Answers
Answer:
y = e·x
Step-by-step explanation:
The equation of a line tangent to a curve at a point is conveniently written in the point-slope form. The slope is the derivative of the function at the point. For your function, the rules applicable to products and exponential functions apply.
__
y = (e^x)(x^2 -2x +2
y' = (e^x)(x^2 -2x +2) +(e^x)(2x -2) . . . . . (uv)' = u'v +uv', (e^x)' = e^x
y' = (e^x)x^2 . . . . . simplify
For x=1, the slope is ...
y' = (e^1)(1^2) = e
__
The point-slope form of the equation for a line is ...
y -k = m(x -h) . . . . . . line with slope m through point (h, k)
y -e = e(x -1) . . . . . . . line with slope 'e' through point (1, e)
y = e·x -e +e . . . . . add e
y = e·x . . . . . . . . . . equation of the tangent line
__
Additional comment
It is often the case that ex is written when e^x is intended. We are trying to avoid that ambiguity here by writing the equation with an explicit "times" symbol.
Related Questions
Charlie takes a gymnastic class once a week. At each class, she buys a bottle of water for $0.75 and a protein bar for $2.50. Which of the following expressions represent the amount of money, in dollars, Charlie spends after attending 12 gymnastics classes? Select all that apply.
Answers
Answer:
$39
Step-by-step explanation:
[tex]12(.75 + 2.50) = 12(3.25) = 12(3) + 12(.25) = 36 + 3 = 39[/tex]
Internet Viewing A researcher wishes to estimate the average number of minutes per day a person spends on the Internet. How olo
large a sample must she select if she wishes to be 99% confident that the population mean is within 10 minutes of the sample
mean? Assume the population standard deviation is 38 minutes. Round your final answer up to the next whole number.
Answers
Using the z-distribution, as we have the population standard deviation, it is found that a sample of 96 people must be taken.
What is the margin of error for the z-distribution?It is given by:
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which:
z is the critical value.[tex]\sigma[/tex] is te population standard deviation.n is the sample size.In this problem, we have a 99% confidence level, hence[tex]\alpha = 0.99[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.99}{2} = 0.995[/tex], so the critical value is z = 2.575.
Additionally, we have that [tex]\sigma = 38, M = 10[/tex], hence we solve for n to find the minimum sample size needed.
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]10 = 2.575\frac{38}{\sqrt{n}}[/tex]
[tex]10\sqrt{n} = 38 \times 2.575[/tex]
[tex]\sqrt{n} = 3.8 \times 2.575[/tex]
[tex](\sqrt{n})^2 = (3.8 \times 2.575)^2[/tex]
n = 95.7
Rounding up, a sample of 96 people must be taken.
More can be learned about the z-distribution at https://brainly.com/question/25890103
Plumber A charges $50 to come to your house, plus $40 per hour of labor. Plumber B charges $75 to come to your house, plus $35 per hour of
labor. If y is the total dollar amount charged for x hours of labor, which of the following systems of equations correctly represents this
situation?
Answers
Answer:
D. y=40x + 50
y=35x + 75
Step-by-step explanation:
x is per hr
it's 40 and 35 dollars per hr
HELP MY SISTER NEEDS HELP IN MATH SHES SO STUCK
Answers
Answer:
J
Step-by-step explanation:
It’s the only one that makes 6Find the area of this trapezoid. Be sure to include the correct unit in your answer.
Answers
Answer:
76 squared cm
Step-by-step explanation
the equation is (b+b*h/2) so u just take 7 plus 12 times 8 divided by 2 and you get 76
Savannah's favorite candles are so popular that the price has been
increased. The price for a 24 oz. candle used to be $20, but now it is $28.
By what percentage has the price been marked up? *
Answer
70%
85%
48%
40%
Answers
Answer:
40%
Step-by-step explanation:
The increase was $8. Divide the increase by the original amount.
8/20 = .4
The decimal answer 0.4 converts to a percent answer of 40%. (.4×100=40)
The candle was marked up 40%.
What’s the answer?????20 points!!!!
Answers
Answer:
i think 6,300
Step-by-step explanation:
Answer:
I believe the answer is c <3
Represent 56÷ 8 = 7 using subtraction. Explain your reasoning.
