find the formula for a function of the form y=ae^(-x)+bx with global minimum at (1,10).
Answers
The formula for a function of the form [tex]y = a\cdot e^{-x} + b\cdot x[/tex] with global minimum at [tex](1, 10)[/tex] is [tex]y = 5\cdot e^{1-x}+5\cdot x[/tex].
We can use first and second derivative tests to determine all coefficients of the function described in statement so that the point given is an absolute minimum. The expressions for such tests are introduced below:
FDT
[tex]-a\cdot e^{-x}+b = 0[/tex] (1)
[tex]b = a\cdot e^{-x}[/tex]
SDT
[tex]y''=a\cdot e^{-x}[/tex] (2)
Where [tex]y'' > 0[/tex].
If we know that [tex](x, y) = (1, 10)[/tex], then we have the following system:
[tex]10 = a\cdot e^{-1}+b[/tex] (3)
[tex]b = a\cdot e^{-1}[/tex] (4)
[tex]y'' = a\cdot e^{-1}[/tex] (5)
By (4) in (3):
[tex]10 = 2\cdot a\cdot e^{-1}[/tex]
[tex]a = \frac{10}{2\cdot e^{-1}}[/tex]
[tex]a = 5\cdot e[/tex]
By (5) we prove that [tex]y'' > 0[/tex], and we get the value of [tex]b[/tex] by (4):
[tex]b = 5[/tex]
Thus, the formula for a function of the form [tex]y = a\cdot e^{-x} + b\cdot x[/tex] with global minimum at [tex](1, 10)[/tex] is [tex]y = 5\cdot e^{1-x}+5\cdot x[/tex].
We kindly invite to check this question on first and second derivative tests: https://brainly.com/question/6097697
Related Questions
Find the coordinates of the vertex of the following parabola using graphing technology. Write your answer as an (x, y) point.
y= -x^2-10x-22
Answers
Answer:
vertex: (-5, 3)
Step-by-step explanation:
Besides providing the graph of the given quadratic equation, I will also demonstrate the algebraic method of solving for the vertex of a parabola.
Method 1: Algebraic SolutionGiven the quadratic equation, y = -x² - 10x - 22, where:
a = -1, b = -10, and c = -22.
Find the x-coordinate of the vertex:In order to find the vertex of the given equation, use the following formula to find the x-coordinate of the vertex: [tex]x = \frac{-b}{2a}[/tex].
[tex]x = \frac{-b}{2a}[/tex]
[tex]x = \frac{-(-10)}{2(-1)}[/tex]
[tex]x = \frac{10}{-2}[/tex]
x = -5
The x-coordinate of the vertex is: x = 5.
Find the y-coordinate of the vertex:Next, substitute the value of the x-coordinate into the given quadratic equation to find its corresponding y-coordinate:
y = -x² - 10x - 22
y = -(-5)² - 10(-5) - 22
y = -25 + 50 - 22
y = 3
Therefore, the vertex of the given parabola is: (-5, 3), where it is the maximum point.
One of the attachments is the screenshot of the graphed quadratic equation (using Desmos), where it shows the vertex as the maximum point.
Method 2: Graphing CalculatorIf you have a graphing calculator (such as the Texas Instruments graphing calculator):
Press Y=Then, simply enter the given quadratic equation, -x² - 10x - 22.Next, press 2ND ⇒ Quit. Press the GRAPH button. Press 2ND ⇒ TRACE Select option 4: maximumIt will ask for the "Left Bound?": move the cursor as close to the maximum point as possiblePress ENTER. Next, it will ask for the "RightBound?" Repeat the same process as in step #7. Press ENTER.It will ask for "Guess?" ⇒ press ENTER, and it will provide the same coordinates for the vertex, (-5, 3).Please let me know if you have any questions or concerns regarding this post.
