(a) It looks like you're saying
[tex]\displaystyle F(x) = \int_0^x (t - 3t^2 + 7) \, dt[/tex]
Find the critical points of F(x). By the fundamental theorem of calculus,
F'(x) = x - 3x² + 7
The critical points are where the derivative vanishes. Using the quadratic formula,
x - 3x² + 7 = 0 ⇒ x = (1 ± √85)/6
Compute the second derivative of F :
F''(x) = 1 - 6x
Check the sign of the second derivative at each critical point.
• x = (1 + √85)/6 ≈ 1.703 ⇒ F''(x) < 0
• x = (1 - √85)/6 ≈ -1.370 ⇒ F''(x) > 0
This tells us F attains a minimum of
[tex]F\left(\dfrac{1-\sqrt{85}}6\right) \approx \boxed{-6.080}[/tex]
(b) Split up the domain of F at the critical points, and check the sign of F'(x) over each subinterval.
• over (-∞, -1.370), consider x = -2; then F'(x) = -7 < 0
• over (-1.370, 1.703), consider x = 0; then F'(x) = 7 > 0
• over (1.703, ∞), consider x = 2; then F'(x) = -3 < 0
This tells us that
• F(x) is increasing over ((1 - √85)/6, (1 + √85)/6)
• F(x) is decreasing over (-∞, (1 - √85)/6) and ((1 + √85)/6, ∞)
(c) Solve F''(x) = 0 to find the possible inflection points of F(x) :
F''(x) = 1 - 6x = 0 ⇒ 6x = 1 ⇒ x = 1/6
Split up the domain at the inflection point and check the sign of F''(x) over each subinterval.
• over (-∞, 1/6), consider x = 0; then F''(x) = 1 > 0
• over (1/6, ∞), consider x = 2; then F''(x) = -11 < 0
This tells us that
• F(x) is concave up over (-∞, 1/6)
• F(x) is concave down over (1/6, ∞)
Which choice is equivalent to the product below?
V8,5
O A. 4/10
O B. 10-12
C. 13
O D. 22/10
Answer:
Option D
2√10
Step-by-step explanation:
√8 • √5 = √8 × 5 = √40 = 2√10
Thus, √8 • √5 = 2√10
-TheUnknownScientist 72
What is the slope of the line (1,4) (3,2)
Step-by-step explanation:
the slope is the ratio of "y coordinate change / x coordinate change".
so, in our case here
x changes by +2 (from 1 to 3).
y changes by -2 (from 4 to 2).
so, the slope is -2/2 = -1.
Help help math math
Answer:
There are 24 different combinations.
Step-by-step explanation:
2x4x3= 24
PLEASE HELP
no linkss
Answer:
-5.2, -4.75, -9/2
Step-by-step explanation:
Max's parents bought $8,000 from the bank for a new car. The interest rate is 6% per year. How much simple interest will they pay if they take 3 years to repay the loan?
Answer:
1440
Step-by-step explanation:
LAST ATTEMPT IM MARKING AS BRAINLIEST!! (Draw a dilation of the figure using the given scale factor )
Answer:
A (2,2) B (2,4) C (3,2) D (3,3)
Step-by-step explanation:
K = 1/2
K is the scale factor so the distance between points will be cut in half
A 4,4 new 2,2
B 4,8 new 2,4
C 6,4 new 3,2
D 6,6 new 3,3
Answer:
A = (2,2)
B = (2,4)
C = (3,2)
D = (3,3)
Step-by-step explanation:
Leave a brainliest if this helped
can someone please find the slope for this?
Which of the following sequences below is a Geometric Sequence?
Select one:
a. -8, -3, 2, 7, ....
b. 1, 3, 9, 27, ....
c. 8, 4, 0, -4, ...
d. 2, 4, 6, 8, ...
B. 1, 3, 9, 27
Geometric Sequence is being multiplied by factor of 3.
