Use the product rule to answer each of the questions below. Throughout, be sure to carefully label any derivative you find by name. It is not necessary to algebraically simplify any of the derivatives you compute.
a. Let m (w) = 3 w^17 4^w. Find m ′(w) .
b. Let h (t) = ( sin (t) + cos (t)) t 4. Find h ′(t).
c. Determine the slope of the tangent line to the curve y = f (x) at the point where a = 1 if f is given by the rule f(x) = e^x sin (x).
d. Find the tangent line approximation L(x) to the function y = g (x) at the point where a = − 1 if g is given by the rule g (x) = ( x^2 + x ) 2^x .
Answers
Answer:
A) M'(w) = w^16 * 4^w [ 51 + 3w In4 ]
B) h'(t) = [ cos (t) - sin (t) ] t^4 + [ sin(t) + cos (t) ] 4t^3
C) f'(1) = e' [sin(1) + cos(1) ]
D) g'(a) = 0 - 1/2
L(x) = - 1/2 ( x + 1 )
Step-by-step explanation:
Attached below is the detailed solution of the problem
A) m(w) = 3w^17 * 4^w
M'(w) = w^16 * 4^w [ 51 + 3w In4 ]
B) h(t) = [sin(t) + cos(t) ] t^4
h'(t) = [ cos (t) - sin (t) ] t^4 + [ sin(t) + cos (t) ] 4t^3
C) f(x) = e^x sin (x). at a = -1
f'(1) = e' [sin(1) + cos(1) ]
D) g (x) = ( x^2 + x ) 2^x .
g'(a) = 0 - 1/2
L(x) = - 1/2 ( x + 1 )
Related Questions
solve the following inequality.
6.3r < -45.36
which graph shows the correct solution?
A) Open circle pointing to the right, starting from -72 to infinity
B) Open circle pointing to the left, starting from -72 to infinity
C) Open circle pointing to the right, starting from -7.2 to infinity
D) Open circle pointing to the left, starting from -7.2 to infinity
Can u help please??
Answers
Answer:
D. Open circle, point is at -7.2 pointing to the left.
Step-by-step explanation:
Got it right on Edge 2021! Hope I helped <3
The sign of the leading coefficient for the polynomial equation of the graph is negative positive zero
Answers
Answer:
The sign of the leading coefficient for the polynomial equation of the graph is NEGATIVE
Hope this helps!
Answer: 1 turning point
Step-by-step explanation:
Enter the correct answer in the box. Write the sum of √28x^6 + 4√7x^6 in simplest form, if x ≠ 0.
Answers
Answer:
21.97025026/250
What do u think the answer is !!
Answers
Answer:
Yeah
Step-by-step explanation:
Just swiss cheese ngl
Answer:
cheddar + turkey
Step-by-step explanation:
.........mmmm....mm..mm.mm.mm
14) What is 50% of 180?
15) What is 25% of 36?
16) What is 100% of 166?
17) What is 150% of 126?
18) What is 10% of 100?
19) What is 200% of 133?
20) What is 25% of 172?
Answers
Answer:
14. 90%
15. 9%
16. 166%
17. 189%
18. 10%
19. 266%
20. 40%
What digit is in ten thousands place 983,471?
Answers
7
The digit in ten thousandths place is 7 as it is the fourth digit to the right of decimal point.
Answer:
8
Step-by-step explanation:
9= one hundred thousands
8= ten thousands
3= one thousands
4= one hundreds
7= tens
1= ones
Why is the percent increase from 45 to 75 not equal to the percent decrease from 75 to 45? Select three options
Answers
Answer:
the answer is 2,3,and 5
Step-by-step explanation:
Answer:
2, 3, and 5
Step-by-step explanation:
Does anyone know the answer?
Answers
Answer:
20 i think
Step-by-step explanation:
78 billion scientific notation
Answers
Answer:
78 x 10^9
Step-by-step explanation:
Hope this helps!
Answer:
7.8 x
Step-by-step explanation:
Scientific notations are being used to write very large or very small numbers. In line with this, the other details regarding 78 million in scientific notation are indicated above.
Evaluate each expression.
b)
d)
169 cm2:13x13=169 13cm by cm
2500 cm2:50x50=2500 50cm by cm
/8
a) 2 + (10 − 3) =2+(10-3)
c)
(4 + 3)2 − (3 − 1)3 =
= 2+(7)=10
=
=
11.
b) (3 + 5) × 6 ÷ 3 + (8 + 52)
d)
18 + (4 + 5)2 × 2
=
=(7)x6/3+(177)
=
=(42/30
=
=
=
=
=
Answers
Answer:
atleast 1
Step-by-step explanation:
Assuming part a is correct, how do you do b and c?
