Answers
Answer:
A. G'(5) = 20
B. G'(5) = -1
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
FunctionsFunction NotationCalculus
Derivatives
Derivative Notation
Derivative Rule [Product Rule]: [tex]\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)[/tex]
Derivative Rule [Quotient Rule]: [tex]\displaystyle \frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}[/tex]
Step-by-step explanation:
Step 1: Define
[Given] F(5) = 4, F'(5) = 4, H(5) = 2, H'(5) = 3
[Given] A. G(z) = F(z) · H(z)
[Given] B. G(w) = F(w) / H(w)
[Find] G'(5)
Step 2: Differentiate
A. G(z) = F(z) · H(z)
[Derivative] Product Rule: G'(z) = F'(z)H(z) + F(z)H'(z)B. G(w) = F(w) / H(w)
[Derivative] Quotient Rule: G'(w) = [F'(w)H(w) - F(w)H'(w)] / H²(w)Step 3: Evaluate
A. G'(5)
Substitute in x [Function]: G'(5) = F'(5)H(5) + F(5)H'(5)Substitute in function values: G'(5) = 4(2) + 4(3)Multiply: G'(5) = 8 + 12Add: G'(5) = 20B. G'(5)
Substitute in x [Function]: G'(5) = [F'(5)H(5) - F(5)H'(5)] / H²(5)Substitute in function values: G'(5) = [4(2) - 4(3)] / 2²Exponents: G'(5) = [4(2) - 4(3)] / 4[Brackets] Multiply: G'(5) = [8 - 12] / 4[Brackets] Subtract: G'(5) = -4 / 4Divide: G'(5) = -1Topic: AP Calculus AB/BC (Calculus I/II)
Unit: Derivatives
Book: College Calculus 10e
Related Questions
Manny buys 16 apples at the market and 8 oranges. what are the ratios of apples to oranges ?
Answers
Answer:
2:1 or 16:8
Step-by-step explanation:
Answer:
2:1
Apple: orange
Step-by-step explanation:
Divide the number of apples by the number of oranges
Is (4, 2) a solution to the system y-x=2 and -3x-2y=-8?
Answers
Answer:
It is only a solution to y = x - 2, not -3x - 2y = -8
Step-by-step explanation:
I) Check y = x - 2:
y = x - 2
2 = 4 - 2
As you can see, (4, 2) is a solution to this system.
II) Check -3x - 2y = -8:
-3x - 2y = -8
(-3)(4) - (2)(2) = -8
-12 - 4 =/= 8
-12 - 4 = -16, not 8. So (4, 2) is not a solution to this system.
Snow Play Ski Park costs $35 entry fee and then $5 per hour. If you have $60, how long can you be at Snow Play Ski Park?
Part A - Identify the independent and dependent variables.
Answers
Answer:
You can be in the snow play ski park 5hours
Step-by-step explanation:
First 60$ - 35$=25$
1h=5$
2h=10$
3h=15$
4h=20$
5h=25$
So you can pay 35$ for the snow play ski park and then you can be there 5hours.So 35$ for the entry+25$ for the 5 hours=60$
PS:Can I be a brainliest pls. And have a nice day and sry for my english i m not so good but i wanted to help you.cya
Uniform Distribution Notation Format Which of the following is the correct notation used for a uniform probability distribution where the smallest value of the random variable X is 9, and the largest value of the random variable X is 28. X - B{9, 28) X - U(28.9) You Answered U - X(9, 28) Correct Answer X - U(9,28)
Answers
Solve: (x −6)−(4.5−x )= −1.5
PLZ HELP
Answers
Answer:
x=9/2 Hope this helps!
Step-by-step explanation:
Let's solve your equation step-by-step.
x−6−(4.5−x)=−1.5
Step 1: Simplify both sides of the equation.
x−6−(4.5−x)=−1.5
x−6+−1(4.5−x)=−1.5(Distribute the Negative Sign)
x+−6+(−1)(4.5)+−1(−x)=−1.5
x+−6+−4.5+x=−1.5
(x+x)+(−6+−4.5)=−1.5(Combine Like Terms)
2x+−10.5=−1.5
2x−10.5=−1.5
Step 2: Add 10.5 to both sides.
2x−10.5+10.5=−1.5+10.5
2x=9
Step 3: Divide both sides by 2.
2x/2=9/2
x=9/2
Answer is 9/2.
Find the area of the shaded figure below
Answers
Answer:
I think 40 units
Step-by-step explanation:
hope you have a wonderful day
#2 What is 18.082 rounded to the nearest whole number?
Answers
Answer:
18
Step-by-step explanation:
Samir and Christian had a total of 360 marbles Samir lost 28 marbles while Christian brought 18 more marbles both of them had an equal number of marbles in the end how many marbles did Samir have at the beginning
Answers
Step-by-step explanation:
Marbles altogether = 360
Marbles Samir Lost = 28
360 - 28 = 332
Marbles Christian bought 18
332 + 18 = 350
Marbles both had in the end = 350 ÷ 2 = 175
Marbles Samir have at the beginning = 175 + 28 = 203
Answer = 203
I was doing my homework when I come across this question, it says "substitute each given value of the variable to find which, if any, is a solution of the inequality." what does this mean?