HELP! Can anyone help me i need help it this question
Answers
Average rate = distance / time
Rewrite distance as an improper fraction":3 1/3 = 10/3
Now you have 10/3 / 1/3
When dividing by a fraction flip the second fraction over and multiply:
10/3 x 3/1 = (10 x 3) / (3/1) = 30/3 = 10
Average rate was 10 miles per hour
Which of the following statements is most correct? Select one:
a. Other things equal, the higher the dividends, the lower the stock price.
b. Other things equal, the investment holding period does not affect the stock price.
c. Other things equal, the higher the required rate of return, the higher the stock price. d. Other things equal, the higher the dividend growth rate, the lower the stock price.
e. Other things equal, the lower the market value of debt, the lower the value of equity.
Answers
Answer:a
Step-by-step explanation:
the answer is a because it is
4 A neghborhood is debating whether or not to have a leash law, which would require all dogs outside of homes to be on a leash. Most of the dog owners live in the
northern part of the
neghborhood. Which of these polls should give the most accurate information?
O A Apoll in which two streets are chosen at random and all the houses are on those two streets are polled.
OB. A poll in which the northernmost street and the southernmost street are both polled
• C. A poll in which 50 people in the neighborhood are chosen by picking addresses out of a hat.
OD. A poll in which 25 people are chosen by picking random phone numbers.
Someone please help
Will give brainliest
Answers
Answer:
C. A poll in which 50 people in the neighborhood are chosen by picking addresses out of a hat.
Step-by-step explanation:
It limits the field to those the law would affect, yet is randomized within that field to not bias the results much.
How to do question 1 ?
Answers
Step-by-step explanation:
srry
Answer:
A
Step-by-step explanation:
I DID THE WORK IN MY HEAD
btw im 11
What is the slope of the line that
passes through the points (-1, 3)
and (2, 10)?
Answers
Answer:
D [tex]\frac{7}{3}[/tex]
Step-by-step explanation:
For find the slope of whatever line we use the next formula:
[tex]m = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
So in our occasion we have:
[tex]y_2 = 10 \quad \text{and} \quad y_1 = 3\\x_2 = 2 \quad \text{and} \quad x_1 = -1[/tex]
Replacing in the equation:
[tex]\frac{10 - 3}{2 - (-1)} = \frac{7}{3}[/tex]
So the answer is [tex]\frac{7}{3}[/tex]
Determine the relationship between The two triangles on whether or not they can be proven to be congruent
Answers
Answer:
ASA congruence
Step-by-step explanation:
here two angles and in between side are equal for these two triangles
The base of a triangle is 7 inches more than its height. If the area of the triangle is 39 square inches, find the base and height of the triangle
The height of the triangle is
Answers
Answer:
the height of the triangle is 6 inches and the base is 7 inches greater, or the base is 13 in
Step-by-step explanation:
The general area-of-a-triangle formula is A = (1/2)(base)(height), or = (1/2)bh.
Here b = h + 7.
Applying the area formula given above: A = 39 in^2 = (1/2)(h + 7)(h), or
78 in^2 = h^2 + 7h,
Rewriting this, in standard quadratic form, we get h^2 + 7h - 78 = 0
-7 ± (49 - 4[1][-78])
Applying the quadratic formula to find h: h = ----------------------------
2
-7 ± (49 + 312) -7 ± 19
or h = ----------------------- = ------------- = {-13, 6}
2 2
Discard the negative 13 root; the height must be a positive quantity.
Thus, the height of the triangle is 6 inches and the base is 7 inches greater, or the base is 13 in
Form an equation to help you solve this problem Four identical lumps of gold on one side of some scales balance with one identical lump and a 22kg mass. Find the mass of one lump of gold. kg
Answers
Answer:
equation= 4x=x+22kg
Step-by-step explanation:
i hope it helped :))
A bottle is filled with 4oz of perfume. If 20% of the perfume evaporates, how many ounces remain?
Answers
4x0.20=0.8
I hope this helps
Answer:
The answer will be:- ( 0.8 oz ).
Answ
Question
Dylan went to the toy store and
bought 3 action figures for $45.
How much did 1 action figure
cost?
*Use the dollar sign"
10
Using the information from
problem #9, write the equation.
What is the equation?
