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
What is the y- intercept of a line that has a slope of 2 and passes through (-1,3)?
Answers
Answer:
y - intercept = 5
Step-by-step explanation:
Equation: y = mx + b
Input the given values
3 = -1(2) + b
3 = -2 + b
5 = b
-Chetan K
You make $85,000 per year and your company matches 50 cents for every dollar you deposit into your 401k plan, up to %5 of your salary. If you contribute $300
every month to your 401k, what will your company contribute each month?
Answers
Answer:
$150 each month
Step-by-step explanation:
divide 300 in half because they contribute 50¢ per dollar
Four bags of Puppy Chow dog food weighs 142 pounds. What is the weight, in pounds, of one bag of Puppy Chow dog food?
Answers
Answer:
Is 35.5
Step-by-step explanation:
Pls give brainliest
Answer:
35.5 Lbs.
Step-by-step explanation:
You would just take 142 and divide that by 4 and you will get the weight of 1 bag. It would be 35.5 pounds.
Jace is deciding between two landscaping companies for his place of business. Company A charges $50 per hour and a $250 equipment fee. Company B charges $75 per hour and a $150 equipment fee. Let A represent the amount Company A would charge for tt hours of landscaping, and let B represent the amount Company B would charge for tt hours of landscaping. Graph each function and determine the number of hours, t, that would make the cost of each company the same.
give me the corrdent plan point i need 2 for example
(5,2) and (4,1) like that on the graph
Answer: ________
dollars per hour
dollars
hours per dollar
hours
my graph is the y axis is 1000 and the x axis is 20
Answers
Answer:
I don't know ✌️. ..............
In △ABC, m∠A = 75° and m∠C = 20°, What is m∠B?
Answers
Answer:
30 degree ok please make me brainliest
Answer:
∠ B = 85°
Step-by-step explanation:
The sum of the 3 angles in a triangle = 180° , that is
∠ A + ∠ B + ∠ C = 180° , substitute values
75° + ∠ B + 20° = 180°
∠ B + 95° = 180° ( subtract 95° from both sides )
∠ B = 85°
Original price of a bicycle $1,600.00 Discount 35.3% Tax 1%? Find the selling price of each item ???
Answers
Subtract the discount ($564.80) from the price then add the tax ($16).
2 Which of the following would result in a
rotation 360° counterclockwise about the
origin?
® (x,y) - (-Y. -x)
© (x, y) - (-y, x)
(x, y) - (-x, -Y)
(x,y) - (x, y)
Answers
Answer:
(d) (x,y) ⇒ (x, y)
Step-by-step explanation:
Rotation 360° about any point brings the object back to its original location. The coordinates are unchanged.
(x,y) ⇒ (x, y)
find a positive coterminal angle for 765 degrees
Answers
Answer:
45 degrees
Step-by-step explanation:
Subtract 360° 360 ° from 405° 405 ° . The resulting angle of 45° 45 ° is positive, less than 360° 360 ° , and coterminal with 765° 765 ° .
Solve the equation for x:
4x2 + 15x = 4
Show steps please
Answers
First multiply the 4 and 2
8 + 15x = 4
Next, subtract the 8 on both sides
15x = -4
x=3.75
it has been suggested that the percentage of drivers in the us that use a blinker when changing lanes is58% you plan to observe 50 cars during a lane change. What type of distribution could you use to determine the number of cars you will observe before finding a car the does not use a blinker during a lane change?
Answers
Since the number of trials is not fixed, an inverse binomial distribution is used.
For each car, there are only two possible outcomes, either they use a blinker during lane change, or they do not. The probability of a car using a blinker during lane change is independent of any other car, which means that the number of cars that do not use a blinker during a lane change is a binomial variable.