Answers
Answer:
Step-by-step explanation:
Perimeter (P) of the quarter circle is the curve + both sides.
Perimeter of the curve
Perimeter of the sides
2 sides = 2r
Step-by-step explanation:
if qs represents an angle bisector solve for x I need help with this
Answers
Answer:
40.5
Step-by-step explanation:
Since QS is an angle bisector then PQs and SQR are similar. Using the similarity theorem;
PQ/PS = QR/SR
45/20 = x/18
Cross multiply
20x = 45 * 18
20x = 810
x = 810/20
x = 40.5
Hence the value of x is 40.5
What is the greatest common factor of 138 and 345?
Answers
Answer:
Step-by-step explanation:
Step by Step Solution. Calculate Greatest Common Factor for : 138, 345. Factorize of the above numbers : 138 = 2 • 3 • 23. 345 = 3 • 5 • 23. Build a prime factors table. ...
Why learn this.
Terms and topics. GCF calculator.
Related links. Greatest common factor (GCF) explained | Arithmetic (video) | Khan Academy. LCM on Purplemath.
Answer:
69 I believe.
Step-by-step explanation:
What is the domain of the function above? I HATE GRAPHS pls help
tyyyy
Answers
Answer:
-1<x<4
BLUE
Step-by-step explanation:
PLEASE HELP WILL MARK BRAINLIEST IF CORRECT
A farm is to be built in the shape of Quadrilateral ABCD, as shown below. All four sides are equal.
A rhombus ABCD is shown with diagonal AC equal to 16.8 feet and diagonal BD equal to 11.9 feet
What is the area of the farm?
57.4 square feet
99.96 square feet
114.8 square feet
133.28 square feet
Answers
Answer:
99.96
but trust me I'm bad with big numbers but I think this ones right.
Answer:
99.96
Step-by-step explanation:
1. The pollution level in the center of a city at 6 am is 30 parts per million and it
grows in linear fashion by 25 parts per million every hour. If y is pollution
and t is time elapsed after 6 am, determine:
a. The equation that relates y with t.
b. The pollution level at 4 o'clock in the afternoon
Answers
Answer:
a) [tex]y(t) = 30 + 25t[/tex]
b) The pollution level at 4 o'clock in the afternoon is of 280 parts per million.
Step-by-step explanation:
The pollution level in the center of a city at 6 am is 30 parts per million and it grows in linear fashion by 25 parts per million every hour.
This means that the pollution in t hours after 6 am is given by:
[tex]y(t) = 30 + 25t[/tex], which is the answer to question a.
b. The pollution level at 4 o'clock in the afternoon
4 in the afternoon is 10 hours after 6 am, so this is y(10).
[tex]y(10) = 30 + 25*10 = 30 + 250 = 280[/tex]
The pollution level at 4 o'clock in the afternoon is of 280 parts per million.
When a normal six sided die is rolled what is the probability of getting a 7
Answers
Answer:
0% chance
Step-by-step explanation:
Answer:
0/6
You can't roll a 7 on a 6 sided die.
5-(x-3)+4x simplify equation
Answers
Answer: 3x+8
Step-by-step explanation:
Answer:
3x+8
Step-by-step explanation:
5-(x-3)=4x
5-x+3+4x
3x+8
PLEASE HELP I DONT GET THIS AND MY MOM IS MAD AT ME
A person is looking from a car to the top of a building. The angle of elevation to the top of the building from the car is 32°. The building is 200 feet away. How tall is the building? Round to the nearest foot.
Answers
Answer:
132.2 ft
Step-by-step explanation:
This is a right angle problem where 32 is the angle and 200 feet is the leg unederneath. To solve for the height we use tangent since we have the adjacent side and we are solving for the opposite side.
Steps:
1. tan32 = x/200
2. (tan32)200=x
3. x=132.2 ft
charlie uses the expression 2x + 2x to represent the perimeter of a square. What does the variable x represent in this expression?
The area
The perimeter
The side lengths
The sum of 2 side lengths
Answers
Answer:
D The Sum of 2 Numbers
Step-by-step explanation:
2+2=4 > 24 > 24 + 24
Answer:
The side length
Step-by-step explanation:
Joanne is buying a pair of shoes in Europe the length of her foot is 27.5cm
Answers
Answer:
42-43 Euro size
Step-by-step explanation:
it is a 9.5 in American so that is the size converted to Euro (42-43).
I don't know if that helped I cant say for sure it is correct.
A scale model of a buliding is 18 inches tall. The actual building is 240 feet tall. What is the scale factor of the model? Write your answer as a fraction in simplest form.
Answers
Answer:
The scale factor of the model is 160.
