(a). Consider the parabolic function f(x) = ax² +bx+c, where a ±0, b and care constants. For what values of a, band c is f
(i) concave up?
(ii) concave down?
[Verify your answer by MATHEMATICA and attach the printout of the commands and output]
Answers
Information about concavity is contained in the second derivative of a function. Given f(x) = ax² + bx + c, we have
f'(x) = 2ax + b
and
f''(x) = 2a
Concavity changes at a function's inflection points, which can occur wherever the second derivative is zero or undefined. In this case, since a ≠ 0, the function's concavity is uniform over its entire domain.
(i) f is concave up when f'' > 0, which occurs when a > 0.
(ii) f is concave down when f'' < 0, and this is the case if a < 0.
In Mathematica, define f by entering
f[x_] := a*x^2 + b*x + c
Then solve for intervals over which the second derivative is positive or negative, respectively, using
Reduce[f''[x] > 0, x]
Reduce[f''[x] < 0, x]
Related Questions
4. While they were out Christmas shopping, Mrs. Berry took
her family to eat at Olive Garden. Their bill total was $65. Since
it is the holiday season-they decided to leave a 25% tip. You
pay at the table at this restaurant. How much would Mrs. Berry
need to leave on the table, including the tip?
A. 81.25
B. 16.25
C.78.00
D. 13.00
Answers
Answer:
B. $16.25
Step-by-step explanation:
All you have to do is find 25% of $65 which is $16.25.
Answer:
C would be the correct answer.
Geez people are already doing Christmas shopping and thanksgiving is next week come on now. Lol I over react when I see Christmas in November.
Step-by-step explanation:
Hope this helps:)
What is 36:216 simplified?
Answers
Answer : 1/6
Explanation : If 216 is divided by 36, you will get your answer 1/6.
Find the slope of the line passing through the points (-8,3) and (-8,-6)
Answers
Answer:
-9/0
Step-by-step explanation:
(x1, y1) and (x2, y1)
(-8, 3) and (-8,-6)
slope/m = y2 - y1 / x2 -x1
= -6 -3 / -8 -(-8)
= -6 -3 / -8 + 8
= -9 / 0
if a child ticket is $5.20 and adult tickets are $9.90 and the total sale is $859.00 if there is 120 tickets total how many children tickets would there be
Answers
Answer:
11
Step-by-step explanation:
Evaluate.
(a – 2b)^3 when a= -3 and b = -1/2 Enter your answer in the box
Answers
Answer:
- 8
Step-by-step explanation:
Substitute the values for a and b into the expression
(- 3 - 2(- [tex]\frac{1}{2}[/tex] ) )³
= (- 3 + 1)³
= (- 2)³
= (- 2) × (- 2) × (- 2)
= 4 × - 2
= - 8
Help me with this question pls
Answers
Answer:
y=-0.25x+2
Step-by-step explanation:
the slope is down one over 4, or -0.25. The y intercept is 2, so b is +2
One metal alloy is 25% copper, while another is 50% copper. How much of each alloy should be used to make 1500g of metal alloy that is 40% copper?
Answers
Answer:
400g
Step-by-step explanation:
A die is rolled 10 times. Find the probability of rolling exactly 1 four.
Answers
Answer:
10 in 60 chance, or simplified to 1 / 6
Step-by-step explanation:
1 in 6 chance of rolling a four in one roll
Multiply both sides by 10
10 in 60
The probability of rolling exactly 1 four is [tex]1.65\times10^{-8}[/tex].
Given that, a die is rolled 10 times.
What is the probability?Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
We know that, probability of an event = Number of favorable outcomes/Total number of outcomes
When throwing die once, we get
Probability of getting 4 = 1/6
Now, a die is rolled 10 times
= [tex](\frac{1}{6} )^{10}[/tex]
= 1/60466176
= [tex]1.65\times10^{-8}[/tex]
Hence, the probability of rolling exactly 1 four is [tex]1.65\times10^{-8}[/tex].
To learn more about the probability visit:
https://brainly.com/question/11234923.
#SPJ2
Imma leave this here until someone answer it :))
Answers
Answer:
Step-by-step explanation:
1) x +y = 3
Subtract 'x' from both sides
y = -x + 3
2) x - 3y = 12
Subtract 'x' form both sides.
