Answer:
[tex]\displaystyle y' = -4(4x - 1)(4 - x^5)^3(22x^5 - 5x^4 - 8)[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightDistributive Property
Algebra I
Terms/CoefficientsFactoringCalculus
Derivatives
Derivative Notation
Derivative of a constant is 0
Basic Power Rule:
f(x) = cxⁿ f’(x) = c·nxⁿ⁻¹Derivative Rule [Product Rule]: [tex]\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)[/tex]
Derivative Rule [Chain Rule]: [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Step-by-step explanation:
Step 1: Define
Identify
y = (4x - 1)²(4 - x⁵)⁴
Step 2: Differentiate
Product Rule: [tex]\displaystyle y' = \frac{d}{dx}[(4x - 1)^2](4 - x^5)^4 + (4x - 1)^2\frac{d}{dx}[(4 - x^5)^4][/tex]Chain Rule [Basic Power Rule]: [tex]\displaystyle y' = [2(4x - 1)^{2 - 1} \cdot \frac{d}{dx}[(4x - 1)]](4 - x^5)^4 + (4x - 1)^2[4(4 - x^5)^{4 - 1} \cdot \frac{d}{dx}[(4 - x^5)]][/tex]Simplify: [tex]\displaystyle y' = [2(4x - 1) \cdot \frac{d}{dx}[(4x - 1)]](4 - x^5)^4 + (4x - 1)^2[4(4 - x^5)^3 \cdot \frac{d}{dx}[(4 - x^5)]][/tex]Basic Power Rule: [tex]\displaystyle y' = [2(4x - 1) \cdot 4x^{1 - 1}](4 - x^5)^4 + (4x - 1)^2[4(4 - x^5)^3 \cdot -5x^{5 - 1}][/tex]Simplify: [tex]\displaystyle y' = [2(4x - 1) \cdot 4](4 - x^5)^4 + (4x - 1)^2[4(4 - x^5)^3 \cdot -5x^4][/tex]Multiply: [tex]\displaystyle y' = 8(4x - 1)(4 - x^5)^4 - 20x^4(4x - 1)^2(4 - x^5)^3[/tex]Factor: [tex]\displaystyle y' = 4(4x - 1)(4 - x^5)^3 \bigg[ 2(4 - x^5) - 5x^4(4x - 1) \bigg][/tex][Distributive Property] Distribute 2: [tex]\displaystyle y' = 4(4x - 1)(4 - x^5)^3 \bigg[ 8 - 2x^5 - 5x^4(4x - 1) \bigg][/tex][Distributive Property] Distribute -5x⁴: [tex]\displaystyle y' = 4(4x - 1)(4 - x^5)^3 \bigg[ 8 - 2x^5 - 20x^5 + 5x^4 \bigg][/tex][Brackets] Combine like terms: [tex]\displaystyle y' = 4(4x - 1)(4 - x^5)^3(-22x^5 + 5x^4 + 8)[/tex]Factor: [tex]\displaystyle y' = -4(4x - 1)(4 - x^5)^3(22x^5 - 5x^4 - 8)[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Derivatives
Book: College Calculus 10e
-2x + 4y = -2 and 6x -y = 28
Answer:
(5,2)
Step-by-step explanation:
I hope that it helped you and that I solved it correctly
Help pure people only
Answer:
Mini golf costs $10 per round and batting cages cost $2.5 each turn.
Step-by-step explanation:
mini golf ([tex]m[/tex])
batting caves ([tex]b[/tex])
Sylvester:
[tex]5m+4b=60[/tex]
Lin
[tex]3m+6b=45[/tex]
System of equations:
[tex]$\left \{ {{5m+4b=60} \atop {3m+6b=45}} \right. $[/tex]
[tex]$\left \{ {{5m(-3)+4b(-3)=60(-3)} \atop {3m(5)+6b(5)=45(5)}} \right. $[/tex]
[tex]$\left \{ {{-15m-12b=-180} \atop {15m+30b=225}} \right. $[/tex]
[tex]18b=45[/tex]
[tex]b=2.5[/tex]
Now let's find [tex]m[/tex]
[tex]3m+6(2.5)=45\\3m+15=45\\3m=30\\m=10[/tex]
Which equation has a k-value of -5? A y=5x+3 B y=5x+5 C y=3x−5 D y=−5x
Answer:
NANI!?5
Step-by-step explanation:
NEEEDDD HHEELLPP NNOOWW. URGENTT giving 100 points and brainliest The mass of an empty jar is 470 g. 6 marbles are placed in the jar. The total mass of the jar and marbles is now 1.1 kg. Two of the marbles are removed. What is the mass of the jar and marbles now?
Answer:
890
Step-by-step explanation:
Well, first we should put 1.1 kg into grams (1 kg = 1000g)
1.1kg= 1100g
[tex]1100-470= 630[/tex] this is how much was added by the marbles
630/ # of marbles gives the mass of each marble
[tex]\frac{630}{6} = 105[/tex]
each marble has a mass of 105 g
1100- 2m(marble)=
1100-2*105
1100-210=
890
Answer:
890 grams
Step-by-step explanation:
Remember that one kilogram is equal to 1000 grams. Therefore, 1.1 kilograms is equal to 1,100 grams. (remember 0.1 means one tenth, and one tenth of 1000 is 100)
1,100 grams is the total measure of the jar with the marbles. Subtract the weight of the jar, 470 grams, to find the measure of the marbles.
1100 - 470 = 630
Now, we can divide 630 grams by the total number of marbles, 6, to find the weight of each marble.
630/6 = 105.
Therefore, each marble weighs 105 grams.
Now, we know that two marbles were removed from the jar that weighs 1100 grams.
Multiply 105 by 2 to find the number of grams that were taken out of the jar:
105*2 = 210
Now, we subtract 210 from 1100
1100 - 210 = 890 grams
Hope this helps :)
Will give brainiest answer
Answer:
144 cm²
Step-by-step explanation:
for the triangle sides: 3 x 4 = 12 ((3 x 4/2)x 2)
for the front: 5 x 11 = 55
for the back: 3 x 11 = 33
for the base: 4 x 11 = 44
12 + 55 + 33 + 44 = 144
Answer:
144 units²
Step-by-step explanation:
We can see this shape is made of 2 shapes that we are familiar with 3 rectangle's and 2 triangles. In order to work out the surface of the prism we need to know how to work out the area of a rectangle and a triangle.
→ Area of triangle = 0.5 × Base × Height
→ Area of rectangle = Length × Width
First let's work out the area of the triangle and then double it to find the added area of the 2 triangle's
Area of triangle = 0.5 × Base × Height
→ Substitute in the values
Area of triangle = 0.5 × 4 × 3
→ Simplify
Area of triangle = 6
Then double this value to find the combined value of the 2 triangle's
6 × 2 = 12
Now the area of the large rectangle
Area of rectangle = Length × Width
→ Substitute in the values
Area of rectangle = 11 × 5
→ Simplify
Area of rectangle = 55
Now the area of the medium rectangle
Area of rectangle = Length × Width
→ Substitute in the values
Area of rectangle = 11 × 4
→ Simplify
Area of rectangle = 44
Now the area of the small rectangle
Area of rectangle = Length × Width
→ Substitute in the values
Area of rectangle = 11 × 3
→ Simplify
Area of rectangle = 33
Now we add all the area's together,
33 + 44 + 55 + 12 = 144
How many kilometers are there ??
Answer:
20
Step-by-step explanation:
1 hour=2 kg
10 hrs=10×2=20
Mark as brainliest please!
simplify x2-9/x2+x-12
(x + 3) (x² - 2x - 6)
______________
x
Answer: (x^4 + x^3 - 12x^2 - 9 ) / x^2
Step-by-step explanation:
x^2 - 9/x^2 +x - 12
(x^2 - 9 + x^3 - 12x^2)/x^2
I will give the brainiest answer
Answer:
6.2857142857 or 6.29 is the circumference of the circle
Hey!!
Solution,
Radius=1
Circumference of circle=2 pi r
= 2*3.14*1
=6.28 units.
Hope it helps
Good luck on your assignment
Mention a few number systems and explain in brief
Answer:
Step-by-step explanation:
The system is common use is the decimal system which is based on 10;
So for example the number 45 :
45 = 4 * 10^1 + 5 * 10^0 and
132 = 1*10^2 + 3*10^1 + 2*10^0.
The single digits in the decimal system are 0,1,2,3,4,5,6,7,8 and 9 .
Then we have 10, 11 and so on
Then there is the binary system which is based on 2 digits
In this system there are only 2 digits 0 and 1, so
10 binary = 1*2^1 + 0*2*0 which is equivalent to 2 in the decimal system.
111 binary = 1*2^2 + 1*2^1+ 1*2*0 = 4 + 2 + 1 = 7 decimal
Another system is the octal system, based on 8.
The digits are 0,1,2,3,4,5,6,7
So 10 octal = 8 + 0 = 8 decimal
and 17 octal = 1*8^1 + 7* 8^0 = 8 + 7 = 15 decimal.
please help asap. I will award
Answer:
12
Step-by-step explanation:
hope this helps! :)
12. A package of 4 chocolate bars cost $3.29.
What is the price per chocolate bar? (Round to 2 decimal places)
Answer:
$0.82
Step-by-step explanation:
The full answer is 0.8225, although I believe that I was supposed to round it to the nearest hundredth, so I did that. What I did was I divided 3.29 by 4.
Answer:
.82 per chocolate bar
Step-by-step explanation:
Take the price and divide by the number of chocolate bars
3.29/4
.8225
Rounding to two decimal places
.82 per chocolate bar
Conner has $25,000 in his bank account. Every month he spends
$1,500. He does not add money to the account. Which equation could
be used to figure out when Conner will run out of money?
Answer: The answer is the last variant.[tex]\boxed{\boxed{25000-1500*x=0}} \\\\\\ \b{For x=16 months} \ \ \ \to \to \to \ \ \ 25000-1500*16= 25000-24000 = \boxed { 1000 < 1500}[/tex]
Step-by-step explanation:
Having trouble with this? Can someone explain this to me please?
Answer:
D
Step-by-step explanation:
D is the correct ratio. If his heart beats 12 times in 10 seconds, then it will beat 72 times in 60 seconds/1 minute if you use the proportion. D is the only correct ratio because it shows 72 beats:1 minute.
2. A system of equations is solved by finding the intersections of when f(x) = g(x).
True or False?
Answer:
It's true
Step-by-step explanation:
The lines intersect where f(x) = g(x)
hope it helps!
What is the surface area of the regular pyramid given below?
A. 144 units2
B. 352 units2
C. 176 units2
D. 208 units
Answer:
The surface area of the pyramid is 208 units²
Step-by-step explanation:
Luckily, since this is a square pyramid, we only need to find two numbers. These two numbers are the area of the base and the area of one triangular side. After we find them, we need to add them all together.
First, the base:
Since it's a square, we can just do 8 · 8 and get 64. Now we have one of the two needed numbers.
Second, one of the triangles:
To start, we multiply the base (8) by the height (9) giving us 72. After we divide that by 2, we have the area of the triangle, which is 36. Now we have the second number down. Now we can...
Finally, add them all together:
Now that we have the area of the base (64) and one of our triangles (36), we need to add them together. We add the base once and the triangle four times (because there are four triangles) to get the total surface area. Our expression looks like this:
64 + 36 + 36 + 36 + 36
After doing some simplifying, we get our final number, 208.
The surface area of the pyramid is 208 units²
The surface area of the regular pyramid in the diagram is 208 units².
What is the Area of a Pyramid?The surface area of the pyramid = Sum of area of the triangular faces + Area of the square base.
Surface area of the pyramid = 2bh + b²
Where b is the base
and h is the perpendicular height of each triangular faces
In the given diagram,
b = 8
h = 9
∴ Surface area of the pyramid = 2×8×9 + 8²
Surface area of the pyramid = 144 + 64
Surface area of the pyramid = 208 units²
Hence, the surface area of the regular pyramid in the diagram is 208 units².
Learn more on Calculating area of Pyramid here: brainly.com/question/22744289
#SPJ7
Find the coordinates of the image.
Answer:3,-7
Step-by-step explanation:
What is data about?
Answer: the quantities, characters, or symbols on which operations are performed by a computer, being stored and transmitted in the form of electrical signals and recorded on magnetic, optical, or mechanical recording media.
Step-by-step explanation:
Data mainly is about taking note of specific observations in numbers, for reference in the future.
What is 2 less than a number
Answer:
2<x
Step-by-step explanation:
less than x
Answer:
n-2
Step-by-step explanation:
lets put the variable N to mean the "number"
Subtraction is used to take away a certain amount, so 2 less than is that certain number subtracted 2
which can be written as n-2
Scientists in Maine estimates the 3 out of every 11 bears are born during the month of April predict how many bears are born in April out of 165 births
Answer fast plsss
Ram baked 946 cupcakes she sold them in a box of 22 for $16.50 a box how many boxes would she need to make at least $300?