Answers
Answer:
15$
Step-by-step explanation:
45 ÷ 3 = 15
The sampling distribution of the ratio of two independent sample variances selected randomly from normal populations with equal variances is:
Answers
Answer: F distribution. chi-square distribution. t distribution. normal distribution.
Step-by-step explanation:
How to solve -2(x+2)^2=5 using the square root method.
Answers
A desk is on sale for 15% off. The sale price is $612.
What is the regular price?
Answers
Answer:
$720
Step-by-step explanation:
Step 1: Set up the expression.
[tex]\frac{612}{1-0.15}[/tex]Step 2: Simplify.
[tex]\frac{612}{0.85}[/tex]Step 3: Convert 0.85 into a fraction.
[tex]612/ \frac{85}{100}[/tex] [tex]612/ \frac{17}{20}[/tex]Step 4: Multiply 612 by reciprocal of 17/20.
[tex]612 * \frac{20}{17}[/tex] [tex]36 * 20[/tex] [tex]720[/tex]Therefore, the regular price was $720.
You are a prisoner sentenced to death. The emperor (who has sentenced you) offers you a chance to live by playing a simple game. He gives you 10 black marbles, 10 white marbles, and 2 empty bowls. He then says, "Divide these 20 marbles into these 2 bowls. You can divide them any way you like as long as you place all the marbles in the bowls. Then I will blindfold you, and ask you to choose a bowl, and remove ONE marble from that bowl you have chosen. You must leave the blindfold on the entire time, and must remove the first marble you touch. If the marble is white you will live, but if the marble is black, you will die."
————
Please help?
Answers
Answer:
YeYEYEyYEEeeeeeeeeeeeeeeeeeeeeEE
Step-by-step explanation: kinda sounds like that epesode from squid game episode 7 i think
At a sale this week, a desk is being sold for $285.60. This is 34% of the original price.
What is the original price?
Answers
well, let's say the original price is "x", which namely 100% of the price of the product, we also know that 285.60 is 34% of that.
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} x&100\\ 285.60&34 \end{array}\implies \cfrac{x}{285.60}=\cfrac{100}{34}\implies \cfrac{x}{285.60}=\cfrac{50}{17} \\\\\\ 17x=14280\implies x = \cfrac{14280}{17}\implies x = 840[/tex]
The table below shows the earnings, in thousands of dollars, for three different commissioned employees.
Employee #1
$2,000 + 3% on all sales
Employee #2
7% on all sales
Employee #3
5% on the first $40,000 + 8% on anything over $40,000
December
4.4
5.6
5.2
January
3.5
3.85
3.6
February
4.7
4.9
4.4
Which employee did not have the same dollar amount in sales for the month of February as the other two employees?
a.
Employee #1.
b.
Employee #2
c.
Employee #3
d.
They each had the same dollar amount in sales.
Answers
The employee who did not have the same dollar amount in sales for the month of February as the other two employees is (a) Employee 1.
What is Percentage?Percentage is defined as the parts of a number per fraction of 100. We have to divide a number with it's whole and then multiply with 100 to calculate the percentage of any number.
Earnings of three employees in the month of February are :
Employee 1 = 4.7 = $4700
Employee 2 = 4.9 = $4900
Employee 3 = 4.4 = $4400
Earnings of employee 1 = $2,000 + 3% on all sales
Let the amount of all sales be x.
2000 + (3% x ) = 4700
2000 + 0.03x = 4700
0.03x = 2700
x = 90,000
Earnings of employee 2 = 7% on all sales
Let the amount of all sales be x.
0.07x = 4900
x = $70,000
Earnings of employee 3 = 5% on the first $40,000 + 8% on anything over $40,000
Let the amount of sales be 40,000 + x.
(0.05 × 40,000) + (0.08 x) = 4400
2000 + 0.08x = 4400
0.08x = 2400
x = $30,000
Amount of sales = $40,000 + $30,000 = $70,000
Hence employee 1 did not have the same amount as the other 2 in February.
Learn more about Percentage here :
https://brainly.com/question/1811849
#SPJ5
12 x 12 x 12 = 4 x # x 4 what number must replace the '#' symbol
Answers
Answer:
I'm pretty sure it's 108.