-3y = -x + 12
Divide the entire equation by (-3)
[tex]\dfrac{-3y}{-3}=\dfrac{-x}{-3}+\dfrac{12}{-3}\\\\\\y = \dfrac{1}{3}x-4[/tex]
3) 5x + 2y = 10
Subtract 5x from both sides
2y = -5x + 10
Divide the entire equation by 2
[tex]\dfrac{2y}{2}=\dfrac{-5x}{2}+\dfrac{10}{2}\\\\\\y = \dfrac{-5}{2}x + 5[/tex]
4) y = 6x + (1/3)
It is already in y =mx +b form
5)
[tex]y=\dfrac{1}{x}*x-15\\\\\\y = 1-15\\\\y = -14\\\\y=0x -14[/tex]
Karen is throwing an orange to her brother Saul, who is standing on the balcony of their home. The height h, in feet, of the orange above the ground t seconds after it is thrown is given by
h(t) = −16t2 + 32t + 2, 0 ≤ t ≤ 2.118.
If Saul's outstretched arms are 16 feet above the ground, will the orange ever be high enough so that he can catch it?
a. No. The orange will reach a maximum height of 4 feet.
b. Yes. The orange will reach a maximum height of 18 feet.
c. There is not enough information given to answer the question.
d. No. The orange will reach a maximum height of 2 feet.
e. Yes. The orange will reach a maximum height of 36 feet.
Answers
Answer:
Yes, the orange will be high enough so
that he can catch it because maximum height
attained if 20 ft.
Step-by-step explanation:
Plz help I need help
Answers
Answer: y = 6x
Step-by-step explanation:
This table portrays a straightforward proportion between x and y. y is very simply 6 times x.
Hope it helps :) and let me know if you want me to elaborate.
Is the value negative 10 to the left or right of a negative 5 on a horizontal number line?
Answers
hope it helped
Answer:
Step-by-step explanation:
there both 5MATH.QUESTION.HELP. BRAINILEST WILL BE GIVEN!!!
Answers
Answer:
C. [tex] 2 \dfrac{1}{3} [/tex]
Step-by-step explanation:
[tex]\dfrac{1}{3} \cdot 7 = \dfrac{1}{3} \cdot \dfrac{7}{1} = \dfrac{7}{3} = 2 \dfrac{1}{3}[/tex]
Please help me with this
Answers
Answer:
264 cm³
Step-by-step explanation:
Consider the L-shaped end of the figure. It is 7 cm wide, and 3+4 = 7 cm high. It can be considered to be a 7 cm square with a portion cut out of the upper right corner. That portion is a square that is 4 cm by 4 cm.
Then the area of the L-shaped end is ...
(7 cm)(7 cm) -(4 cm)(4 cm) = (49 -16) cm² = 33 cm²
The volume of the figure is the product of this area and the overall length, which is 8 cm.
V = Bh = (33 cm²)(8 cm) = 264 cm³ . . . volume of the figure
_____
Additional comment
There are other ways the volume can be figured. For example, it can be considered as a 7 × 8 × 3 cm block with a 3 × 4 × 8 cm block on top. That gives a volume of ...
V = LWH . . . . for each block
V = (7 cm)(8 cm)(3 cm) +(3 cm)(4 cm)(8 cm) = 168 cm³ +96 cm³ = 264 cm³
Use a coordinate plane to create a rectangular park that has one corner at (−412, 312) and a perimeter of 30 units. Label the coordinates of each corner of the park. Then plot points with mixed number coordinates inside the park to represent a swing set, a slide, and a bench. Plot the slide farthest from the x-axis and the bench closest to the x-axis. What are the coordinates of the points you plotted?
Answers
A rectangle has four sides, where the opposite sides are equal
The possible coordinates are: (-4.5, 3.5), (-4.5,10.5), (3.5,3.5) and (3.5,10.5)
The coordinate point is given as:
[tex]\mathbf{(x,y) = (-4\frac12,3\frac12)}[/tex]
Express as decimal
[tex]\mathbf{(x,y) = (-4.5,3.5)}[/tex]
The perimeter is said to be 30 units.