Step-by-step explanation:
18 inches : 240 feet tall is also equal to
18 inches : 2880 inches
2880/18 = 160
What is the equation of the line that passes through the point (5, -6) and has a
slope of 3/5
Answers
Answer:
y = 3/5x + -9
or y = 3/5x - 9
Step-by-step explanation:
Since you are already given the slope for this equation all you have to do is plug in the ordered pair in this equation: y = mx+b
Here is what this equation stands for:
y = the y in the order pair you are given, in this case it would be -6
m = This is the slope, sometimes you may not be given the slope so you would have to find it, but in this case, you are given it, the slope is 3/5
x = the x in the ordered pair you are given, in this case it would be 5
b = This is the y-intercept, you will mostly be solving for this most of the time
(5,-6)
(x, y)
y = mx+b (Use this Formula)
-6 = 3/5(5) +b (The numbers have been substituted within the formula)
-6 = 3+b (simplify the equation by multiplying the slope by the x)
-6-3 = b ( once simplified the left side of the equation, go to the right side, but remember when you do that you have to change the sign because you are eliminating 3 on the left side completely, "what you do on one side, do it to the other side")
-9 = b (solve)
y = 3/5x + -9 (plug in the slope and B(y-intercept) within the formula - y = mx+b, make sure that you are not plugging in x and y for this step)
I Hope This Helped You Understand this Problem Better/More!!! Stay Safe and Healthy!
What is the area of the figure below?
15 in 2
20 in 2
30 in 2
25 in 2
Answers
Answer:
25 [tex]in^{2}[/tex]
Step-by-step explanation: we can move the little triangle on the side to the missing part of the square and it says the length of the little triangle is 2 so we can do 2+3 since the height of the square with the missing side is 3. then we end up with the height being 5 and the base being 5. we know that A=bh so we can do A=5x5 and get 25 in squared
pls mark me branliest!!
Answer:
25ft2
Step-by-step explanation:
Q4. Three students A, B and C had 3 soil samples. Each student poured 180 mL of water
into the soil samples they had. Time taken for the percolation of water through the three
soil samples was 25 min, 10 min and 40 min respectively. Which student had the soil with
the highest percolation rate?
Answers
Answer:
Student B
Step-by-step explanation:
Soil percolation is the porosity of soil to the downward flow of water through it. A soil with high percolation allows water to drain through it downwards in a less period of time.
From the given experiment by students, it takes 25 min for water to percolate through the soil sample of student A, 10 min for the soil sample of student B and 40 min for the soil sample of student C. Thus, the student that had the soil sample with highest percolation rate is B.
Someone please explain how to do this!!
Answers
Answer:
o because the square is not of 4
Use the volume formula to find the volume of the prism. (look at the pic for the options)
Answers
Answer:
not stealing points but do not go on that website. totally fraud smh
MUST HELP!!!! (50 POINTS) +BRAINLEST +5 STARS +THANKS ON PROLFILE!!!!
Figure A’B’C’ is an __________________________of figure ABC.
*fill in the blank*
Answers
Answer:
similar shape!!!!
Step-by-step explanation:
Answer:
Dialation
Step-by-step explanation:
Dilation is an increase in size, but does not change the shape
What simplified ratio correctly compares 36 inches to 4 feet?
Drag and drop the appropriate numbers into the boxes.
:
2 3 4 6 9 36
Answers
Answer:
3/4 or 3-4
.......................
A scientist is investigating whether percent concentration can be used to predict density in apple juice. A scientist selected a random sample of 12 apple juice varieties and recorded the density, in pounds per cubic inch, and the percent concentration of each apple juice variety. The scientist wants to estimate the mean change in the density, in pounds per cubic inch, for each increase of 1 percent concentration of apple juice. Assuming the conditions for inference have been met, which of the following inference procedures is most appropriate for this investigation?
a. A linear regression t-interval for slope.
b. A matched-pairs t-interval for a mean difference.
c. A two-sample t-interval for a difference between means.
d. A one-sample t-test for means.
e. A two-sample z-interval for a difference between proportions
Answers
Answer:
The most appropriate inference procedure for the investigation is;
a. A linear regression t-interval for the slope
Step-by-step explanation:
Given that the slope of an horizontal line is zero, we have that there is no change in the y (dependent) variable when there is a change in the x-variable, therefore, it is important to find the true relationship between the two variables, 'x', and 'y'
The confidence interval of the slope is calculated and analyzed to determine if it excludes or includes, 0, such that, if the confidence interval exclude 0, then, it is unlikely that the slope is 0, therefore, there the relationship between the variables, 'x', and 'y' is significant
Therefore, a linear regression t-interval for the slope is most appropriate.
HELP ASAP PLEASE
Which best describes parallel lines?
Otwo lines that are always equidistant
O two lines that curve to form a circle
O two lines that intersect at multiple points
O two lines that originate from the same point
Answers
_________________________
_________________________
are parallel lines
Harley read 5 books in january, 8 books in february, 4 books in march and 7 books in april. what is the average number of books harley reads per month
A: 7
B: 6
C: 6.5
D: 3
Answers
Answer:
B: 6
Step-by-step explanation:
Find the mean:
5+8+4+7= 24
24/4=6