Answers
Step-by-step explanation:
B. Yes, we are 99% confident that the population mean is within the interval.
C. Yes, 225 is below the interval minimum, so it is reasonable to conclude the average cholesterol level is greater than 225 mg/dl.
D. No. Increasing the sample size would decrease the margin of error, so the ends of the interval would move closer to the sample mean of 251.9. So the interval minimum would still be higher than 225.
a chemical change creates a new
Answers
Answer:
A new substance with new and different physical and chemical properties.
Step-by-step explanation:
Chemical reactions involve combining different substances. The chemical reaction produces a new substance with new and different physical and chemical properties. Matter is never destroyed or created in chemical reactions. The particles of one substance are rearranged to form a new substance.
If you find my answer helpful
Pls consider marking my answer as Brainliest! It would mean a lot!
NEED HELP WITH MATH! Will Give Brainliest! Image is below.
Answers
Answer:
#2
Even though the graph dips down, x is still increasing, and y will increase as will .
As x is decreasing, y is also decreasing.
The last school year enrollment of Genoa Middle school was 465 students. This year the enrollment is 525.
Answers
Answer:
465 to 525
Step-by-step explanation:
60 difference
adult men weights mean of 190 30 3 random men mean weight
Answers
Answer:
is this the question ?
Step-by-step explanation:
1079 divided by 4 Yeah Also whoever helps thank you :D
Answers
Answer:
269.75
Hope this helps:)
Step-by-step explanation:
The nth term of an AP is given by 2n +9 find the first term
Answers
A normal population has mean =μ7 and standard deviation =σ5. (a) What proportion of the population is less than 18?
Answers
Answer:
P(x< 18) = 0.986
Step-by-step explanation:
Step 1: find the z-score using the formula, z = (x - µ)/σ
Where,
x = randomly chosen values = 18
µ = mean = 7
σ = standard deviation = 5
Proportion of the population that is less than 18 = P(x < 18)
Plug in the values into z = (x - µ)/σ, to get z-score.
z = (18 - 7)/5
z = 11/5 = 2.2
Step 2: Find P(x< 18) = P (z<2.2) using z-table.
The probability that corresponds with z-score calculated is 0.986.
Therefore,
P(x< 18) = 0.986
What is the value of a in the proportion???? need help!!!
Answers
Answer:
90
Step-by-step explanation:
90-15/90= 5/6
90-15= 75
75/90= 83.3333 or 5/6
A scanner can scan 20 pages and 120 seconds. How many pages can scan in 4 minutes?
Answers
Answer:
40 pages
Step-by-step explanation:
120 or 2 min x 2 = 4
20 x 2 = 40
Sorry I couldn't explain more, but I hope this helps!
Answer:
40 pages
Step-by-step explanation:
convert 4 mins -> 240 secs
then cross multiply 20/120 and x/240 (x represents the pages scanned)
u then get 120x=4800
simplify(divide)-> x=40
Mr.Watts is a famous motivational speaker. He travels across the country by jet and gives an average of seven presentations a week. He gives his
speeches in auditoriums that are always full and hold an average of 1000 people each. He charges $40 per person at each of these speeches. His
average expenses for each presentation, including renting the auditorium, are about $20,000. The cost of meals, motels, jet travel, and support
personnel total $60,000 per week. How many weeks will Mr. Watts need to travel if he wants to earn $560,000 per year?
Answers
Answer:
Mr watts needs 7 weeks
Step-by-step explanation:
The average expense per presentation = $20,000
Since Mr. Watts can give about 7 presentations per week, hence the average expense per presentation for a week = $20000 × 7 = $140000
Also the cost of meals, motels, jet travel, and support personnel total $60,000 per week. Hence the total cost per week is:
Total cost = $140000 + $60000 = $200000
The revenue gotten is $40 per person and can take 1000 people per each presentation. Hence:
Revenue per week = $40 per person × 1000 people × 7 days = $280000
Let assume the number of weeks needed to earn $560000 be x. Hence:
280000x - 200000x = 560000
80000x = 560000
x = 7
PLEASE HELP ME ON ALL ASAP!!!! I WILL GIVE BRAINLIEST!!!
Answers
Answer:0=16 1=23 2=30 3=37 4=44
Step-by-step explanation:
Just one more question I need this in a step by step please
Answers
Answer:
2x+20+3x+40=90
5x+60=90
5x=30
x = 6
2x+20 = 2(6)+20
12+20
=32
3x+40 = 3(6)+40
18+40
=58
Answer:
Here we can first find the value of x simply by using the concept of corresponding angles.
As we know that angle with measurement 2x+20Degree and the right angle below are corresponding as we can consider the line (underlined in red) as a transversal intersecting lines underlined in green. {PLEASE SEE THE ATTACHMENT TO SEE THE HIGHLIGHTED LINES}
So, we get 2x+20 degree = 90 degree.
