Answer:
see explanation
Step-by-step explanation:
Using the product rule
Given
y = f(x)g(x) , then
[tex]\frac{dy}{dx}[/tex] = f(x).g'(x) + g(x).f'(x) ← product rule
(a)
let
f(x) = (3x - 1)³ , then using the chain rule
f'(x) = 3(3x - 1)² × [tex]\frac{d}{dx}[/tex](3x - 1) = 3(3x - 1)² × 3 = 9(3x - 1)²
let
g(x) = 2x + 5 ⇒ g'(x) = 2
Then
[tex]\frac{dy}{dx}[/tex] = (3x - 1)³ . 2 + (2x + 5) × 9(3x - 1)²
= 2(3x - 1)³ +9(3x - 1)²(2x + 5) ← factor out (3x - 1)²
= (3x - 1)²[ 2(3x - 1) + 9(2x + 5) ]
= (3x - 1)² [ 6x - 2 + 18x + 45 ]
= (3x - 1)²(24x + 43)
--------------------------------------------------------------
(b)
let
f(x) = 3x - 2 ⇒ f'(x) = 3
let
g(x) = 2x² + 3 ⇒ g'(x) = 4x
Then
[tex]\frac{dy}{dx}[/tex] = (3x - 2).4x + (2x² + 3). 3 ← distribute parenthesis
= 12x² - 8x + 6x² + 9
= 12x² - 8x + 9
Note
It is usual to simplify after differentiating the expressions
A motorboat travels 172 km in 3 hours going upstream and 372 in 4 hours going downstream. What is the rate of the boat in still water and what is the rate of the current?
Answer:
The rate of the boat is 75.17 km/h and the rate of the stream is 17.83 km/h
Step-by-step explanation:
System of Equations
Let's call:
B = speed (rate) of the boat in still water
S = speed (rate) of the stream
The boat travels 172 km in 3 hours when going upstream, that is when the speed of the stream subtracts its own speed. The speed is the distance divided by the time, thus:
[tex]\displaystyle B-S=\frac{172}{3}[/tex]
Multiplying by 3:
3B - 3S = 172 [1]
The boat travels 372 km in 4 hours downstream when the speed of the current adds to its own:
[tex]\displaystyle B+S=\frac{372}{4}=93[/tex]
B + S = 93
Solving for B:
B = 93 - S [2]
Substituting in [1]
3(93 - S) - 3S = 172
Operating:
279 - 3S - 3S = 172
279 - 6S = 172
Subtracting 279:
- 6S = 172 - 279
- 6S = -107
Multiplying by -1 and solving for S:
[tex]S = \frac{107}{6}\approx 17.83\ km/h[/tex]
From [2]:
[tex]B = 93 - \frac{107}{6}[/tex]
[tex]B=\frac{451}{6}\approx 75.17\ km/h[/tex]
Pls help!!! Pls and thank you!! So much
Answer:
I solved it for u!
Hope it helps
Step-by-step explanation:
Another way, it an isosceles triangle so the base will be same, so angle 3 and angle 1 will be same after u find angle 3, then angle 1 will be equal to it
So here angle 3 = 64°
So angle 1= 64°
Lee needs some school supplies. He will buy 3 notebooks for $1.29 each, 2 dozen
pencils at $3.45 a dozen and a box of pens for $14.85.a box. Lee estimates that he
will spend about $25 on these school supplies.
Is Lee's estimation reasonable? How much will he spend exactly?
I= $164.50, P = $940, t = 2.5
Find the annual interest rate
250.35 that the anwers hope this help a lot
At a school, 460 of the students walk to school.
the number of students who ride the school bus is 110% of the number of students who walk. How many students ride the school bus?
Answer:
506
Step-by-step explanation:
To find a percent answer is easy, just do this:
Enter your base number here: 460
Enter your percent here: 110%
460 x (convert 110% to a decimal) 1.1 = 506
Your welcome =)
Answer:
The answer is 506
Step-by-step explanation:
The product of two consecutive integers is 72. Write a quadratic equation to find the integers, and then solve it.
