Answer:
[tex]\displaystyle \frac{d}{dx}[\log \big( \sec (x^2) \big)] = \frac{2x \tan x^2}{\ln 10}[/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 = \log \big( \sec (x^2) \big)[/tex]
Step 2: Differentiate
Logarithmic Differentiation [Derivative Rule - Chain Rule]: [tex]\displaystyle y' = \frac{(\sec x^2)'}{\ln (10) \sec x^2}[/tex]Trigonometric Differentiation [Derivative Rule - Chain Rule]: [tex]\displaystyle y' = \frac{\sec x^2 \tan x^2 (x^2)'}{\ln (10) \sec x^2}[/tex]Simplify: [tex]\displaystyle y' = \frac{\tan x^2 (x^2)'}{\ln 10}[/tex]Basic Power Rule: [tex]\displaystyle y' = \frac{2x \tan x^2}{\ln 10}[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
Failure to turn in the assignment on time will result in a loss of 5 points.
a
If you do not turn it in by Monday, January 17, 2021, at 8:00 a.m., you will receive 0 points for the assignment.
4 A store is having a 10% -off sale on all merchandise.
If Mai buys one item and saves $18, what was the original price of her purchase?
Answer:
Step-by-step explanation:
If may buys an item that, after 10% sale, costs 18 dollars
let x be original price
discount is 10%x=0.10 x
x- 0.10x=18
0.90x=18
x=18/0.90=20
x=20
Help I’ll mark brainliest
Answer:
ACD
Step-by-step explanation:
2-2(x-25) what is the answer?
Answer:
F= 2
F=-2
F=x-25
Step-by-step explanation:
6) Change the amount of sugar to show a sweeter atole.
Atole
Total
Flour (tbsp)
5
Sugar (tbsp)
5
Dan buys a car for £1700.
It depreciates at a rate of 4% per year.
How much will it be worth in 4 years?
Answer:
Step-by-step explanation:
100%-4%=96%
96/100=0.96
£1700*0.96^4=£1443.89
Answer:
1143.89Step-by-step explanation:
I HOPE it's help you
Determine which, if any, of the given values is a solution.
8p − 16 = 40
p = 5; p = 7; p = 9
p = ?
Answer:
p – 7 = -12
The answer
P = 7
8p - 16 = 40
40 + 16 = 56
8p = 56
56 ÷ 8 = 7
8. A haircut is $120, how much is a 15% tip? *
Answer:
18
Step-by-step explanation: 120 times 0.15
Answer:
$18
Step-by-step explanation:
To work out 15% using a calculator:
0.15 multiplied by 120 which is 18
To work out 15% without a calculator:
10% of 120 is 12. (Just remove the last number whenever you want to get 10% or add it on as a decimal if it's greater than 0. e.g. 10% of 40 is 4 but 10% of 48 is 4.8)
To add the 5% divide 12 by 2 which is 6.
Add the 10% to the 5% to get the 15%.
12+6=18
1 foot = 12 inches therefore 5 feet = what
Answer:
60 inches
Step-by-step explanation:
1 foot = 12 inches
5 feet = ?
5*12 = 60
[tex]1\cdot \text{foot} = 12\cdot \text{inches} \implies 5 \cdot\text{foot} =5\cdot 12 \cdot\text{inches} \implies 5 \cdot\text{foot} =60 \cdot\text{inches}[/tex]
Tyre measured the average monthly temperature in degrees Fahrenheit for several months. If February is set ect 2 and June is oud to 6 what function best models these data from February to June?
Answer:
it will be d
Step-by-step explanation:
Answer:
f(x)=11x+12
Step-by-step explanation:
it shows that the intercept is around halfway between 0 and 20, and the plots are not exactly at the 10s marks, if you look- June is supposed to be 6, but it’s closer to 66. since 6*11=66, i’d say 11x+12 is the answer.
Determine if the statement is true or false. Any linear system with more variables than equations cannot have a unique solution.
Answer:
True
Step-by-step explanation:
Suppose a system contains a large number of variables than equations, then there is a need to make assumptions of some values for the extra variables in order to solve the system. So, the assigning of these values can be done in several ways. Thus, the system cannot contain a unique solution.
Also, for a system of the linear equation:
[tex]AX = B[/tex] can have a unique solution if:
Augmented matrix(rank) = coefficient matrix(rank) = no. of variables.
Provided that there exist fewer equations and more variables,
Then;
coefficient matrix(rank) < no. of variables
Thus, the system cannot contain a unique solution.
please hurry!!!