Answers
Answer:
56-8-8-8-8-8-8-8=0
Step-by-step explanation:
Probably just wants to show how many times you subtracted 8 until you got 0
A Man borrowed Rs 500 for 3 years at the rate of 5% find his interest and amount
Answers
Answer:
Total amount = $575.00I = PRT/100 = $75.00Equation:Total amount = interest + principle
Step-by-step explanation:
Formula:- I = PRT/100
Where,
I is interestP is principleR is rateT is time⇒ I = 500×5×3/100
⇒ I = 7500/100
⇒ I = 75
Interest is $75.00
The total amount accrued, principal plus interest, from simple interest on a principal of $500.00 at a rate of 5% per year for 3 years is $575.00.
answers :
A. 80 degrees
B. 180 degrees
C. 110 degrees
D. 140 degrees
Answers
Answer:
D) 140 degrees
Step-by-step explanation:
Radius is perpendicular to tangent line
Draw DA, construction
DA is an angle bisector, m<BAD = 20,
Now, DBA and DCA are congruent right triangles
This is due to LA congruency
90 + 20 + x = 180
x = 70
BDA = CDA
so 70 + 70 = 140
D) 140 degrees
(I'm not that good at geo, so :( )
what is an area of a trapezoid
Answers
Answer:
144
Step-by-step explanation:
Required area= Area of rectangle +2×(Area of Triangle)
=(10×8)+2×(1/2×8×8)
=80+64=144 in²
Answer:
144 in²
Step-by-step explanation:
To solve for the area of a trapezoid divided into a parallelogram (in this case a rectangle) and two triangles, you calculate the area of each part and add it together.
the area of a triangle = (base • height) / 2
the area of a parallelogram = (base • height)
so:
1. Calculate area of first triangle. 8 • 8 = 64, 64/2 is 32
2. Calculate the area of the second triangle. Since in this situation you have two equal triangles, you multiply the answer to the first part by 2 and get 64 in² again.
3. Calculate the area of the rectangle. 8 • 10 = 80 in²
4. Add the two numbers together. 80 + 64 = 144 in²
Deposit $130 at 9.4% compounded daily for 2 years
Answers
Answer:
$ 155.59 after two years
Step-by-step explanation:
Future Value = 130 ( 1 + .094)^2
Start time 8:10 am end time 10:55 am elPSED TIME’
Answers
Answer:
14 hours, 45 minutes
Step-by-step explanation:
The time between 8:10:00 AM and 10:55:00 PM is,
14 hours, 45 minutes, and 0 seconds or 14.75 hours
Which function is the inverse of f(x)=-5x-4
Answers
multiplication of -5 and x
A medical team has found that the blood concentration of a particular medicine has a
decay rate of 40% in 24 hours. How much of an initial dose of 1,000 mg of the medicine
will be detected after 48 hours? Round to the nearest mg. Use the formula A=A0e^-kt. (the value of T is 48/24=2)
A. 360 mg
B. 449 mg
C. 600 mg
D. 920 mg
E. 200 mg
Answers
1) Debbie bought 8 oranges and 7 apples for $10.20. Katrina bought 5 oranges and 14 apples for $12.15. How much did one apple and one orange cost?
2) Joel and Janie are selling fruit. Joel sold 2 small boxes of fruit and 5 large boxes for $31. Janie sold 4 small boxes of fruit and 7 large boxes for $47. How much does one small box of fruit and one large box of fruit cost?
3) Carmen is trying to decide which jet ski rental plan to use. Plan A charges a one-time fee of $40 and $25 per hour. Plan B charges a one-time fee of $60 and $15 per hour. After how many hours will the plans cost the same?
4) Julie and Wendi purchased cell phones. Julie’s phone cost $50 and she pays $0.35 per minute. Wendi’s phone cost $70 and she pays $0.15 per minute. After how many minutes of use will Julie’s phone cost more than Wendi’s?
5) 78 students went on a field trip. They went by van or car. The total number of cars and vans were 10. Each car held 5 students and each van held 12 students. How many cars and how many vans went on the field trip?