TE Irene has a collection of 32 dolls that have either blue eyes or green eyes. She has 14 more green-eyed dolls than blue-eyed dolls. How many dolls of each type does Irene have? Let x represent the number of green-eyed dolls. Let y represent the number of blue-eyed dolls.
The formula
x + y = 32
Find our X value
y + 14 = x
Sub for x
(y + 14) + y = 32
Remove Parathesis
y + 14 + y = 32
Add
2y + 14 = 32
Subtract
2y = 18
Divide
y = 9
Sub for y
x + 9 = 32
Subtract
x = 23
Double Check:
9 + 14 = 23
23 + 9 = 32
I hope this helps! :)
For the following problem, y varies directly as x If y = 34 when x = 4 , find y when x is 3.
Answer:
Step-by-step explanation: plug in 3 for X and then solve
Give me 5 stars
Directions: Compare the sides and angles by filling in the blank with a < or > symbol.
The correct comparison as shown in the figures are:
QR < QSAB > CDm<FJG > m<HJGm<QSP > m<QSRFrom the given diagram, we are to fill in the blank spaces with a < or > symbol.
21) The measure of the angles is a function of the measure of the sides.
Since the angle facing the side QR is less than that of QS, hence QR < QS
22) Similarly for this figure, the angle facing the side AB is greater than that of CD, hence AB > CD
23) Also, for this figure, the side facing the angle m<FJG is greater than the side facing the angle m<HJG, hence m<FJG > m<HJG
24) Also, for this figure, the side facing the angle m<QSP is greater than the side facing the angle m<QSR, hence m<QSP > m<QSR
Learn more on angles here: https://brainly.com/question/16281260
can you help me solve 4x - 15 = 17 - 4x
[tex]4x-15 = 17-4x\\\\\implies 4x +4x = 17 +15\\\\\implies 8x = 32\\\\\implies x = \dfrac{32} 8\\\\\implies x = 4[/tex]
Need help find the value of x
A2 + B2
Best answer gets a brainliest and thank and 5 star
Answer:
a+b)(a-b)
(Step-by-step explanation:
40% of the plants in Marcy's garden are root vegetables. If 20 plants are root vegetables, how many plants are in Marcy's garden in all?
Answer:
dont do anything if im wrong but i thinks its 50 plants
Step-by-step explanation:
EUse the Fundamental Theorem of Calculus to find y′. pls help
Use This Since You provided no context:
The fundamental theorem of calculus is a theorem that links the concept of differentiating a function (calculating the gradient) with the concept of integrating a function (calculating the area under the curve). ... This implies the existence of antiderivatives for continuous functions.
1) f(4) = g(4)
2) f(4) = g(-2)
3) f(2) = g(-2)
4) f(-2) = g(-2)
Answer: 4)
Step-by-step explanation:
f(4) = -14
g(4) = 10
g(-2) = 4
f(2) = -8
f(-2) = 4
The correct statement is 4) f(-2) = g(-2)
Or by inspection, we can see that the graph f(x) intersects g(x) at x = -2 and y = 4. So, f(-2) = g(-2) = 4 is true
What is the greatest possible error for a measurement of 2 fluid Ounces?
Answer:
2.35
Step-by-step explanation:
2 x 2 eqaul 9 times 2
rotate point B about point F 288 degrees clockwise
When a shape is rotated, it must be rotated through a point
The new position of point B is point A
The angle of rotation is given as:
[tex]Angle = 288^o[/tex]
The shape is a regular pentagon (with 5 sides).
The smallest angle of rotation that maps the pentagon onto itself is calculated using:
[tex]\theta = \frac{360}n[/tex]
So, we have:
[tex]\theta = \frac{360}5[/tex]
[tex]\theta = 72[/tex]
Let the number of rotations be n.
So, we have:
[tex]\theta \times n= Angle[/tex]
This gives
[tex]72 \times n= 288[/tex]
Divide both sides by 72
[tex]n= 4[/tex]
This means that the new position of B is 4 points away from B.