Answer:
9 x 8
Step-by-step explanation:
Answer:
ok so basically what you do is since you know they are consecutive numbers, one is x and the other is x+1. Now when you multiply x and x+1 you get 72 , so this basically turns into a quadratic where x(x+1)=72. Thus,X^2+x=72. subtract 72 from both sides- x^2+x-72=0. Then you can solve for x using the quadratic formula or some other way and you get x to be 8 or -9. OH WAIT THERE IS ANOTHER SOLUTION IT IS -9 AND -8. . Anyway yea hoped this helped.
Step-by-step explanation:
Order from least to greatest.
1.603; 1.036; 1.36; 1.063
Answer:
1.036, 1.063, 1.36, 1.603
Step-by-step explanation:
Hope this helped, have a great day :)
6d + 7 = 61 what does d equal?
Answer:
i would reword this to 6x+7=61
Step-by-step explanation:
So.
move the 7 to the right side of the equation but as an opposite number so in this case its gonna be a negative
61-7=54
then you divide the number and get your missing numbers
54/6=9
d=9
plug it in
6(9)+7=61
destiny just recived two seprate gifts from her great-grandmother
Answer:
And 2 from grand-pa pa
Step-by-step explanation:
Answer: 6 snack bags
Step-by-step explanation:
In rder to know mnay bags destiny ca make, we need a number is a factor of 18 and 12, so that the 18 chocolate candy bars and the 12 cookies can be divided up evenly.
So, if there were 2 bags, thre would be 18÷2=9 chocolate candy bars and 12÷2=6 cookies in a bag. This creates identical snack bags, but isn't the greatest number of bags!
To find the greatest snack bag, we want to find the greatest common factor of 18 and 12
To do so, let's find factors of 18 ans 12
18: 1, 2, 3, 6, 9, 18
12: 1, 2, 3, 4, 6, 12
The greatest common factor of 18 and 12 is 6. in math notation this looks like:
gcf (18, 12) = 6
The greatest number of identical bags can make is 6
what is the solution for 10x + 3 = 6x +5
Answer:
x=1/2
Step-by-step explanation:
10x+3=6x+5
10x-6x=5-3
4x=2
divide both by 4
x=1/2
Answer:
Therefor X = 1/2
Correct answer ✅
Pls help me I’ll give 100 points
Answer:
Try option B
Step-by-step explanation:
sub to Pen Paper
Hi there!
So what we have to do here is...
turn 2³ - 1 into 2·2·2-1=4·2=8-1=7.
[tex]\frac{35}{7}=5[/tex]
Final Result: 5
How to find percents of numbers using multiples of 100, 10, and 1%?
I need this for my summary, please help!!
Answer:
Im not too sure what the question is
Step-by-step explanation:
but when finding the percent of any number, 10% will always move the decimal over to the left once. So 10% of 300 is 30.0 This also works for 1%, you just move the decimal over twice. So 1% of 300 is 3
Help me solve this ! Thank you ,
Answer:
170.8
Step-by-step explanation:
Every day Jin reads for 0.75 hours in the morning and 1.25 hours in the evening. He uses the expression 0.75d+1.25d to keep track of the number of hours he has read for any number of days, d. If Jin reads for 20 days, how many hours has he read?
Answer: 40 hours.
Step-by-step explanation: You can combine the like terms 0.75d and 1.25d to make 2d. 2 hours times 20 days is 40 hours.
guys im in school right now helppppppp please xoxo
Answer:
question A: 50%
Step-by-step explanation:
For question A: the percentage is ( enroll(2014) - enrol(2012) ) / enrol(2012) for that is 0.5 = 50%, same method for the other questions
What is a point-slope equation of the line with a slope -10 that goes through the point (1,4)
A. y + 4 = 10 (x + 1)
B. y + 4 = -10( x + 1)
C. y - 4 = 10 (x - 1)
D. y - 4 = -10 (x - 1)
Answer:
D. y-4=-1(x-1)
Step-by-step explanation:
What five digits appear as the last digit of the multiples of 2
Answer:
0, 2, 4, 6, 8
Step-by-step explanation:
the first couple of multiples of 2 are...
