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
In this picture B,D, and Fare
midpoints. AC=50, CE=60, and
BD=35
5
AE=[?]
Enter
Answer:
AE = 70
Step-by-step explanation:
since triangle BDF bisects each side of triangle AEC, then triangle BDF is a medial triangle and the result is the following:
all four triangles are congruent (their sides are proportional)
sides that measure 25: BA, BC, DF
sides that measure 30: CD, DE, FB
sides that measure 35: FA, FE, BD
if FA = 35 and FE = 35 then AE = 70
solve {6x-5y=21 2x+5y=-5 with elimination please help fast :(
Answer:
19
Step-by-step explanation:
Help I will give breinlits
Michael wants to plant a circular flower garden in his backyard. If the radius of his garden is 12.5 feet, what is the circumference of the
garden in terms of pi?
Answer: 78.54
Step-by-step explanation: :D
Please help will mark Brainliest
Can y’all give a mini explanation too
A dozen eggs cost $1.25 at one market. At a competing market, 1 1/2 dozen eggs cost $2.00. Which is the better buy?
Answer: 1 dozen eggs
hope this helps :)
Write a 2 paragraphs telling me how you have used algebra in your life outside of school
Angle ABC is similar to angle LMN. Also, angle B measures 35º and angle C measures 95°
What is the measure of angle L?
Answer:
angle L is 50 degrees! hope this helps
Step-by-step explanation:
idek lol i guessed and got it right
What is 1.092 as a fraction
Answer:
273/250
Step-by-step explanation:
Set it as this 1st because you need to put it in a format like this. You can multiply the top and bottom by 1000
1.092/1 to 1092/1000
Then u need to simplify it by dividing the top and bottom
(I divided by 4)
273/250
Please mark Brainliest, I have worked so hard the last few days :(
work must be shown, 15 points if answered, + brainlynessiest answer
Answer:
40cm
Step-by-step explanation:
if the area is 100 then you have to do the square root of 100 which is 10.
each side is 10.
10 x 4 because 4 equal sides
40
AYO YALL I NEED HELP HOMIES
Answer:
your answer will be, 67.25
Step-by-step explanation:
I got chu homie
jonothan paid $7.56 for 9 cupcakes if each cupcake cost the same amount,what was the cost of 1 cupcake
Answer:
.84
Step-by-step explanation:
i hope this helps
You randomly choose one of the following numbers shown. Find the probability the event can occur choosing a number greater than 4. (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11)
======================================================
Explanation:
The event space is the set of outcomes we want to happen.
The event space is {5, 6, 7, 8, 9, 10, 11} which consists of getting a value greater than 4. There are 7 items in this event space. Let A = 7.
The sample space consists of all possible outcomes. The sample space is {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11} and there are 11 items in the sample space. Let B = 11.
Divide the values of A and B to get the answer we're after
A/B = 7/11
This is the probability of selecting a value greater than 4.
3/8 + 1/8 + 2/3 - 1/2
Answer:
0.66666666666666
Hope This Helped Have a Good Day! :)
Step-by-step explanation:
Fill in the blank to complete the equation below.
12 + 16
= 2(___ + 8)
PLEASE HELP ASAP
A contractor buys 16 yd of nylon carpet and 22 yd of wool carpet for $1902. A second purchase, at the same prices, includes 20 yd of nylon carpet and 21 yd of wool carpet for $2033. Find the cost per yard of the wool carpet.
Answer:
$53
Step-by-step explanation:
Given that, two type of clothes nylon and wool carpet.
Let the price of one yard of nylon carpet = $[tex]x[/tex]
Let the price of one yard of wool carpet = $[tex]y[/tex]
Price for 16 yd of nylon carpet and 22 yd of wool carpet = $1902
Price for 20 yd of nylon carpet and 21 yd of wool carpet = $2033
Writing equations as per given statement:
[tex]16x+22y=1902 ...... (1)\\20x+21y=2033 ...... (2)[/tex]
Here, we have to find the value of [tex]y[/tex].
By equation (1), we get:
[tex]16x = 1902 - 22y \\\Rightarrow x = \dfrac{1}{16}(1902-22y) ..... (3)[/tex]
Putting the value from equation (3) to equation (2):
[tex]20 (\dfrac{1}{16}(1902-22y) ) + 21y =2033\\\Rightarrow 9510-110y + 84y = 8132\\\Rightarrow 26y=1378\\\Rightarrow \bold{y = 53}[/tex]
Therefore, the cost per yard for the wool carpet is $53.
Can u create an equation for a line parallel to the given line that passes through the origin?
Lamar is studying. The number of minutes he has studied varies directly with the number of calories he has burned. See the graph belon.