However, we are counting the number of trials until observing a car that does not use a blinker during a lane change, hence, it is an inverse binomial variable.A similar problem is given at https://brainly.com/question/25644451
2 (n - 1) + 47 = 2 (3n - 1)
Answers
[tex]\\ \sf\longmapsto 2(n-1)+47=2(3n-1)[/tex]
[tex]\\ \sf\longmapsto 2n-2+47=6n-2[/tex]
[tex]\\ \sf\longmapsto 2n+47=6n[/tex]
[tex]\\ \sf\longmapsto 4n=47[/tex]
[tex]\\ \sf\longmapsto n\approx 12[/tex]
Answer:
n = 11.75
Step-by-step explanation:
2(n - 1) + 47 = 2(3n - 1) Distribute the multiplier
2n - 2 + 47 = 6n - 2 Combine terms
47 = 4n divide
n = 11.75
What is the 5th term of the linear sequence? 1,7,13,19,25,...
Answers
Answer : 31
Explanation : Every numbers have a gap of 6 as you can see:
1 + 6 = 7
7 + 6 = 13
13 + 6 = 19
19 + 6 = 25
So,
25 + 6 = 31
Hope This Helps You!
What is the value for x if 2x+3=20 that makes the equation true
Answers
Answer:
x = 8.5
Step-by-step explanation:
2x+3=20
2x = 17...........subtract 3 from both sides
x = 8.5............divide both sides by 2
evaluate -x^3 - 3x^2 + 4 when x = -2
Answers
-(-2)^3 = 8
-3(-2^2)= -12
Then add 4
-12 + 4 + 8 = 0
Answer:
32
Step-by-step explanation:
x = -2
-x^3 - 3x^2 + 4
-(-2)^3+6^2+4
8+36+4=48
Hope this helps :)
I need word form and decimal
(I already shaded it in so that is all I need
Answers
The shading is correct for each of the three problems. Nice work.
==========================================
Problem 13
Word form = one tenth
Decimal form = 0.1
Explanation: The 1 is in the tenths place for the decimal value 0.1 to represent the fraction 1/10.
==========================================
Problem 14
Word form = eighty-five hundredths
Decimal form = 0.85
Explanation: The 8 is in the tenths place, and the 5 is in the hundredths place. Overall, 0.85 represents 85 out of 100, aka 85/100.
==========================================
Problem 15
Word form = thirty-nine thousandths
Decimal form = 0.039
Explanation: The second zero is in the tenths place. The 3 is in the hundredths place. The 9 is in the thousandths place. The decimal represents 39/1000 which you can think of it as 039/1000.
Eighty five hundredths, 0.85
Thirty nine thousandths, 0.039
Hope this helps!!!
-6 10/9 divided by 6/5
Answers
Answer:
-160/27
Step-by-step explanation:
I hope this helps if I’m wrong I apologize
Please hurry will mark brainliest if you answer correctly
Answers
Six times a number plus 7 is equal to 55. What is the number?
Answers
Answer:
6x_+7=55, the answer is 13, why? well because if you add 6+7 you will have 13, now you can multiple that by 5, and you will have 55 as an answer, did I helped you?
2x+3-3=-6
solve right please
Answers
Finding the value of x,
→ 2x + 3 - 3 = - 6
→ x + (3 - 3) = - 6/2
→ [ x = -3 ]
Thus, the value of x is -3.
Solve by factoring 12x^3+12x^2=0
Answers
12x^2(x + 1) = 0
Now you can do two parts
12x^2 = 0, x = 0
x + 1 = 0, x = -1
Solution: x = 0, x = -1
Factor out the GCF
12x^2(x + 1) = 0
Now you can do two parts
12x^2 = 0, x = 0
x + 1 = 0, x = -1
Solution: x = 0, x = -1
brainliest pls
Five kittens are sharing 6 cups of milk equally. How much milk does each kitten get?
Answers
Answer:
1 1/5
Step-by-step explanation:
We know that there is 5 kittens that have to eat six bowls of milk
Each cat would get 1 whole bowl of milk. All the kittens have to share 1/5 of the sixth bowl of milk.
Five kittens are sharing 6 cups of milk equally so 1 1/5 cup of milk is given to each kitten.
What is meant by Mathematical expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)
Expressions in writing are made using mathematical operators such addition, subtraction, multiplication, and division.. For instance, the mathematical equation for "4 added to 2" will be 2+4.
Arithmetic operations are the most fundamental type of mathematical expression. Any combination of numbers and a mathematical operation, such as multiplication, addition, subtraction, or division, are considered arithmetic operations. For instance, the arithmetic operation 9 + 14/2 - 6*(5 + 3) results in -32.