So, we have:
[tex]\mathbf{P = 2(L + W)}[/tex]
This gives
[tex]\mathbf{2(L + W) = 30}[/tex]
Divide through by 2
[tex]\mathbf{L + W = 15}[/tex]
This means that the sum of the dimensions is 15 units.
So, we can assume that:
Length = 8
Width = 7
So, the other coordinates are calculated as follows:
[tex]\mathbf{(x,y) = (-4.5,3.5+7) = (-4.5,10.5)}[/tex]
[tex]\mathbf{(x,y) = (-4.5 + 8,3.5) = (3.5,3.5)}[/tex]
[tex]\mathbf{(x,y) = (-4.5+8,3.5+7) = (3.5,10.5)}[/tex]
So, the possible coordinates are: (-4.5, 3.5), (-4.5,10.5), (3.5,3.5) and (3.5,10.5)
See attachment for the graph of the rectangle
Read more about rectangles at:
https://brainly.com/question/22010143
What is the ratio of 8 triangles to 10 stars in simplest form?
Answers
4:5
Steps:
A ways to find a ratio is finding what they both can be divided by, to turn them both into the simplest form.
8 and 10 can both be divided by 2
8/2 = 4
10/2 = 5
4 triangle: 5 stars
4:5
What is the slope and the y-intercept of the graph of y = 8/9x - 8
Answers
y-intercept: (0,-8)
If needed hope this answers your question!!
Kevin plans to retire in 30 years, and he plans to save up $250,000 for retirement. He has two options
• Plan 1: compounded monthly with an APR of 3.3%
• Plan 2: compounded quarterly with an APR of 3.5%
Compare these two options to see which one is more beneficial for Kevin. When you make the comparison,
you should at least calculate
1. the amount he needs to deposit each time period
2. the total interest accrued
Answers
The rate of growth of the amount invested with time in Plan 1 is slightly higher than the amount invested in Plan 2.
The option most beneficial to Kevin by comparison is Plan 1Reasons:
The number of years for the investment = 30 years
The amount he plans to save = $250,000
The investment plan options are;
Plan 1: Compounded monthly investment with APR, r = 3.5%
The formula for monthly contributions is presented as follows;
[tex]\displaystyle FV = \mathbf{\frac{PMT \cdot \left( 1 + \frac{r}{n}\right)^{n\cdot t} - 1}{\frac{r}{n} }}[/tex]
Which gives;
[tex]\displaystyle 250,000 = \mathbf{\frac{PMT \cdot \left( 1 + \frac{0.033}{12}\right)^{360} - 1}{\frac{0.033}{12} }}[/tex]
Solving gives;
The amount he needs to deposit each month, PMT ≈ $256.18The total deposit = 360 × $256.18 = $92,224.2
Total interest accrued = $250,000 - $92,224.2 ≈ $157,775.78Plan 2: Compounded quarterly, with APR, r = 3.3
Which gives;
[tex]\displaystyle 250,000 = \mathbf{\frac{PQT \cdot \left( 1 + \frac{0.035}{4}\right)^{120} - 1}{\frac{0.033}{4} }}[/tex]
The amount he needs to deposit each quarter ≈ $769.34The total deposit = $769.34 × 120 = $92,321.3336
Total interest accrued = $250,000 - $92,321.3336 ≈ $157,678.67
The total interest accrued by investing in plan 1 which is approximately
$157,775.78 is larger than the interest accrued on Plan 2 which is
approximately $157,678.67
The option most beneficial to Kevin is Plan 1, due to the higher total interest accruedLearn more here:
https://brainly.com/question/20382843
Which transformation of f(x) will produce the same graph as g(x)?
f(x) = 3x
g(x) = f(x) + 3
Answers
Answer:
its D.
Step-by-step explanation:
Answer:
its not D. I tried it and marked it wrong for some reason.
Step-by-step explanation:
happens to be this happaned a few times already but ill see whats up
Please help I will give brainliest
Answers
Answer: It goes 1/2 up each time
hope that helps i acc had some dfm on gradients
M=-1, b=2 write an equation of a line with the given slope m and y- intercept b
Answers
Answer:
y = - x + 2
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + b ( m is the slope and b the y- intercept )
Here m = - 1 and b = 2 , then
y = - x + 2 ← equation of line
If the radius of a right circular cylinder is doubled and height becomes 1/4 of the original height, then find the ratio of the curved surface areas of the new cylinder to that of the original cylinder.
