Answer:
Step-by-step explanation:
a) The first derivative helps considering f decreases or increases. Also, when f'(x) = 0, the function gets local max/min depends on how it acts.
The second derivative helps determining the concave up/down.
At x = -5, f"(-5) = -1 <0 That means the function f have concave down. Also, it shows f increases before -5 and decreases after -5.
Hence f'(-5) = 0 shows f gets maximum at -5.
b) At the point where f" =0, the function has a reflecting point and we need more information to determine if f has a local max/min there.
Using concepts of critical points, it is found that:
a) At x = −5, f has a local maximum.
b) At x = 1, f has neither a maximum nor a minimum.
-----------------------
A critical value of a function f(x) is a value of [tex]x^{\ast}[/tex] for which: [tex]f^{\prime}(x^{\ast}) = 0[/tex].
The second derivative test is also applied:
If [tex]f^{\prime\prime}(x^{\ast}) > 0[/tex], [tex]x^{\ast}[/tex] is a minimum point.If [tex]f^{\prime\prime}(x^{\ast}) < 0[/tex], [tex]x^{\ast}[/tex] is a maximum point.If [tex]f^{\prime\prime}(x^{\ast}) = 0[/tex], [tex]x^{\ast}[/tex] is neither a maximum nor a minimum point.Item a:
[tex]f^{\prime}(-5) = 0, f^{\prime\prime}(-5) = -1[/tex], thus, a maximum point, and the correct option is:At x = −5, f has a local maximum.
Item b:
[tex]f^{\prime}(1) = 0, f^{\prime\prime}(1) = 0[/tex], thus, neither a maximum nor a minimum point, and the correct option is:At x = 1, f has neither a maximum nor a minimum.
A similar problem is given at https://brainly.com/question/16944025
Reflect on the concept of function. What concepts (only the names) did you need to accommodate the concept of function in your mind? What is the simplest function you can imagine? In your day to day, is there any occurring fact that can be interpreted as a function? Is it possible to view a function? What strategy are you using to get the graph of a function?
Answer:
Step-by-step explanation:
For this kind of question you'd be better off if you'd write down and share your own answers to these conceptual questions and then ask for Brainly feedback on what you have written. You'll need to understand the concept of "function" often in algebra and beyond.
What concepts (only the names) did you need to accommodate the concept of function in your mind? input, output, rule, domain, range, mapping, variation (direct and inverse)
Simplest function: y = c (there's only one x-value and y equals that value)
In your day to day, is there any occurring fact that can be interpreted as a function? An electronic parking meter: the amount of time you can park at the meter without risking getting a ticket is dependent upon the number of quarters you insert into the meter, e. g, 15 minutes for 25 centers, 30 minutes for 50 cents, and so on.
Is it possible to view a function? Sure. Graph the function.
What strategy are you using to get the graph of a function? Set up a coordinate plane. Label the horizontal axis "x" and the vertical axis "y". Choose x (input) values that are included in the domain of the function. If the domain includes '0' you will be finding the 'y-intercept' of the function. Write the input and output as a point: (x, y). Plot that point. Choose other x values within the domain and calculate the corresponding y value for each. Plot several more points and draw a line or a curve through them. Of course there are more sophisticated strategies for graphing functions. Remember: If you're working with a function, there is never more than one output or y value for any particular input value.
Please hurry
On each bounce, a ball dropped from 100 feet rises to the height
from which it has fallen. How high does the ball rise, in feet, on the 10th bounce?
Answer:
D
Step-by-step explanation:
divide 10 times starting with 100.
The answer is 25/256 or 0.09765625
The height of the ball dropped from 100 feet on the 10th bounce is 0.09766 feet
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let y represent the height of the ball after x bounce. Given that the ball rises to the height from which it has fallen, hence:
y = 100(1/2)ˣ
After the 10th bounce:
y = 100(1/2)¹⁰ = 0.09766
The height of the ball dropped from 100 feet on the 10th bounce is 0.09766 feet.
Find out more on equation at: https://brainly.com/question/2972832
The cost of producing x soccer balls in thousands of dollars is represented by h(x) = 5x + 6. The revenue is represented by k(x)
= 9x - 2. Which expression represents the profit, (k-h(x), of producing soccer balls?
Answer:
4x - 8
Step-by-step explanation:
k - H(x)
(9x -2) - (5x + 6)
4x -8
WRITING BOOK
Personal Writing
AD 1
NUMBERS
Which of the following cannot be an integer?