For the class picnic, 25 liters of punch were purchased. 6 liters were left over. How many gallons of punch were used at the picnic? (1 liter is approximately 0.26 gallons)
Answer:
Gallons of punch used = 4.94 gallons
Step-by-step explanation:
Given that:
Liters of punch purchased = 25 liters
Liters of punch left over = 6 liters
Liters of punch used = 25 - 6 = 19 liters
According to the given statement;
1 liter = 0.26 gallons
19 liters = 0.26*19 gallons
19 liters = 4.94 gallons
Hence,
Gallons of punch used = 4.94 gallons
2) You traveled 210 miles in 3.5 hours.
How many miles will you travel per hour?
Answer:
= 56.7 miles per hour
Step-by-step explanation:
Step-by-step explanation:
To find the average speed for the entire journey, we need to find the entire distance and the total time
Entire distance = 210 miles + 130 miles = 340 miles
Total time = 3.5 hours and 2.5 hours = 6 hours
Average speed = distance/ time = 340 miles/ 6 hours
= 56.66666666666 miles per hour
Rounding to the nearest tenth
= 56.7 miles per hour
Answer:
60 miles
Step-by-step explanation:
Step 1:210=3.5
x =1
Step 2: cross multiply3.5×x= 210×1
3.5x=210
Step 3: divide both sides by the coefficient of x which is 3.53.5x/3.5=210/3.5
x=60
Answer= 60 miles
A multiplier of 1.641 corresponds to a percentage increase or decrease of what percent?
Answer:
A multiplier of 1.641 corresponds to a percentage increase or decrease of 64.1%.
Step-by-step explanation:
To determine a percentage increase or decrease of a certain number, a calculation consisting of the multiplication of said number by 1 plus the decimals corresponding to the percentage to be increased must be performed. Thus, for example, if you want to increase a number by 50%, you must multiply that number by 1.50. Therefore, if you multiply a number by 1,641, this implies that you are wanting to increase or decrease the initial number by 64.1%.
Alex has a video game membership that costs $36 per month. Which table shows the sum of the amounts that Alex will pay for his video game membership over the next 4 months?
Answer:
$144 at the end of 4 months
Step-by-step explanation:
$36 x 4 =144
Answer:
It will be $144
Step-by-step explanation:
because you do 36 times 4 and u get $144
This list shows the number of years that 99 U.S. Supreme Court Justices served.
0
4
6
8
13
15
18
22
26
31
1
4
6
9
13
15
19
23
26
32
1
4
6
9
14
16
19
23
27
33
2
5
7
9
14
16
20
23
28
33
2
5
7
10
14
16
20
23
28
33
2
5
7
10
14
16
20
23
28
34
3
5
7
10
15
17
20
24
29
34
3
5
8
11
15
17
20
24
30
34
3
5
8
13
15
18
21
26
30
36
4
5
8
13
15
18
21
26
31
Miguel is making a frequency table of this data. He decides to group the years in intervals of 5 beginning with 0 to 4, 5 to 9, 10 to 14 and so on. How many intervals will he need all together?
a.
5
c.
7
b.
6
d.
8
Answer:
8
Step-by-step explanation:
0
4
6
8
13
15
18
22
26
31
1
4
6
9
13
15
19
23
26
32
1
4
6
9
14
16
19
23
27
33
2
5
7
9
14
16
20
23
28
33
2
5
7
10
14
16
20
23
28
33
2
5
7
10
14
16
20
23
28
34
3
5
7
10
15
17
20
24
29
34
3
5
8
11
15
17
20
24
30
34
3
5
8
13
15
18
21
26
30
36
4
5
8
13
15
18
21
26
31
a.
5
c.
7
b.
6
d.
8
Answer:
The correct answer is:
Step-by-step explanation:
D.)8
Acellus
Find the next two terms in this
sequence.
2, 6, 10, 14, 18, [?],[
Answer:
22,26
Step-by-step explanation:
Just add 4 every time
Solve 18 > 12 + 2. Graph the solution.
Answer:
Step-by-step explanation:
7
2
Decimal Form:
3.5
Mixed Number Form:
3
12
A rectangle has a length that is 4 meters more than the width. The area of the rectangle is 117 square meters. Find the dimensions of the rectangle.
Answer choices are on picture.
Answer:
Its the first choice. Width:9 Length:13
Step-by-step explanation:
If the length is 4 meter more than the width than that means whatever the width is you must add 4 to it, in this case the width is 9 so add 4 to it which equals 13. If the length matches your answer it is the correct choice.
