angle of a line is 180 degrees. This is a very important fact, because this means that (5x - 16) + (x + 10) = 180 degrees.
Note: The parenthesizes are not needed, but I put them there to symbolize the adding of those two angles that make up the line.
Adding like terms, we get:
6x - 6 = 180
Move the -6 over to the right side.
We get:
6x = 186
Dividing both sides by 6, we get the value of x:
x = 31
If you have any questions, please don't be afraid to ask!
PLEASE HELP. EMERGENCY THIS IS TIMED! It's about translations. I will mark brainiest!
Nancy and Lisa played 20 sets of tennis. Nancy won 12 of them. If they
played 60 sets, how many would Lisa win?
Answer:
36
Step-by-step explanation:
20*3=60
12*3=36
Its proportional
Answer:
36
Explanation:
60/20=3
12x3=36
Solve the Equation for f: -2/3f-4=10
50 Points
Answer:
f= -21
Step-by-step explanation:
please mark brainlliest if you want.
Answer:
F=-21
Step-by-step explanation:
-2/3f-4=10
Multiply both sides
-2f-12=30
Add 12 to 30
-2f=42
Divide by -2
F=-21
a submarine dives 20 meters each minute. what is the total change in depth after 10 minutes
Answer: 200 Meters after 10 minutes.
Step-by-step explanation:
To find the answer you must multiply 20 for every minute.
Hope this helped :D
Pls answer if you know the ANSWER
Answer:
I was going to answer then I realized I don't know the answer. Sorry.
Step-by-step explanation:
PLEASE HELP!!!!!!!!!!!!
9514 1404 393
Answer:
a Plane FGI
Step-by-step explanation:
A plane is named either by its designator (Q) or by three non-collinear points in the plane. Here, the point I must be used, as the other designated points in the plane are all on the same line. The appropriate choice is ...
Plane FGI
Find the value of x, please help
Answer:
x = 90 (verified answer) ✅Step-by-step explanation:
There are 360° of measure in a quadrilateral. By the definition of a parallelogram, we know that the angle opposite the labeled angle will have the same measure as that labeled angle.
So, 12x + 12x + 8x + 8x = 360
Simplifying all the x's gives us:
40x = 360
Divide by 40
x = 90
Now, we check this
40 (90) = 360
360 = 360 ✅
PLEASE ANSWER ASAP FOR BRAINLEST!!!!!!!!!!!!!!
Elena gets a base pay of $1,500 per month. She also earns a commission of 8% of the total sales dollars that she makes. What are Elena’s earnings for a month in which she has sales of $32,000?
Answer:
You have to divide the total sales by 8 percent. 32,000/ 0.8 =40,000
So your answer is 40,000.
Step-by-step explanation:
Answer:
4060
Step-by-step explanation:
8/100(32000)+1500=4060