A. 0.8
B. -3
C. 4
D. 25
Answer:
A
Step-by-step explanation:
Integers are negative and positive whole numbers
Answer: A. 0.8
Step-by-step explanation:
An integer is a whole number (not a fractional number) that can be positive, negative, or zero. Examples of integers are: -5, 1, 5, 8, 97, and 3. Examples of numbers that are not integers are: -1.43, 1 3/4, 3.14
A way that landowners took advantage of sharecroppers was by:
A. allowing only whites to farm the land.
B. allowing only African Americans to farm the land.
O c. taking their seeds and tools.
D. paying less for crops raised by African Americans.
SUBMIT
The answer is d . Paying less for crops raised by Africa. Americans
Answer: C. Paying less for crops raised by African-Americans
Step-by-step explanation:
Please answer this correctly
Answer:
41-60 => 5
Step-by-step explanation:
41-50 => 2
51-60 => 3
So 2+3 =5
Answer:
5
Step-by-step explanation:
Add up the number of children between 41 and 60
41-50: 2
51-60: 3
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total 5
Carefully review the research matrix presented below. If this is a within subjects design, how many total participants will be used in the experiment?
Immaculate Appearance Neat Appearance Sloppy Appearance
15 participants 15 participants 15
participants
a. 15
b. 30
c. 45
d. 60
Answer:
c. 45
Step-by-step explanation:
there are 15 participant in each category, and there are 3 categories, so total participants = 15 * 3
= 45
Hope this helps, and please mark me brainliest if it does!
What is the next number in the sequence: 3, 8, 12, 48, 29, __
Answer:
144
Step-by-step explanation:
Answer:
116
Step-by-step explanation:
3x4=12
12x4=48
8x4=32
32-3=29
29x4=116
Hope it's clear
Use z scores to compare the given values. Based on sample data, newborn males have weights with a mean of 3259.6 g and a standard deviation of 722.4 g. Newborn females have weights with a mean of 3031.2 g and a standard deviation of 495.9 g. Who has the weight that is more extreme relative to the group from which they came: a male who weighs 1700 g or a female who weighs 1700 g? Since the z score for the male is zequals nothing and the z score for the female is zequals nothing, the female female male has the weight that is more extreme.
Answer:
Since the z score for the male is z=-2.1589 and the z score for the female is z=-2.6844, the female has the weight that is more extreme.
Step-by-step explanation:
To find the z score, we use the following equation:
[tex]z=\frac{x-m}{s}[/tex]
Where m is the mean and s is the standard deviation.
So, the z score for a male who weighs 1700 g is:
[tex]z=\frac{1700-3259.6}{722.4}=-2.1589[/tex]
At the same way, the z score for a female who weighs 1700 g is:
[tex]z=\frac{1700-3031.2}{495.9}=-2.6844[/tex]
Finally, -2.6844 is farther from zero than -2.1589, so the female has the weight that is more extreme.
Having integrated with respect to ϕ and θ, you now have the constant 4π in front of the integral and are left to deal with ∫[infinity]0A21(e−r/a)2r2dr=A21∫[infinity]0r2(e−r/a)2dr.
What is the value of A21∫[infinity]0r2(e−r/a)2dr?Express your answer in terms of A1 and a.
Find the unique positive value of A1.
Express your answer in terms of a and π.
Answer:
Step-by-step explanation:
[tex]\int\limits^{\infty}_0 {A^2_1} (e^{-r/a})r^2dr= {A^2_1}\int\limits^{\infty}_0r^2(e^{-r/a})^2\, dr)[/tex]
[tex]=A_1^2\int\limits^{\infty}_0 r^2e^{-2r/a}\ dr[/tex]
[tex]=A_1^2[\frac{r^2e^{2r/a}}{-2/a} |_0^{\infty}-\int\limits^{\infty}_0 2r\frac{e^{-2r/a}}{-2/a} \ dr][/tex]
[tex]=A^2_1[0+\int\limits^{\infty}_0 a\ r\ e^{-2r/a}\ dr][/tex]
[tex]=A^2_1[\frac{a \ r \ e^{-2r/a}}{-2/a} |^{\infty}_0-\int\limits^{\infty}_0 \frac{a \ e^{-2r/a}}{-2/a} \ dr][/tex]
[tex]=A_0^2[0-0+\int\limits^{\infty}_0 \frac{a^2}{2} e^{-2r/a}\ dr\\\\=A_1^2\frac{a^2}{2} \int\limits^{\infty}_0 e^{-2r/a}\ dr\\\\=A_1^2\frac{a^2}{2} [\frac{e^{-2r/a}}{-2/a} ]^{\infty}_0[/tex]
[tex]=\frac{A_1^2a^2}{2} -\frac{a}{2} [ \lim_{r \to \infty} [e^{-2r/a} -e^0]\\\\=\frac{A_1^2a^2}{2} -(\frac{a}{2}) (0-1)[/tex]
[tex]=\frac{A_1^2a^3}{4}[/tex]
[tex]\therefore A_1^2\int\limits^{\infty}_0 r^2(e^{-r/a}) \ dr =\frac{A_1^2a^3}{4}[/tex]
Find the unique positive value of A1
[tex]=4\pi (\frac{A_1^2a^3}{4} )\\\\=A_1^2a^3\pi\\\\A_1^2=\frac{1}{a^3\pi} \\\\A_1=\sqrt{\frac{1}{a^3\pi} }[/tex]
Use the distributive property to remove the parentheses .