Answers
Given info:-If the radius of a right circular cylinder is doubled and height becomes 1/4 of the original height.
Find the ratio of the Curved Surface Areas of the new cylinder to that of the original cylinder ?
Explanation:-
Let the radius of the right circular cylinder be r units
Let the radius of the right circular cylinder be h units
Curved Surface Area of the original right circular cylinder = 2πrh sq.units ----(i)
If the radius of the right circular cylinder is doubled then the radius of the new cylinder = 2r units
The height of the new right circular cylinder
= (1/4)×h units
⇛ h/4 units
Curved Surface Area of the new cylinder
= 2π(2r)(h/4) sq.units
⇛ 4πrh/4 sq.units
⇛ πrh sq.units --------(ii)
The ratio of the Curved Surface Areas of the new cylinder to that of the original cylinder
⇛ πrh : 2πrh
⇛ πrh / 2πrh
⇛ 1/2
⇛ 1:2
Therefore the ratio = 1:2
The ratio of the Curved Surface Areas of the new cylinder to that of the original cylinder is 1:2
help please i got absolutely no clue how to solve this
Answers
Answer:
A)
Step-by-step explanation:
To complete the square, we need to find such p and q that:
r^2 - 12r - 27 = (r - p)^2 - q = r^2 - 2pr + h^2 - q
Because we know that 2pr = 12r, then p = 6
(r - p)^2 - q = (r - 6)^2 - q = r^2 - 12r + 36 - q
We know that 36 - q = -27, so q = 36+27 = 63
Now we can solve for = 0
(r - 6)^2 - 63 = 0
(r - 6)^2 = 63
r - 6 = √63 or r - 6 = -√63
r = 6 + √63 = 6 + 3√7 or r = 6 - √63 = 6 - 3√7
A marketing analyst runs a bivariate regression model to forecast sales at a retail store based on advertising. Her model returns the following parameter estimates: b0: 145.7 b1: 99.1 Standard Error: 72.37 She wished to forecast sales for a store where advertising equals 163. What is the forecasted standard deviation of the sales distribution for this store
Answers
Answer:
yes sir
Step-by-step explanation:
6.8py
a train moves at a constant speed. it can travel 150 miles in 2 1/2 hours. how long will it take for the train to travel 360 miles
Answers
Answer:
6 hours
Step-by-step explanation:
It travels 150 miles in 2.5 hours. 150 ÷ 2.5 = 60. 360 ÷60 = 6
Answer:
6 hours
Step-by-step explanation:
Pls help im very tired and exhausted
Answers
Answer:
C that's right
I'm not wrong
Step-by-step explanation:
correct me if I'm wrong
(5x + 3) (3x2 + 4x + 4)
Answers
Answer:
dggdhdhdhshsjshdhdhhshshshshdhdhsbsbsbd
but if youre factoring its (5x + 3) • 2 (2x + 5)
How do you write 19/25 as a percentage?
Answers
Answer:
76%
Step-by-step explanation:
25*4=100
19*4=76
I need help with this question please
Answers
Answer:
w = [tex]\frac{t}{4}[/tex]
Step-by-step explanation:
We have t = 4w, the question is asking to rearrange the equation to make "w" the subject, meaning that we have to isolate the variable w.
When we have a number (usually known as a coefficient) next to a variable and want to get rid of it, we need to divide it by both sides. Therefore :
t = 4w
[tex]\frac{t}{4} =\frac{4w}{4}[/tex]
[[tex]\frac{t}{4} =w[/tex]]
Since "t" is an undefined variable and has no initial value, you cannot divide it by anything, therefore it'll stay as [t/4 = w]
You have $600,000 saved for retirement. Your account earns 5.5% interest. How much, to the nearest dollar, will you be able to pull out each
month, if you want to be able to take withdrawals for 20 years?
Answers
9514 1404 393
Answer:
$4127
Step-by-step explanation:
The amortization formula is good for finding this value.
A = P(r/12)/(1 -(1 +r/12)^(-12t))
where P is the amount invested at rate r for t years.
A = $600,000(0.055/12)/(1 -(1 +0.055/12)^(-12·20)) = $4127.32
You will be able to withdraw $4127 monthly for 20 years.