2, 4, 6, 8, 10
the last digits are 0, 2, 4, 6, 8...
so, 0, 2, 4, 6, 8 are the last digits!
HELP PLEASE!!!!!!!
A restaurant sells 10 garden salads. If garden salads represent 20% of their total salad sales, how many salads did they sell?
Krutika, David and Mark share some sweets in the ratio
2:2:1. Krutika gets 48 sweets. How many sweets are there
altogether?
Answer:
120
Step-by-step explanation:
Krutika:48
David: 48
Mark: 48÷2= 24
Because 2 : 2 : 1
48+48+24=120
(5x^2-3)+(2x^2-3x^3)
Answer:
[tex]-3x^{3}+7x^{2} -3[/tex]
Step-by-step explanation:
Hello
If someone can help me find X that’s the only problem I’m having with this math equation please and thankss!
Answer:
X=5
Exlanation
Can someone please help me with number 16?
Answer:
I got 105°
Step-by-step explanation:
Triangle ABC is an isosceles triangle so base angles are equal. <A = 30° (given)
180 - 30 = 150°
150/2 = 75°
the little triangle is also isosceles. the original base angles have been bisected so the base angles are 37.5.
37.5 X 2 = 75°
180-75 = 105°
D = 105°
what is the ratio 5/7 to 2/7
Answer: What is the ratio of 7 to 2?
Students learn that a ratio is a comparison of two numbers or quantities. For example, if there are 2 shaded parts of a picture and 7 unshaded parts, the ratio of shaded parts to unshaded parts is 2 to 7. Note that the ratio 2 to 7 can also be written as 2:7 or 2/7
What is the ratio of 7 to 5?
20 : 28
5 : 7 = 20 : 28. And 7 is a fourth of 28.
Step-by-step explanation:
Help! Show work! Triangle PQR ≅ Triangle XYZ
PQ = 3a + 4 and XY = 5a – 12. Find a and PQ.
Answer:
a= 8 and PQ= 28
Step-by-step explanation:
since triangle XYZ and triangle PQR are congruent, we will write the equation like this:
PQ=XY
3a+4= 5a—12
3a—5a= —12—4
—2a= —16
a= 8
SUBSTITUTE THE VALUE OF A IN THE EQUATION TO GET THE VALUE OF PQ
PQ= 3a+4
PQ= 3(8)+4
PQ= 24+4
PQ= 28
There are 16 ounces in a pint and 8 pints in one gallon. How many ounces are in one gallon?
Answer:
128 oz
Step-by-step explanation:
128 ounces in the us
solve for x each figure is a parallelogram
Answer:
[tex]18x + 8= (180 - 46) = 134 \\ 18x = 126 \\ \boxed{x = 7}[/tex]
7 is the right answer.(I need to turn this in tomorrow, please help)
Who is drinking the fastest
Answer: Caiden
Step-by-step explanation:
For Caiden, at the second minute, the water is already at 7 ounces. However, Bella is still at 8 ounces. And Caiden is drinking at a speed of 2.5 ounces per minute while Bella is drinking at a speed of 2 ounces per minute.
Hope that helped!
answers for the 2 boxes please
Answer:
(-3,-6)
Step-by-step explanation:
can you help me with this question
Increase 40 by 50%
Answer:
60
Step-by-step explanation:
first you have to find 50% of 40 but multiplying 40 by .5 to get 20. then you add 20 to 40 to get your answer
Answer:
60!
Step-by-step explanation:
100% is 40
to increase that by 50, do 1.5 times 40
the answer to that is 60