6) 168 students went on a field trip. They took a total of 10 vans and buses. Each bus held 42 students, and each van held 6 students. How many vans went on the field trip?
7) Christina spent $81.25 on books. Comic books cost $2.25 each and novels cost $7.00 each. If she bought 15 books, how many comic books did she buy?
8) Tina bought 8 pieces of clothing for a total of $164. Jeans cost $22 each and shirts cost $18 each. How many shirts did Tina buy?
9) Farmer Brown had 25 cows and chickens. They had a total of 72 legs. How many cows and how many chickens did Farmer Brown have?
10) Farmer Brown had 28 cows and chickens. They had a total of 96 legs. How many cows and how many chickens did Farmer Brown have?
What you need to do:
Please WRITE both equations for each problem, identify what your variables represent, and solve the system.
I don’t know what to do, so please help me understand by explaining how you got the answer.
I WANT TO LEARN FROM YOU! :)
- Will give BRAINLIEST if it gives me the option -
Answers
Farmer Brown had 25 cows and chickens. They had a total of 72 legs. How many cows and how many chickens did Farmer Brown have?
Solution:Let the number of cows be "x" and the number of chickens be "y".
According to question,
x + y = 25 4x + 2y = 72 -->(ii)
=> 4(x + y) = 25 × 4
=> 4x + 4y = 100 -->(i)
By Elimination method,
Equation (i) - (ii)
(4x + 4y) - (4x + 2y) = 100 - 72
=> 4x + 4y - 4x - 2y = 28
=> 2y = 28
=> y = 28/2
=> y = 14
Putting the value of "y" in Equation (ii)
4x + 2y = 72
=> 4x + 2 × 14 = 72
=> 4x + 28 = 72
=> 4x = 72 - 28
=> 4x = 44
=> x = 44/4
=> x = 11
Therefore,Total number of cows = 11
Total number of chickens = 14
Note: In the second equation of this question I've taken 4 and 2.
The reason behind it is simple. Since, I've assumed the number of cows is "x" and a cow has four legs that why infront of "x" I've put 4.
And a chicken has 2 legs and I've assumed it as "y" therefore infront of "y" I've put 2.
======================================
Question no.10:Farmer Brown had 28 cows and chickens. They had a total of 96 legs. How many cows and how many chickens did Farmer Brown have?
Solution:Let the number of cows be "x" and the number of chickens be "y".
According to question,
x + y = 28 4x + 2y = 96 -->(ii)
=> 4(x + y) = 28 × 4
=> 4x + 4y = 112 -->(i)
By Elimination method,
Equation (i) - (ii)
(4x + 4y) - (4x + 2y) = 112 - 96
=> 4x + 4y - 4x - 2y = 16
=> 2y = 16
=> y = 16/2
=> y = 8
Putting the value of "y" in Equation (ii)
4x + 2y = 96
=> 4x + 2 × 8 = 96
=> 4x + 16 = 96
=> 4x = 96 - 16
=> 4x = 80
=> x = 80/4
=> x = 20
Therefore,Total number of cows = 20
Total number of chickens = 8
Note: In the second equation of this question I've taken 4 and 2.
The reason behind it is simple. Since, I've assumed the number of cows is "x" and a cow has four legs that why infront of "x" I've put 4.
And a chicken has 2 legs and I've assumed it as "y" therefore infront of "y" I've put 2.
Hope it helpsI will give brainlisted for the correct answer. Due today!
Answers
Step-by-step explanation:
This is what we know...
Jake: 168 pg at 24 pg / day If Julio reads at a rate of 1 1/4 what Jake reads we take the 24 pg and multiply that by 1.25 24 x 1.25 = 30 So now you know the Julio reads 30 pgs each day. Now you divide Jake's 168 pgs by 24 and you get that it would take him 7 days to read the book. At 5 days Jake still has 48 pages to read. Now, Julio's 180 pages divided by his 30 pages / day which will be 6 days to complete his book. At 5 days he will have only 30 pages to read.