My mother pays my brother twice as much allowance each week as she pays me because he cleans the bathrooms. Together we get $27 each week. How much is my brother's allowance each week? A. $4.50 B. $9 C. $18 D. $27
Answer:
B
Step-by-step explanation:
Brother= 9*2=18
Me= 9
B+M= 18+9= 27
Answer:
C. $18
Step-by-step explanation:
The ratio between brother and her is 2:1. Therefore, there are 3 parts. $27/3 = $9. Thus, her brother gets 2*$9 = $18 and she gets 1*$9 = $9
Answer plz!
Which choices are equivalent to the expression below? Check all that apply.
The right options are:
Option AOption COption Eplease see the attached picture
Hope it helps
Good luck on your assignment
There are currently 4 people signed up to play on a baseball team. The team must have at least 9 players.
Which of the following graphs includes the possible values for the number of people who still need to sign up for the team?
Answer:
B
Step-by-step explanation:
B is correct because it includes 5 and everything higher than that. There needs to be at least 5 more people signing up, and this number line is the only one that shows that, since it includes 5 and more.
Would the answer be b an d for this
Answer:
PROBABLY A and maybe D... here's why
Step-by-step explanation:
i think its A because it goes in a straight line while the others are just wonkity wonk and D also has straight lines not goes all over the place. Idk if this is right but its what would be right for me because i'm learning about proportional graphs and how it could work and if it has to make a straight line for you than im glad this answer could help!
i tried :) hope it helps!
Let f(x)=3x + 5 and g(x) = 3x2 - x - 10. Find (f/g)(x) and state it’s domain
Answer:
9x²-3x-25, Domain is all real numbers
Step-by-step explanation:
f(g(x)) = 3(3x²-x-10)+5
= 9x²-3x-30+5
= 9x²-3x-25
Domain is all real numbers
* ANSWER ASAP *
This is difficult for me, and i don't get it??
Answer:
28
Step-by-step explanation:
DI is a radius, which is half of a diameter. CJ is a diameter, so you just double toe radius which is 14, to get 28.
Answer:
28
Step-by-step explanation:
Since DI is 14, then DJ would be the same length, and so would DC. So we add DJ plus DC, which is 14+14. 28 is our answer.
Manuel's bank charges a $2 internal fee for using an ATM from another bank. Manuel withdraws $60 from an ATM owned by another bank that charges a $3 usage fee. What is the decrease in Manuel's account from this transaction? Enter your answer as a whole number, such as 5.
2+3+60=65
total is $ 65 ONLY IF U COUNTING THE WITHDRAWL MONEY TOO.
$5 is the answer IF U AINT COUNTING TE WITHDRAWL MONEY
hope this help ya
Answer:$65
Step-by-step explanation: It decreases by $65 because the the fees from his bank and the other bank equal 5 plus the original 60 he was taking out
65°
6
B
с
?
BC
Round your answer to the nearest hundredth.
Answer:
5.44 = BC
Step-by-step explanation:
sin theta = opp /hypotenuse
sin 65 = BC / 6
6 sin 65 = BC
5.437846722 = BC
To the nearest hundredth
5.44 = BC
Solve the equation. 5= w/2.2
Answer:
11
Step-by-step explanation:
[tex]5=\dfrac{w}{2.2}[/tex]
Multiply both sides by 2.2 to isolate w:
[tex]w=5\cdot 2.2=11[/tex]
Hope this helps!
Answer:
[tex] \boxed{\sf w = 11} [/tex]
Step-by-step explanation:
[tex]\sf Solve \ for \ w: \\ \sf \implies 5 = \frac{w}{2.2} \\ \\ \sf \implies \frac{w}{2.2} = 5 \\ \\ \sf Multiple \: both \ side \ by \ 2.2 : \\ \sf \implies \frac{w}{ \cancel{2.2}} \times \cancel{2.2 }= 5 \times 2.2 \\ \\ \sf \implies w = 5 \times 2.2 \\ \\ \sf 5 \times 2.2 = 11 : \\ \sf \implies w = 11[/tex]
SS
question 6/12
A text message can have a maximum of 160 characters. If Daisy has typed 3 sentences with 45
characters each, then which equation can be solved to find the number of characters she can still
type. Let "c" equal number of Daisy characters left.
Answer:
c = 160 - 3(45)
Step-by-step explanation:
if c = the number of characters left;
160 = maximum number of characters that can be used in a text
3*45 = number of characters in sentences already used. (There are 3 sentences of 45 characters.)
(# of char left) = (max # char) - (# char already used) so:
c = 160 - 3*(45)
c = 160 - 135
c = 25