Point A is 4 points away from B, in clockwise direction
Hence, the new position of point B is point A
Read more about rotation at:
https://brainly.com/question/2283733
Which of the following integers is less than -23?
a) o
b) -13
c) 13
d) -25
Answer:
i think d) -25 is answer
Step-by-step explanation:
good luck
Answer:
d) -25
Step-by-step explanation:
Because -25 is less than -23 . as it is negative integers
Please hurry and answer!
This graph gives growth of a plant overtime what is the slope of the line, and what does the slope mean in situation
select from the drop down menus to correctly complete the statement
The slope is blank which means that the plant blank by blank everyday
Using the slope of the linear function, it is found that:
The slope is of 0.5, which means that the plant grows by 0.5 inches each day.A linear function is modeled by:
[tex]y = mx + b[/tex]
In which:
m is the slope, which is by how much the output y changes when the input x changes by 1.b is the y-intercept, which is the value of y when x = 0.In this problem:
x is the time in days.y is the height in inches.Two of the points are: (0,0) and (2,1).
The slope is given by change in y divided by change in x, hence:[tex]m = \frac{1 - 0}{2 - 0} = \frac{1}{2} = 0.5[/tex]
Then, applying the interpretation:
The slope is of 0.5, which means that the plant grows by 0.5 inches each day.To learn more about slopes and linear functions, you can take a look at https://brainly.com/question/16302622
Answer:
hes correct. the slope is 0.5 and it grows 0.5 inches everyday
Step-by-step explanation:
Is this table proportional?
XY
1 3 3
4 12
5 15
7 21
A number is between 63 and 68 It has prime factors of 2 and 11 whats the number
Answer:
66
Step-by-step explanation:
66 is the only number between 63 and 68 that is divisible by both 2 and 11.
66/2=33 66/11=6
Domain and Range from this functions
F(x)= (1/4x-1)^3 +2
Answer:
Domain:(−∞,2)∪(2,∞),{x|x≠2}
Range:(−∞,0)∪(0,∞),{y|y≠0}
You go to a restaurant and get a bill for $95. You need to tip the waitress. The service was good so you decide on tipping the waitress 20%. What is the tip that the waitress will receive
Answer:
19 dollars.
Step-by-step explanation:
0.20 x $95.00=$19.00.
HELP!? ✋
What strategies help prevent cancer?
Select all that apply.
Question 8 options:
using sunscreen
avoiding tobacco
getting enough sleep
eating a healthy diet
round 78300 nearest hundred
Answer:
78300 rounded to the nearest hundred is 78300.00 it would basically be the sam thing as 78300
Step-by-step explanation:
Hope this helps :)
Solve the system of equations using the substitution method.
S 4x + 5y=7
ly=3x +9
Enter your answers in the boxes.
2
X=
y=
Answer:
x = -2.
y = 3.
Step-by-step explanation:
If y = 3x + 9
Substitute this value for y in the first equation.
4x + 5(3x + 9) = 7
4x + 15x + 45 = 7
19x = 7 - 45
19x = -38
x = -38/19
x = -2.
with this value of x, substitute -2 in the second equation
y = 3(-2) + 9
y = -6+9
y = 3.
check if your values are all correct
4(-2) + 5(3) = 7
-8 + 15 = 15 - 8 = 7
Correct!
The verticles of a triangle are the points R(3,c),Q(9,2) and R(3c,11) where c is constant. Given that angle PQR is 90
Answer:
Step-by-step explanation:
Find c if ∠PQR = 90°?
I will ASSUME you mean point P is at (3. c)
slope of PQ is (2 - c) / (9 - 3) = (2 - c) / 6
slope of QR is (11 - 2) / (3c - 9) = 9 / (3c - 9)
perpendicular lines have negative reciprocal slopes.
(2 - c) / 6 = -1(3c - 9)/9
9(2 - c) = -6(3c - 9)
18 - 9c = -18c + 54
9c = 36
c = 4
Lucy wants to bake a circular apple pie with a radius of 5 in. What is the minimum circumference of the pie pan?
a
Please be accurate of your answer and explain.
Answer: 6 in.
Step-by-step explanation: