Answer:
[tex]\displaystyle \frac{dy}{dx} = -4x \sin x^2 \sin (\cos x^2) \cos (\cos x^2)[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationBasic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Derivative 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
[tex]\displaystyle y = \sin^2 (\cos x^2)[/tex]
Step 2: Differentiate
Basic Power Rule [Derivative Rule - Chain Rule]: [tex]\displaystyle y' = 2 \sin (\cos x^2) \Big( \sin (\cos x^2) \Big)'[/tex]Trigonometric Differentiation [Derivative Rule - Chain Rule]: [tex]\displaystyle y' = -2 \sin (\cos x^2) \cos (\cos x^2) (\cos x^2)'[/tex]Trigonometric Differentiation [Derivative Rule - Chain Rule]: [tex]\displaystyle y' = -2 \sin x^2 \sin (\cos x^2) \cos (\cos x^2) (x^2)'[/tex]Basic Power Rule: [tex]\displaystyle y' = -4x \sin x^2 \sin (\cos x^2) \cos (\cos x^2)[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
What is the product of (9)(-9)(-1)?
Answer:
The answer is 81
Step-by-step explanation:
Hope this helps
Alexa is making a recipe that requires 1 cup of water and 4 cups of flour which of the following combination shows the same ratio of water to flour
A rental car company charges a basic fee plus a price per mile. One customer drove 250 and paid 56.50, while another customer drove 400 and paid 79. Write an equation in slope - intercept form for the cost of renting a car. Use your equation to find how much it would cost to drive 325 miles?
Answer:
y = 0.15x+19 and
67.75
Step-by-step explanation:
Let us assume y for total cost and x no of miles.
Then x and y are related by a straight line.
Two points lying on the line are
(250,56.50) and (400,79)
Use two point formula
y-56.50/(79-56.50) = x-250/(400-250)
y-56.50 = 22.5(x-250)/150
y = 22.5x/150 -37.50+56.50
Or y = 0.15x+19
To find out cost for 325 miles:
x=325
y= 0.15(325)+19
= 48.75+19
=67.75
Angle Bisector Solve for Y
As <ABC=40
3x-1+34-2x=40
x =40-34+1 = 7
In triangle ABD
3x-1 + 90 +3y + 6= 180
3(7) +3y +95 =180
3y= 180-95-21=64
Y =64/3
A bakery has 72 half gallons of milk. It takes 1 2/3 cups of milk to make the cake. Note that 1 cup= 1/8 half gallon= 0.125 half gallon. How many cakes can the bakery make? A. 43 cakesB. 288 cakesC. 345 cakesD. 576 cakes
To determine the number of cakes the bakery can make, the required milk per cake in cups is converted to half gallons and then divided into the total available milk in half gallons. Upon calculation, the bakery can make approximately 345 cakes. Thus, the correct answer to the student's question is option C) 345 cakes.
To solve how many cakes the bakery can make using 72 half gallons of milk and with each cake requiring 1 2/3 cups of milk, we must first convert the cups needed for one cake into half gallons. Since 1 cup equals 0.125 half gallons, 1 2/3 cups is equivalent to 1.6667 * 0.125 half gallons. Now, let's calculate the number of cakes:
1 2/3 cups of milk for one cake = 1.6667 * 0.125 half gallons = 0.2083 half gallons per cake.Total available milk in half gallons = 72.Number of cakes = Total available milk / Milk per cake = 72 / 0.2083.After performing the division, we find that the bakery can make approximately 345 cakes. Therefore, the correct answer is C. 345 cakes.
Which shows the repeated multiplication for 9³?
a 9 • 9 • 9
b 9 • 9 • 9 • 3
c 3 • 3 • 3 • 3 • 3 • 3 • 3 • 3 • 3
d 9 • 3
its A. because the exponent which in this case is 3, is multiplied 3 times. so 9 is multiplied 9 times
A. because 9 is being multiplied 3 times by itself
if 5/8 yards of fabric costs 3.75 dollars what does one yard cost
The cost of one yard of fabric, based on given prices, is 6 dollars. This is calculated by taking the total cost and dividing by the total quantity, using the concept of ratio and proportion in mathematics.
Explanation:This problem revolves around the concept of unit rates in mathematics, especially ratio and proportion. If 5/8 yards of fabric costs 3.75 dollars, then to find the cost of one yard, known as the unit rate, we need to divide the total cost by the total quantity. Therefore, the cost of one yard would be 3.75/(5/8), which equals 6 dollars. Hence, one yard of fabric costs 6 dollars.
Learn more about Unit Rate here:https://brainly.com/question/11258929
#SPJ3
a cookie recipe calls for a half cup of chocolate chips per 3 dozen cookies. How many cups of chocolate chips should be used for 10 dozen cookies?
To answer this question, you should set up a proportion that demonstrates the ratio of chocolate chips to cookies.
[tex]\frac{0.5}{36} =\frac{x}{120}[/tex]
36 and 120 are used because 1 dozen=12.
Cross multiply and solve for x to get the answer.
[tex]60=36y[/tex]
[tex]\frac{5}{3}=x[/tex]
The answer is [tex]\frac{5}{3}[/tex] cups.
The number of cups of chocolate chips that should be used for 10 dozen cookies is 1 2/3 cups.
Based on the information given, the expression to solve the question will be:
0.5/3 = x/10
Cross multiply
3 × x = 0.5 × 10
3x = 5.
x = 5/3
x = 1 2/3 cups
Therefore, the number of cups of chocolate chips that should be used for 10 dozen cookies will be 1 2/3 cups.
Read related link on:
https://brainly.com/question/11164105
Which expression can be used to convert 22 Australian dollars to US dollars? Assume 1.2 Australian dollars equals 1 US dollar
Answer:
The conversion factor to use here is ($1 US dollar) / (1.2 Austr. dollars), and the
final result is 22 Austr. dollars = US$18.33.
Step-by-step explanation:
The relevant conversion factor here is
1 US dollar
-----------------------
1.2 Aust. dollars
Then:
22 Aust. dollars 1 US dollar
------------------------ * ------------------------- = 18.33 US
1 1.2 Austr. dollars
Find the value of x that will make L||M.
Answer: 60!
It’s already answered but I need some points ✊
Handsome Jack is buying a pony made of diamonds. The price of the pony is PPP dollars, and Jack also has to pay a 25\%25%25, percent diamond pony tax.
Which of the following expressions could represent how much Jack pays in total for the pony?
Choose 2 answers:
A: P+1/4
B: P + 0.25 P
C: (P + 1/4) P
D : 5/4 P
E: 0.25P
Answer:
B: P + 0.25 P
D : 5/4 P
Step-by-step explanation:
The price is P.
The tax is 25% of P, or 0.25P.
The total price is the price plus the tax,
P + 0.25P = P + 1/4P = 4/4P + 1/4P = 5/4P
A percentage is a number expressed fraction of hundred
The correct options for the expression that represent how much Jack pays in total are;
B: P + 0.25·P
D: (5/4)·P
Reason:
The given parameters are;
Material from which the pony is made = Diamond
Price of the pony = P dollars
Amount Jack has to pay as diamond pony tax = 25%
Required:
The expression that represents how much Jack pays per pony
Solution:
The amount Jack pays, A = The price of the pony + Tax
The amount paid as tax = 25% of P = 0.25·P
∴ A = P + 0.25·P
The total amount Jack pays in total for the pony, A = P + 0.25·P[tex]\therefore A = P + 0.25 \cdot P = P + \dfrac{1}{4} \cdot P = \dfrac{5}{4} \cdot P[/tex]
Therefore; The total amount paid = P + 0.25·P = (5/4)·PThe correct options are; B: P + 0.25·P, and D: (5/4)·P
Learn more about proper fractions here:
https://brainly.com/question/15998712
Each week leslie jogs 20 minutes for every 10 minutes that she lifts weights. Is the number of minutes Leslie jogs each week proportional to the number of minutes that she lifts weights each week?
It is proportional because the ratio never changes and increases at a constant rate.
Please answer quickly thanks :)))
move te dotty thing to the midle them sumbtract 5 1/2
u are very smart
Algebra 2...can someone tell me how to do this???
Use the 2 dots on the line located at (0,1) and (-3,0).
The slope is the change in Y over the change in X:
Change in Y = 0-1 = -1
Change in X = -3 - 0 = -3
Slope = -1 / -3 = 1/3
They intercept in this case is Y1 which = 1.
The equation is y = 1/3x + 1
If the outlier is removed, which measure will not change?
range
mode
median
mean
A Light Blue Paint Is Made By Mixing 2 Parts Of Blue Paint To 7 Parts Of White Paint. Using A Proportion Determine How Many Pints Of Blue Paint (n) Should Be Mixed With 28 Pints Of White Paint To Make This Light Blue Color
g4222222222222222222222222222222222222222222222222222222222222222222222222222 add me on ps4 Whisperbrahh
Karissa begins to solve the 1/2 (x-14)+11=1/2x-(x-4)
Answer:
Step-by-step explanation:
C)0
The incomplete work of a student to solve an equation is shown below:
Step 1: 3x + 12 = 3
Step 2: ?
