let f be the function given by f(x)=sin x + e^-x +3x. which of the following statements is true for y=f(x).
Applying derivatives, it is found that the correct options are:
A. [tex]y^{\prime\prime}(x) = -\sin{x} + e^{-x}[/tex]
D. [tex]y - y^{\prime\prime\prime\prime}(x) = 3x[/tex]
The function given is:
[tex]f(x) = \sin{x} + e^{-x} + 3x[/tex]
It's first four derivatives are:
[tex]y^{\prime}(x) = \cos{x} - e^{-x} + 3[/tex]
[tex]y^{\prime\prime}(x) = -\sin{x} + e^{-x}[/tex]
Hence, option A is correct.
[tex]y^{\prime\prime\prime}(x) = -cos{x} - e^{-x}[/tex]
[tex]y^{\prime\prime\prime}(x) \neq y^{\prime}(x)[/tex], hence, option B is incorrect.
[tex]y^{\prime\prime\prime\prime}(x) = sin{x} + e^{-x}[/tex]
It is not the multiplication of the first and of the third derivative, hence option C is incorrect.
[tex]y - y^{\prime\prime\prime\prime}(x) = 3x[/tex]
[tex]\sin{x} + e^{-x} + 3x - \sin{x} - e^{-x} = 3x[/tex]
[tex]3x = 3x[/tex]
Hence, option D is correct.
A similar problem is given at https://brainly.com/question/17042788
Sandy planted a tree and wanted to record its growth. The graph shows growth of the
tree over time.
1
The equation for the tree's growth is y =
+ 20.
2x
Select the meaning of the slope and y-intercept from the drop-down menus.
The given equation of the height of the tree is the equation of a straight line.
The slope is the number of units of growth each time period.The y-intercept is the initial height of the tree.Reasons:
1. The equation of the tree's growth is presented as follows;
y = 20 + 2·x
The equation of the tree is in the form of the equation of a straight line,
which is, y = m·x + c
Where, by comparison, we have;
m = The slope = 2
c = The y-intercept = 20
y = The height of the tree
x = The time of measurement of the growth of the tree
Therefore;
The slope = The height to which the tree grows within each time period.Therefore, the tree grows by 2 units of the height each time period of measurement
The y-intercept = The height of the tree at the start of the measurement.Therefore, the tree was 20 units of the length measurement at the start of the record.
Learn more about the equation of a straight line here:
https://brainly.com/question/20898425
Answer:
Step-by-step explanation:
First Box: In the scenario, the slope represents
the growth rate of the tree per year.
Second Box: In the scenario, the y-intercept represents
the tree's initial height.
A local store sells bags of game pieces with various colors. Four out of every 19 pieces are red. The store sold a bag with 76 game pieces. What number of the game pieces are red? Write your answer as a whole number.
Answer:
16 game pieces that are red
Step-by-step explanation:
3х – 11 = 22 solve x
Answer:
x=11
Step-by-step explanation:
3x-11=22
3x-11+11=22+11
3x=33
3x/3=33/3
x=11
Step-by-step explanation:
3x = 22 + 11
3x = 33
3x = 33/3
3x = 11
lets simplify
please help step by step
Please find attached photograph for your answer.
Hope it helps.
Do comment if you have any query.
Pregnant women have the option of being scanned for Cystic Fibrosis risks in their unborn babies. If a mother or a father have a certain recessive gene, the baby is at risk for Cystic Fibrosis. Given the three events, which of the following statements is true? Select all that apply.
Event A: The mother or father carries the recessive gene.
Event B: The father carries the recessive gene.
Event C: The baby is at risk for Cystic Fibrosis.
Answer:
Pregnant women have the option of being scanned for Cystic Fibrosis risks in their unborn babies. If a mother or a father have a certain recessive gene, the baby is at risk for Cystic Fibrosis.
Given the three events, which of the following statements is true?
Select all that apply.
Event A: The mother or father carries the recessive gene.
Event B: The father carries the recessive gene.
Event C: The baby is at risk for Cystic Fibrosis.
Select all that apply:
Event A and Event B are mutually exclusive.
Event B and Event C are mutually exclusive.
Event A and Event C are not mutually exclusive.
Event A and Event C are mutually exclusive.
Event A and Event C are not mutually exclusive.
Remember that in general, A and B are mutually exclusive events if they cannot occur at the same time. This means that A and B do not share any outcomes and P(A AND B)=0.
In this question, note that if the mother or father carries the recessive gene for cystic fibrosis, the baby is at risk. So here, A and C are not mutually exclusive, and B and C are not mutually exclusive.
A and B are not mutually exclusive because they share an outcome: the father carrying the recessive gene.
Step-by-step explanation:
A rat is 24 cm long and a mouse is 8cm long. So a rat is how many times long as the mouse?
Answer:
3?
Step-by-step explanation:
is this a trick question..
24/8=3 cm
So a rat is 3 cm times as long as a mouse
There are 56 fourth graders going on a field trip. The teacher wants to divide them evenly into groups of 4 students and no more than 8 students. What are ways to divide the students evenly into groups
56 ÷14 =4
Step-by-step explanation:
dividing
56÷7=8
60 children went to the beach.. 4/5 of them could swim. How many 60 children went to the beach. children could not swim?
Answer:
75
Step-by-step explanation:
60 divided by 4/5 is 75
Seth has 15 cans of regular soda and 20 cans of diet soda. He wants to create some identical refreshment tables that will operate during the high school football game. He also doesn't want to have any sodas left over. What is the greatest number of refreshment tables that Seth can stock? How many regular sodas will be at each table? How many diet sodas will be at each table?
Johnny Rockefeller had a bad credit rating and went to a local cash center. He took out a $100.00 loan payable in two weeks for $107.50. What is the percent of interest paid on this loan?
Answer:
7.5% Because out of 100 parts there are an additional 7.5 of them. Good luck mate.
What is the slope-intercept equation
for the following line?
y = [?]x+O
Answer:
the answer is Y=1x+1
A freight train 22.5 miles per 60 miles to its destination how far from the destination will the train be in 2.5 hour
What is the distance between the two points (-7, -7) and (4, -3)?
a. 5
C. 10.44
b. 7
d. 11.7
Please select the best answer from the choices provided
Zack bought 2 1/2 pounds of green grapes and 1/5 of a pound of red grapes. How much
more did the green grapes weigh than the red grapes?
Answer:23/10 pounds heavier
Step-by-step explanation:
first we transform the mixed fraction to a normal fraction
2 1/2 = 5/2
Now transform
5/2 = 25/10
1/5 = 2/10
25/10 - 2/10 = 23/10
So the green grapes weigh 23/10 pounds more than the red grapes.
Select the correct answer.
In the graph, what does A represent?
A.
foci
B.
minor axis
C.
major axis
D.
vertices
Answer:
B minor axis..................:)
In his free time. Gary spends 8 hours per week on the internet. and 11 hours per week playing video games. If Gary has 5 hours of free time per day, approximately what percent of his free time is spend on the internet and playing video games
54%
18%
38%
4%
Answer:
54%
Step-by-step explanation:
freetime total in 1 week
7=5*7=35
(videogames+internet)/totaltimeperweek=(8+11)/35=19/35≈.542857143≈54%
the answer is 54%
A world-famous prix fixe menu includes the following choices.
Beverage (choose one): wine, soft drink, coffee, tea, milk, juice, or cappuccino
First course (no choice): baguette, bruschetta, whole roasted garlic, and butter
Second course (choose one): quesadilla, onion soup, salad, Caesar salad, lettuce wedge, spinach salad, or romaine salad
Third course (choose one): rib eye steak, swordfish, rack of lamb, whitefish, grilled chicken, southern fried chicken, lobster, or vegetarian plate
if you choose steak, then choose one of the following: fries, mashed potatoes, creamed corn, spinach, broccoli, or grilled onions
Fourth course (choose one): chocolate cake, cinnamon tart, apple tart, pecan tart, creme brulee, mango sorbet, or chocolate tart
How many different choices are possible?
Using the fundamental counting theorem, it is found that 107,016 different choices are possible.
Fundamental counting theorem:
States that if there are n things, each with [tex]n_1, n_2, …, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
In this problem:
For the beverage, there are 7 options, hence [tex]n_1 = 7[/tex]For the first course, there are no choice, hence an arrangement of 4 options, that is, [tex]n_2 = 4! = 24[/tex]For the second course, there are 7 options, hence [tex]n_3 = 7[/tex]For the third course, there are 7 non-steak options, plus 6 steak options, hence [tex]n_4 = 13[/tex]For the fourth course, there are 7 choices, hence [tex]n_4 = 7[/tex]Then, applying the theorem:
[tex]N = 7(24)(7)(13)(7) = 107016 [/tex]
107,016 different choices are possible.
A similar problem is given at https://brainly.com/question/19022577
According to Belgium's 2018 Labor data: Number of employed= 1300, Number of unemployed = 300, Adult population =3,000. The unemployment rate of Belgium in 2018 was
a.10%
b.13%
c.18.75%
d.63.3%.
i need help on this math problem
Answer:
I think the first one goes with the second one
Step-by-step explanation:
Abby has $32 to spend on party supplies. After buying 9 packs of noisemakers, she has $20 left.
How much did each pack of noisemakers cost?
A
$0.75
B
$1.15
C
$1.33
D
$12.00
Answer:
$1.33
Step-by-step explanation:
32-20 = 12
12/9 = $1.33
What is the image of the point (1,-4) after a rotation of 180° counterclockwise
about the origin?
Answer:
(-1, 4)
Step-by-step explanation:
Rotation 180° negates both coordinates:
(x, y) ⇒ (-x, -y)
The direction (clockwise or counterclockwise) is irrelevant. It is the same as reflection across the center of rotation (the origin).
(1, -4) ⇒ (-1, 4) . . . . after rotation 180°
Simplify this equation
Answer:
I think the answer might be 12x⁷
When you roast coffee, it loses 12% of its weight. How much fresh coffee do you need in order to get 14 2/25 lb of roast coffee?
Answer:
X - X/12 = 14 2/5 = 72/5 1/12 of X is lost in roasting
(12 X - X) / 12 = 72/5
11 X / 12 = 72/5
11 X = 864 / 5
X = 864 / 55
15.71 lbs handy to use calculator here
Or 864 / 55 = 15 39/55 lbs
Answer:
16 lbs
Step-by-step explanation:
I don’t understand any of the below. Can you please help?
-25 + (-12)
14 - (-20)
-4 + (-10)
Answer:
1. -37
2. -34
3. -14
Step-by-step explanation:
1. -25 then ++- is negative so -25-12 so add them becuase negative + negative adds then keep the negative sign. THIS HELPS WITH EVERYTHINGB
I need help with this problem! please hurry have 3 more after so let me know if you want to do them to and ill give 200 points.
I have my final exam soon 29/11/2021 , thank you all who helped me in math :>
Answer:
okay
Step-by-step explanation:
I NEED HELP ASAP PLEASE HELP! AT BATTING PRACTICE TJ HAD 20 BASEBALLS PITCHED TO HIM HIT HIT THE BALL 7 TIMES! WHAT PERCENT OF THE BALLS DID TJ HIT?
a company blends 1000 bushels of two types of apples to make a beverage that contains 12% real-juice content. One of the two types of apple contains 10% real-juice content and the other contains 15% real juice content. how many bushels of each type of apple are needed?
Answer:
400 bushels of the 15%
600 bushels of the 10%
Step-by-step explanation:
x bushels of the 15% plus the balance of 1000 bushels at 10% yield 1000 bushels at 12%
15x + 10(1000 - x) = 12(1000)
distribute
15x + 10000 - 10x = 12000
Combine like terms
5x = 2000
Divide both sides by 5
x = 400 bushels of the 15%
1000 - x = 600 bushels of the 10%
The number of bushels of the 15% is 400, and the number of bushels of the 10% is 600.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
We have:
A company blends 1000 bushels of two types of apples to make a beverage that contains 12% real-juice content.
Let x be the bushels.
One of the two types of an apple contains 10% real-juice content and the other contains 15% real juice content.
The linear equation can be framed:
15x + 10(1000 - x) = 12(1000)
By using the distributive property:
15x + 10000 - 10x = 12000
5x = 2000 (combine like terms)
x = 400 bushels of the 15%
= 1000 - x
= 1000 - 400
= 600 bushels of the 10%
Thus, the number of bushels of the 15% is 400, and the number of bushels of the 10% is 600.
Learn more about the linear equation here:
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if someone helps me with dis ill def give em brainliest
Answer:
with what?
Step-by-step explanation:
I think you forgot to attach something.