The area of a rectangle is the product of its dimensions. The dimension of the rectangle is: [tex]Length = 13m[/tex] and [tex]Width = 9m[/tex]
Given that:
[tex]L =4 + W[/tex]
[tex]Area = 117[/tex]
The area of a rectangle is:
[tex]Area = L \times W[/tex]
So, we have:
[tex]L \times W= 117[/tex]
Substitute [tex]L =4 + W[/tex]
[tex](4 + W) \times W = 117[/tex]
Expand
[tex]4W + W^2 = 117[/tex]
Rewrite as:
[tex]W^2 + 4W- 117 = 0[/tex]
Expand
[tex]W^2 + 13W - 9W - 117 = 0[/tex]
Factorize
[tex]W(W + 13) - 9(W + 13) = 0[/tex]
Factor out W + 13
[tex](W - 9)(W + 13) = 0[/tex]
Solve for W
[tex]W = 9[/tex] or [tex]W = -13[/tex]
The dimension cannot be negative.
So:
[tex]W = 9[/tex]
Recall that:
[tex]L =4 + W[/tex]
[tex]L = 4 + 9[/tex]
[tex]L = 13[/tex]
So, the dimension of the rectangle is:
[tex]Length = 13m[/tex]
[tex]Width = 9m[/tex]
Read more about areas at:
https://brainly.com/question/15218510
According to a survey of workers,2/20 of them walk to work, 1/20 bike, 4/20 carpool,13/20 and alone. What percent of workers walk or bike to work?
A 16 ft tall adult giraffe standing next to a
baby giraffe casts a 8 ft shadow. If the
baby giraffe is 6 ft tall, then how long is
its shadow?
Answer:
The shadow is 3 ft tall
Step-by-step explanation:
The older giraffe is 16 ft tall and 8 is half of 16 and 8ft is the length of the shadow so that means that half of the small girafe would be 3ft because half of 6 is 3.
Sorry if its not correct
5 A contractor is laying out the sides of a
rectangular porch. She knows that the porch will
form a rectangle if it can be broken up into two
right triangles, as shown below.
The lengths of the two longer sides of the porch
are 24 feet and the lengths of the two shorter
sides are 17 feet. Enter the length of the diagonal
of the porch in feet, rounded to the nearest tenth.
Which of the following is not a function?
The answer is the first choice
Step-by-step explanation:
because the two goes into 4 and 5, in order for it to be a function the x value has to be used once
Question 4 Which expression is equivalent to ^4 sqrt x^7 y
Answer:
jojo siwa
Step-by-step explanation:
A fully loaded and fueled spacecraft can weigh close to 4.8 million pounds. What is this weight converted to tons?
(Type an integer or a decimal.)
Answer:
2,400 tons
Step-by-step explanation:
Answer:
24,00 tons
Step-by-step explanation:
2. in a class of 50 students, the number of females is 2 more than 5 times the number of males. How many males and females are there in the class?
Answer:
The number of male students is 8, while the number of female students is 42.
Step-by-step explanation:
To determine the number of male and female students in the class, knowing that in total there are 50 students, and that the number of female students is two more than five times the number of male students, the following equation must be performed:
X + (5X + 2) = 50
6X + 2 = 50
6X = 50 - 2
X = 48/6
X = 8
Thus, the number of male students is 8, while the number of female students is 42.
find the value of the ratio a:5.7=8:12
Answer:
a = 3.8
Step-by-step explanation:
a : 5.7 = 8 : 12
It can be also written as -
[tex] \frac{a}{5.7} = \frac{8}{12} [/tex]
[tex] = > \frac{a}{5.7} = \frac{2}{3} [/tex]
Multiplying 5.7 on both the sides ,
[tex] = > \frac{a}{5.7} \times 5.7 = \frac{2}{3} \times 5.7 [/tex]
[tex] = > a = \frac{2}{3} \times 5.7 = 3.8[/tex]
48 oz. for $3.99
36 oz. for $2.59
12 oz. for $1.99
which is the best deal
Answer:
Step-by-step explanation:
12 oz for 1.99$
Answer:
12 oz. for $1.99
Step-by-step explanation:
Please help me I’m so close to passing
Answer:
314 meters
Step-by-step explanation:
The circumference of any circle is pi (3.14). To find your answer, Multiply 3.14 with 100 (as in meters) to get 314. Your answer is 314 meters.
Did I put the correct answer ?
Answer:
yes
Step-by-step explanation:
A yard is 3.1 meters long and 1.4 meters wide. What is the area of the yard? Group of answer choices
Answer:
The area of the yard is 4.34.
Step-by-step explanation:
a = l x w
a = 3.1 x 1.4
a = 4.34