Step 3: x = −9 ÷ 3
Step 4: x = −3
What is the missing Step 2?
Answer:
3x=-9
Step-by-step explanation:
3x+12=3
3x=3-12 --------------Move 12 to the right of the equals sign, it becomes -123x=-9
The missing step to solve the given equation is 3x= 3-9.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.
The given equation is 3x+12=3.
Step 1: 3x+12=3
Step 2: 3x= 3-9
3x= -9
Step 3: x= -9 ÷3
x= -9/3
Step 4: x= -3
Therefore, the missing step to solve the given equation is 3x= 3-9.
To learn more about an equation visit:
https://brainly.com/question/14686792.
#SPJ3
There are five fewer trucks than cars in the parking lot. If there are eight trucks how many cars are there
There are 5 fewer trucks, that means there are 5 more cars than trucks
So no. of cars = 8+5 = 13
3 problems based on rational and irrational numbers properties only
The discussion covers rational and irrational numbers' properties, particularly focusing on the absence of the smallest positive rational number and the non-manifold nature of rational numbers.
The properties of rational and irrational numbers are fundamental concepts in mathematics, particularly when studying the real number system. Rational numbers include integers and fractions where the numerator and the denominator are integers (e.g., 2/3), while irrational numbers are those that cannot be expressed as such a simple ratio (e.g., √2 or π). The completeness axiom of the real numbers ensures that every number on the number line has a place, whether rational or irrational. An example of how rational and irrational numbers interact is that a graph of a function defined only on rational numbers could approach but never touch an irrational number, which is illustrated in the claim that there is no smallest positive rational number, akin to how there is no smallest positive real number. This is due to the density of rational numbers—between any two rational numbers, there is another rational number.
Example Problems:
Prove by contradiction there is no smallest positive rational number.Discuss why a graph of a function restricted to rational inputs could approach but not contain an irrational number like √2.Explain why the rational numbers are not a manifold by considering an arbitrarily small neighborhood around √2.For which of the following statements is the inverse false?
ANSWER
The correct answer is D
EXPLANATION
The conditional is
"If an angle's measure is [tex]35\degree[/tex], then it is an acute angle"
The above statement is true because both the premise and the conclusion are true.
Now let us consider the inverse of the above statement.
"If an angle's measure is not[tex]35\degree[/tex], then it is not an acute angle"
The above statement is false.
For example [tex]60\degree[/tex] is an acute angle even though its measure is not [tex]35\degree[/tex]
A "principal square root" is always...
A: a negative fraction
B: a positive integer
C: a negative integer
D:a positive fraction
Really none of the above.
A principal square root of a real number is a positive real number (or a positive real number times i, if you're up to complex numbers, but let's assume not.) It's not necessarily a positive integer, √2 being the obvious example.
Is √2 a positive fraction? We can write it as √2 / 1 so I suppose it is. It's certainly not a rational number. Even if we grant irrationals as fractions surely √0=0 isn't a positive fraction. So "always" isn't correct.
I'd go with none of the above, but if I had to choose I'd choose D.
Eric is having a party. he'll have 3 tables for every 6 guests. complete the table showing the number of tables and the number of guests
The relationship between the number of tables and guests for Eric's party maintains a consistent ratio of 1 table for every 2 guests. By setting up a proportional table, we can see this ratio and calculate the number of tables needed for any given number of guests.
The question involves creating a table to show the relationship between the number of tables and the number of guests at Eric's party. Since we know that there are 3 tables for every 6 guests, we can create a proportional table that maintains this 1:2 ratio (one table for every two guests). For example, if there were 12 guests, you would need 6 tables (because 12 guests divided by the ratio of guests to tables, which is 2, equals 6 tables). Similarly, if there were 18 guests, you would need 9 tables, as 18 divided by 2 equals 9.
Proportional Table for Eric's Party:
6 guests - 3 tables12 guests - 6 tables18 guests - 9 tables24 guests - 12 tables30 guests - 15 tables... and so on.This table can be continued in the same manner as long as you keep the same ratio of 1 table for every 2 guests.
How to write 5+0.1+0.03+0.006 in standard form
Answer:
5.136.
Step-by-step explanation:
We have been given a number in expanded form [tex]5+0.1+0.03+0.006[/tex]. We are asked to write our given number in standard form.
To convert our given number in standard form, we will add all the values to get digits in tenths, hundredths and thousandths place as:
5
0. 1
0.03
+ 0.006
5.136
Therefore, our given number in standard form would be 5.136.
GEOMETRY PEOPLE HELP ME PLEASEEEEE!!!!!!!!!!!!!!!!!!!!!!!!!!
I WILL GIVE BRAINLIEST!!!!!!!!!!!!