= 2x+20=90
= 2x=90-20
= 2x=70
= x= 70/2
= x=35 degree.
Now as we know the value of x we can find the other unknown angle by substituting it in the equation for the other angle.
Therefore, 3x+40degree= 3*35+40
105+40
= 145 degrees.
How many kilograms of potatoes will each person get if 5 people share 1/3 of a kilogram of potatoes equally?
Answers
Answer:
1/15 kg
Step-by-step explanation:
Divide by 5 can be written as multiply by 1/5
1/3 * 1/5 = 1/15
Which point is on Analyn's graph
Answers
Which line is perpendicular to y=2x-7
Answers
Answer:
y=-1/2x−5/2
Step-by-step explanation:
The equation of a line perpendicular to given line is y=-x/2.
The given equation of a line y=2x-7 and passes through the point (0, 0).
What is slope of an equation?The slope formula is used to calculate the inclination or steepness of a line. It finds application in determining the slope of any line by finding the ratio of the change in the y-axis to the change in the x-axis.
The standard form of equation of a line is y=mx+c, where m=slope and c=y-intercept.
So, slope of a given equation is y=2x-7
m=2
Now, slope of a line perpendicular to given line is -1/m = -1/2
Put m= -1/2 and (0, 0) in y=mx+c and simplify.
That is, 0=0+c
c=0
Then, the equation of a line is y=-x/2
Therefore, the equation of a line perpendicular to given line is y=-x/2.
To learn more about the equation of a line visit:
https://brainly.com/question/21511618.
#SPJ5
"Your question is incomplete, probably the complete question/missing part is:"
Which line is perpendicular to y=2x-7 and passes through (0, 0).
does the surface in contact with ground affect the going motion of the car ?why?
Answers
Answer:
Yes, it does. The ground is bumpy and it creates friction acting against the car's motion.
(you can include my example too depending on what your teacher is looking for)
Step-by-step explanation:
This is a fun one! Think about a ball rolling on a smooth surface, now on a bumpy sandpapery one. Which one do you think is faster? The smooth surface! This is because of this friction of the sandpaper which slows down the ball. On the other hand, the smooth one has very little friction. The same applies to cars.
HELP ME ASAP!!! I WILL MARK BRAINLIEST!!
Answers
Answer:
Brand A ($2) is more expensive than Brand B ($1.50) (see below)
Step-by-step explanation:
First, you will have to find the slopes of both lines. Slope is y/x, which is the cost/meter or cost per meter.
Using the slope formula:
y2 — y1
m = ---------------
x2 — x1
Plug in any two points from both lines:
y2 — y1
m = --------------- = graph 1 (0, 0), (1,2)
x2 — x1
2 — 0
m = ---------------
1 — 0
2
m = --------------- = $2/m
1
_______graph 2_______
y2 — y1
m = --------------- = graph 2 (0, 0), (4, 6)
x2 — x1
6 — 0
m = ---------------
4 — 0
6 3
m = --------------- = ----------- = $3/2 m
4 2
Because you are unable to have an exact cost per meter of Brand B, you can use a ratio:
$3 = $x
2m = 1m
Cross multiply:
3 (1) = 2x
3 = 2x
x = (3 ÷ 2)
x = 1.5
So Brand B is $1.50 per meter while Brand A is $2.00 per meter. Brand B is cheaper.
what is 0.067 reccuring as a fraction
Answers
Answer:
67/1000
Step-by-step explanation:
How to translate 0.067 to a fraction:
So you can there is the tenths place (which is considered 0 on the decimal behind the point.) The hundredths place (where the 6 is placed), and the thousandths place (where the 7 is placed.)
Since the 7 is placed at the thousandths place, that means the denominator would be 1000. The number behind the point is .067.
So the fraction would be this:
67/1000
(Also it's at it's simplest form.)
You choose a card from a deck of 52 cards. Without replacing the card, you choose a second card. What is the probability of choosing two red cards?
Answers
Answer: 13/51
Step-by-step explanation: After shuffling there are 52 permutations of 52 cards. Each has the probability of occurrence equal to another, that is the probability of any sequence of cards is 1/52.
Let's count only those where there is a red card on the first place and black card on the second. There are 26 red and 26 black cards. Therefore, we have 26 ⋅26 choices for a pair of two first cards. The sequence of other 50 cards in unimportant and any permutation among them is fine for us since we fixed the first two.
Therefore, we have 26 ⋅ 26 ⋅50 different permutations when the first card is red and the second is black.
Therefore, we have 26 ⋅ 26 ⋅50 different permutations when the first card is red and the second is black.
The final probability, therefore, is
26 ⋅26 ⋅50 / 52 = 26 ⋅26 / 52 ⋅ 51 = 13 / 51
13/51 is the final answer