Given,
6 cup of milk so there are 5 kitten
To give 6 cup of milk to 5 kitten is=6/5
= 6/5
=1 1/5
Therefore Five kittens are sharing 6 cups of milk equally so 1 1/5 cup of milk is given to each kitten.
To learn more about Mathematical expression refer to:
https://brainly.com/question/1859113
#SPJ2
asap asnwerrrrrrrrrrrrrrrrrrrrrrrr
Answers
Hope this helps!
What is the answer to this question?
Answers
Answer:
The answer should be A.
Step-by-step explanation:
I need help please please whoever gets it correct I’ll give bairnlast
Answers
Answer:
(-1,-1)A
B (1,-3)
C (-2,-4)
use the correct trig function to find the value of x. SOH, CAH, TOA
Answers
Answer:
About 11.025
Step-by-step explanation:
[tex]\sin{58^\circ}=\dfrac{x}{13}\\\\x=13\cdot\sin{58^\circ} \approx11.025[/tex]
Find the error(s) and solve the problem correctly. Be sure to explain and show your work. Where did the "wrong answer" come from? sin 52° Answer: sin 52 = .9866
Answers
The error of the evaluation comes from the fact that Sin 52° = 0.7880.
According to the question;
we are required to determine what's wrong with the evaluation..By evaluation;
Sin 52° when evaluated by means of a scientific calculator or tables gives; 0.7880.The error can be determined by evaluating; the inverse sine of 0.9866.
Sin-¹ .9866 = 80.6.Read more;
https://brainly.in/question/14817452
Write a related function for –6x + 8x – 5 = 3.
Answers
Answer:
Answer:
x=4
Step-by-step explanation:6x+8x=2x
5+3=8 (when you move a number to the other side of an equals sign, it changes its value)
2x=8
2x/2 and 8/2
x=4
The related function for –6x + 8x – 5 = 3 is;
x = 4
Algebraic ExpressionsWe are given the equation;
–6x + 8x – 5 = 3
Let us simplify the numbers that have the variable x first. Thus;
–6x + 8x – 5 = 3 gives;
8x - 6x - 5 = 3
>> 2x - 5 = 3
Use addition property of equality to add 5 to both sides;
2x - 5 + 5 = 3 + 5
>> 2x = 8
Use division property of equality to divide both sides by 2 to get;
x = 8/2
Thus;
x = 4
Read more about algebra expressions at; https://brainly.com/question/4344214
maria has a share of 2/10 slice of cake what is the difficult form of the fraction
A. 0.02
B.0.2
C.0.002
D.0.20
Answers
~fractions
= 2 ÷ 10
= B. 0,2 ✔️
the method is attached
~ nice to help you ^^
what is the correct order of reasons to complete the proof??
Answers
Answer: Choice B
I, I, V, II
======================================================
Explanation:
When doing any proofs, we always repeat what is given to us. In this case, the given statements are
QT = RSQS = RTIt seems weirdly redundant to repeat these statements back to the teacher, but this is how all proofs start off. You state what is given and the reason is simply "given". So far the answer is narrowed down to choice B or choice C, due to the "statement I" listed twice like that.
From those statements, we build toward what we want to prove. Those two given statements tell us we have two pairs of congruent sides. If we could prove a third pair of sides are congruent, then we can use SSS which stands for "side side side". It turns out that we are more or less automatically given the third pair of sides in the form QR = QR, which is true by the reflexive property. This property says that any segment is congruent to itself. So we'll have statement V listed after statement I twice. The sequence so far is I, I, V. At this point, we can conclude that choice B must be the final answer. Sure enough, statement II involves SSS just like mentioned earlier.
Mary’s sister is 7 years older than Mary. Their combined ages add up to 35. How old is Mary
Answers
Answer:
Mary - 14
Mary's sister - 21
Step-by-step explanation:
Let x be the age of Mary = x
age of Mary's sister = x + 7
Add up to 35
x + x + 7 = 35
2x = 35 - 7
2x = 28
2x/2 = 28/2
x = 14
Now substitute the value of x
Mary = 14
Mary's sister = 14 + 7 = 21
21 + 14 = 35