2. Marissa labeled the corners of both the picture and the mat as shown. Complete the table
3. Marissa thinks that there could be a pattern between the scale factor and perimeter of an image and its pre-image and between the scale factor and area of an image and its pre-image.
(a) Determine the perimeter and area of the picture and the perimeter and area of the mat.
(b) Create a table that shows the perimeter and area of the picture and the perimeter and area of the mat for scale factors of 2, 3, and 4.
Table
________________________________
Scale factor 3.
(-1-3,2+3) --> A(-4,5)
(1+3,2+3) --> B(4,5)
(1+3,-2-3) --> C(4,-5)
(-1-3,-2-3) --> D(-4,-5)
(-2-3,3+3) --> E(-5,6)
(2+3,3+3) --> F(5,6)
(2+3,-3-3) --> G(5,-6)
(-2-3,-3-3) --> H(-5,-6)
___________________________________
Scale factor 4
(-1-4,2+4) --> A(-5,6)
(1+4,2+4) --> B(5,6)
(1+4,-2-4) --> C(5,-6)
(-1-4,-2-4) --> D(-5,-6)
(-2-4,3+4) --> E(-6,7)
(2+4,3+4) --> F(6,7)
(2+4,-3-4) --> G(6,-7)
(-2-4,-3-4) --> H(-6,-7)
______________________________________________________
Second Image.
Scale Factor 2
Length = 6
Width = 8
Perimeter = 2(6+8)= 2(14) = 28
Area = 6 times 8 = 48.
Scale Factor 3
Length = 8
Width = 10
Perimeter = 2(8+10)= 2(18) = 36
Area = 8 times 10 = 80.
Scale Factor 4
Length = 10
Width = 12
Perimeter = 2(10+12)= 2(22) = 44
Area = 10 times 12 = 120.
_____________________________________________
Scale Factor 2
Length = 8
Width = 10
Perimeter = 2(8+10)= 2(18) = 36
Area = 8 times 10 = 80.
Scale Factor 3
Length = 10
Width = 12
Perimeter = 2(10+12)= 2(22) = 44
Area = 10 times 12 = 120.
Scale Factor 4
Length = 12
Width = 14
Perimeter = 2(12+14)= 2(26) = 52
Area = 12 times 14 = 168.
Why are you guys adding? Aren't you supposed to multiply the cordinates by the scale factor?!?!?!?!
Isabella sells 36 tickets to the school talent show each ticket cost $14 how much money does Isabella collect the tickets she sells
36*14=504
She gets $504 from selling 36 tickets at $14 each.
X+5 = 57-26
Solve for x!!
First, we must subtract
57
-
26
______
31
Second, we isolate the variable!
X + 0 = 31 - 5
X+0 = 26
X=26
Finally,Plug it in
26 + 5 = 57 - 26
26 + 5 = 31
31 = 31
Check
Hope I helped!
Good Luck!
x + 5 = 57 - 26
x = 57 - 26 - 5
x = 26
Which inequality matches the graph?
b is the answer because it hits positive two on the x axis and -3 on the y axis
tell whether in the sequence is arithmetic if it is what is the common difference 20,11,2,-7
The sequence 20 , 11 , 2 , -7 is an arithmetic sequence.
The common difference is (20 - 11) = (11 - 2) = (2 - -7) = 9
The common difference is 9.
Yes, the given sequence is arithmetic. The common difference is -9.
Arithmetic sequenceAn arithmetic sequence is a list of numbers in which the difference between any two consecutive terms is always the same. This constant difference is called the common difference.
For the sequence shown:
1st Term: 20
2nd Term: 20 - 9 = 11
3rd Term: 11 - 9 = 2
4th Term: 2 - 9 = -7
In other words, the common difference in the arithmetic sequence is -9.
More on arithmetic sequence can be found here: https://brainly.com/question/35880655
#SPJ3
I know that: the first term of the sequence is -2, and the fifth term is -1/8
.
What do you know?
Solution
Here the first term = -2
5th term = -1/8
Now we have to find the common ratio (r)
Fifth term A5 = -1/8
-1/8 = [tex]a_{1} r^{4}[/tex]
Here [tex]a_{1} = -2[/tex]
Plug in [tex]a_{1} = -2[/tex] in the fifth term and find the value of r.
-1/8 = -2[tex]r^{4}[/tex]
r^4 = 1/16
Taking 4th root, we get
r = 1/2
Now let's find the second term.
first term *r = -2 *1/2 = -1
2nd term = first term * 1/2 = -1
3rd term = second term * 1/2 = -1 * 1/2 = -1/2
4th term = 3rd term *r = -1/2 *1/2 = -1/4
Thank you :)