Step-by-step explanation:
12 x 12 x 12 = 1,728
4 x 4 = 16
1,728 ÷ 16 = 108
Show your work and write an expression using the following criteria:
1. A dividend greater than 1,000
2. The quotient is 58 with a remainder of 22
Answers
Answer:
This is correct explanation
Step-by-step explanation:
A dividend is a number we want to divide by another number. It's supposed to be greater than 1000.
Quotient - the integer result of division. Remainder - well, what remains.
9/4 = 2, with remainder 1.
You want to find a number greater than 1000, which, when divided by another number, results in 37, with a remainder of 4.
I would multiply 37 by an increasing number until we get a product greater than 1000. This number is the one you are dividing by. Now add 4 to the product, so that when the sum is divided by the number you found we'll get a remainder of 4.
PLEASE HELP I HAVE 3 MINUTES LEFT TO DO THIS TY
Which expression is equivalent to 5(8 + 9)?
O 40 + 45
O 13 + 9
O 13 + 14
O 40 + 9
Answers
Answer:
40+45
Step-by-step explanation:
17x5 is 85
Answer:
40 + 45
Step-by-step explanation:
5(8 + 9)
= 5*8 + 5*9
= 40 + 45
help pls ill give brainly
Answers
Answer:
Find the Diameter!
To find the diameter, get the cirumference, divide it by 2, and multiply it by Pi (3.14)
For this certain equation, it appears the circumference is 13. 13/2 is 6.5. 6.5 times 3.14 is 20.41.
Answer:
I think the other guy is correct I'm just putting this here so you can give him/her brainliest
Step-by-step explanation:
Can someone give more explanation
Answers
You just have to underline the word that connects two sentences .
for example: In number 2. Sophia ate a lot. She is still hungry. These are two sentences the word 'yet' connects two sentences. that is called conjunction.
1.= under line so
2.= under line yet
3.= under line but
4.= under line so
The variables x and y are related proportionally. When x = 8, y = 14. Find y when x = 48. When x = 48, y = what.
Answers
Y might be 84. Considering 6*8=48, it would probably be the same with Y, so 14*6=84.
Hopefully this is correct but sorry if it isn't.
A 6 pound bag of grass seed covers 7,000 square feet. How many pounds would be needed to cover 23,000 square feet?
Write answer as an integer or a reduced fraction.
Answers
Answer:
Step-by-step explanation:
You can setup a proportion as follows:
4 lb = 9000 ft2
x lb = 25000 ft2
Solve for x = 25000 ft2 x 4 lb / 9000 ft2 = 11.11 lb ~ 11 lb rounded to a whole number
Evaluate.
-1
(1/5) ⋅ 4^0
0
1
5
20
Answers
Answer:
the answer is 5 I think I hope
The total cost for tuition plus room and board at State University is $2737. Tuition costs $787 more than room and board. What is the tuition fee?
What is the cost of tuition?
Answers
Progressions A person borrowed a sum of Rs. 3400 from his provident fund account on the condition to repay in 22 monthly installment of Rs. 150 and last installment of Rs. 100. Calculate the S.I. at the rate of 4.5% pa, which he , has to pay as the 24th installment?
Answers
question but I am solving four questions, Please try to
understand me and its my humble request to create
separate post for each question.
6. Elena writes the equation 6x + 2y = 12. Write a new equation that has:
a. exactly one solution in common with Elena's equation
b. no solutions in common with Elena's equation
c. infinitely many solutions in common with Elena's equation
Answers
Answer:
2x ×2y=15. then solve for equation x and y
What is the value of the expression 4.2(x−y)4 , when x = 12 and y = 5.6 as a decimal?
Answers
Answer:
6.72
Step-by-step explanation:
PLEASE HELP WITH THIS ONE QUESTION
Answers
Answer:
Left 3 down 4
Step-by-step explanation:
I'm not sure how to explain it, but I can give advice. A site that really helped me with this was Desmos Graphing Calculator.