-8(y-v-3)
Answer:
-8y +8v +24
Step-by-step explanation:
-8(y-v-3)
Multiply each term inside the parentheses by -8
-8y -v*-8 -3*-8
-8y +8v +24
___________________________________
Hey!!!
solution,
-8(y-v-3)
= -8y+8v+24
_________________________________
Here,
You have to remember these things:
(+)*(+)=(+)(+)*(-)=(-)(-)*(-)=(+)(-)*(+)=(-)Hope it helps.
Good luck on your assignment
Describe the steps you would use to solve the
following inequality
2x - 3
Answer: No answer
Step-by-step explanation:
Not an inequality, inequalities are of the form 2x - 3 > something.
If it's 2x - 3 > 0 for example, then add both sides by 3 to get 2x > 3, then div by 2 to get x > 3/2.
Hope that helped,
-sirswagger21
Look at the work shown for the division problem shown on the right. The remainder is 8 . Now, evaluate f (x) = 2x4 – 4x3 – 11x2 + 3x – 6 for x = –2. f (–2) = 8 Compare the values you entered above. f (–2) is the remainder when dividing the polynomial by x + 2. Divide 2x4- 4x3 - 11x2 + 3x - 6 by x + 2.
Answer:
1st : 8
2nd: 8
3rd: equal to
Polynomial is an equation written as the sum of terms of the form kx^n.
where k and n are positive integers.
The remainder of the polynomial when divided by x + 2 is -60.
What is a polynomial?Polynomial is an equation written as the sum of terms of the form kx^n.
where k and n are positive integers.
We have,
2[tex]x^{4}[/tex] - 4x³ - 11x² + 3x - 6 divide by x + 2.
Now,
x + 3 ) 2[tex]x^{4}[/tex] - 4x³ - 11x² + 3x - 6 ( 2x³ - 2x² - 5x + 18
2[tex]x^{4}[/tex] + 6x³
(-) (-)
-2x³ - 11x² + 3x - 6
-2x³ - 6x²
(+) (+)
- 5x² + 3x - 6
-5x² - 15x
(+) (+)
18x - 6
18x + 54
(-) (-)
-60
We see that,
The remainder is -60.
f(-2) = 2[tex]x^{4}[/tex] - 4x³ - 11x² + 3x - 6
f(-2) = 2 x 16 + 32 - 44 - 6 - 6 = 32 + 32 - 44 - 12 = 64 - 56 = 8
Thus,
The remainder of the polynomial when divided by x + 2 is -60.
Learn more about polynomials here:
https://brainly.com/question/2284746
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Ann pays $300 for membership to a local gym. She is allowed to bring one guest on any visit. John pays Ann $5 to go to the gym with her occasionally. Describe what the expression 300 - 5t could represent. Then evaluate the expression for T equals five 10 15 and 20
Answer:
f
Step-by-step explanation:
A cell phone company is offering 2 different monthly plans. Each plan charges a monthly fee plus an additional cost per minute. Plan A: $ 40 fee plus $0.45 per minute Plan B: $70 fee plus $0.35 per minute a) Write an equation to represent the cost of Plan A b) Write an equation to represent the cost of Plan B c) Which plan would be least expensive for a total of 100 minutes?
*Please Show Work*
Answer:
Plan A would be the least expensive
Step-by-step explanation:
Plan A= $0.45x100= 45, 45+40=$85
Plan B= $0.35x100= 35, 35+70= %105
(Each plan is for 100 minutes)