Which inequality is graphed on the number line
Answers
Answer:
2nd option: 3a-11≤7
Step-by-step explanation:
Step 1: The inequality on the number line is:
[tex]a \leqslant 6[/tex]
Step 2: Take a look at the options. First we know that we want values of a which are less than 6 so we get rid of option 1 and 3.
Step 3: Since 6 is included in the inequality so we need to have a ≤ so 2nd option is correct.
QUICK NOTE: if we solve the inequality shown in the 2nd option we'll see it's gonna be a≤6
take a look:
[tex]3a - 11 \leqslant 7 \\ 3a \leqslant 18 \\ a \leqslant 6[/tex]
Please is for 30 points
Answers
Find the equation of the axis of symmetry and the coordinates of the vertex of the graph of the function y = 4x2 + 5x – 1.
Answers
Answer:
The option u chose is the correct one
Find the distance of CD and the coordinate of the midpoint of CD
Answers
Answer:
Explanation:
Formula to calculate the distance between two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is,
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Therefore, length of CD having coordinates C(3,1) and D(3, 3),
[tex]CD=\sqrt{(3-3)^2+(1-3)^2}[/tex]
[tex]=2[/tex] [tex]units[/tex]
Formula to find the midpoint of CD is,
[tex]M=\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}[/tex]
[tex]=(\frac{3+3}{2},\frac{1+3}{2})[/tex]
[tex]=(3,2)[/tex]
Therefore, length of CD = 2 units and (3, 2) are the coordinates of the midpoint of CD.
These are similar figures. Solve for x
Answers
1.1 Outline any FOUR non-price competition strategies that food outlets like Nandos, KFC, Chicken Licken and other businesses specialising in chicken, ensure their operational success in the monopolistic competitive firm.
Answers
The food outlets can use these four non-price competition strategies to ensure their operational success in the monopolistic competitive market are:
Physical and quality improvementsOutlet locationTaste differentiationConsumer advertising.What are non-price competition strategies?Non-price competition strategies are competitive approaches that can help food outlets to de-emphasize pricing as a competitive strategy.
Instead of pricing, the food outlets can improve the physical and quality aspects of their chicken brands, increase consumer advertising, trade promotions, product differentiation, and locate their outlets in niche markets.
Thus, physical and quality improvements, outlet location and trade promotions, differentiation, and advertising can become non-price competition strategies for these food outlets.
Learn more about non-price competition strategies at https://brainly.com/question/1580879
Please help on math.
Answers
Answer:
Step-by-step explanation:
2hrs=70
so 4.5/2=2.25
2.25 times 70=$157.50
Find the remainder when f(x)=−2x3+x2−4x+1 is divided by x+3.
Answers
Answer:
4 the answer is 4
Step by step explanatin:
Find the dimensions and solve for the volume.
What is the volume of this prism?
Length: ? Cm
Width: 5 cm
Height: 2 cm
Volume: ? Cm
3
Answers
Length is not given or any diagram hasn't been attached.
Length to be taken as x
L=xB=5H=2Now
Volume:-
V=LBHV=5(2)xV=10x cm³Find the area of the triangle below.
Be sure to include the correct unit in your answer.
Answers
Answer:
30yd²
Step-by-step explanation:
A = a*b/2 = 5yd * 12 yd / 2 = 60 yd² / 2 = 30 yd²
Answer: 30 yd²
Step-by-step explanation:
Let's start by flipping the triangle over to become a standard right-angled triangle so that the side measuring 5 yards becomes the bottom and 12 yards becomes the height.
The area of any triangle is
Area = 1/2 x breadth x height
Area = 1/2 x 5yd x 12yd = 5 x 12/2 = 60/2 = 30yd²
Can you answer both of them pls and do it as soon as possible I don’t have enough time
Answers
Answer:
green
Step-by-step explanation:
Green covers 1/4 of the circle space where the spinner can stop
8. Calir read for 4 hours last week. Luiz
read 6 times as long. Which equation
would show how long Luiz read?
Answers
The ElA predicts that the United States has 216 billion barrels of crude oil reserves left. If 4 billion barrels are extracted each year, and extraction grows by 0.5% per year, how long will the reserves last?
Answers
Anwer o.5
Step-by-step explanation:
because 0.5 x 1 = 0.5