Number of
minutes
Calories burned
Compute -10 -6.4 + 3.7
Answer:
-12.7
Step-by-step explanation:
Not really anything to explain
Answer:
-12.7
Step-by-step explanation:
Follow order of operations
So sincde addition and subtraction are the only things presented here, just do the equation from left to right
-10-6.4=-16.4
-16.4+3.7= -12.7
Don’t forget to put the negative sign
Ari and his 3 brothers want to take a school trip to Washington D.C. They have $320 saved. each of them will save $18 a week until they have at least $647 to pay for the trip. how much money will they save after 4 weeks?
Answer:
536 if adding the 320
Step-by-step explanation:
(3x 18) 4 +320= 536
(3x18)4 = 216
Answer:
$608
Step-by-step explanation:
Well first you have to see that there is 4 people going ari and his 3 brothers. Then I multiplied 4 people times 18 dollars a week. I got 72. After that I multiplied 72 dollars by 4 because of the 4 weeks they will be collecting money and I got 288. Lastly I added the 288$ to the 320 dollars they already saved and in total I got $608.
$608
HOPE THIS HELPS!!!
Need help with Geometry!
This is the last question that I am stuck on. It's the only one that I got wrong.
Answer:
m∠3 = 143°
Step-by-step explanation:
m∠1 = 53°
m∠2 = 180 - (90 + 53) = 37°
m∠3 = 180 - 37 = 143°
Answer:
143
Step-by-step explanation:
solution:
angle 1 = 53°
angle D = 90°
angle 3 = angle 1+ angle D [sum of two]
= 53°+90° [interior angle is equal ]
=143° [to an exterior angle]
Suppose a researcher is testing a new vaccine on mice to see how well it prevents the flu virus. The lab has 1000 mice available for testing purposes, and each mouse has an identification number. The researcher needs 30 mice to properly run her study of the new flu vaccine. She is considering five different sampling methods. Match the sampling method to each description.
a. The researcher uses a computer program to randomly choose 30 of the 1000 mice to use in her study.
b. The researcher chooses the first 30 mice she can reach from the door to the mouse room.
c. The mice are kept in cages on 10 different shelves in the mouse room. The researcher chooses three mice from each shelf.
d. Each cage holds five mice. The researcher randomly chooses six cages to use in her study.
e. The researcher generates a list of identification numbers that has been sorted from smallest to largest. She randomly picks one mouse from the list, and then chooses every fourth mouse until she has 30.
1. cluster
2. convenience
3. systematic
4. simple random
5. stratified
Solution :
Sampling may be defined as the technique of selecting the individual members or the subset of the population to make a statistical inferences and estimates the characteristics of the entire population.
There are several sampling methods. This includes : Systematic sampling, clustered sampling, stratified sampling, quota sampling, judgement sampling, random sampling, convenience sampling and many more.
In the context, the sampling methods for each of the descriptions are :
a). The researcher use computer program to randomly choose a sample of 30 mice of the 1000 mice for using her study
--- Simple Random
b). The researcher chose the 1st 30 mice as she can reach the door to the mouse room
--- Convenience sampling
c). The mice those whose are kept in the cages on 10 various shelves in mouse room. The researcher or the experimenter chose the three mice from each shelve.
---- Stratified sampling
d). Each of the cage have 5 mice and the researcher randomly chooses 6 cages for her study
----- Cluster sampling
e). The researcher generates the list of the identification numbers which has been sorted from the smallest to the largest. The researcher randomly picks 1 mouse form the list and selects every 4 mouse until the researcher has 30 mice.
---- Systematic sampling
3 coins are tossed and two six-sided dice are rolled. What is the probability of getting 3 heads and even number in the dice? show your work for brainliest.
Answer:
1/2
Step-by-step explanation:
Half of the coin sides are heads (Because there is two sides) and half of the numbers on a dice are even. Have a great night/day!
It takes a while for new factory workers to master a complex assembly process. During the first month that the new
employees work, the company tracks the number of days that they have been on the job and the length of time it takes
them to complete an assembly. Determine the most likely correlation.
A.Positive
B.Negative
C.No correlation
D.Curved
Answer:
Will I think it will be A
Step-by-step explanation:
because it say it was a positive
led Question
1. How did you compute sums of dollar amounts that were not whole numbers? For example,
how did you compute the sum of $5.89 and $1.45? Use this example to explain your strategy.
Your answer
Answer:
Computing the sum of $5.89 and $1.45 we get: $7.34
Step-by-step explanation:
We need to explain, how can we compute the sum of $5.89 and $1.45?
Computing the sums of dollar amounts is same as computing the sum of simple decimal expressions. Each value will be added to its corresponding values and we will get the answer.
Computing the sum of $5.89 and $1.45
[tex]\:\:\:\:\:\$ \:\:5.89\\+\$ \:\:1.45\\------\\\:\:\:\:\:\$ \:\:7.34[/tex]
So, we will start adding from right side, 9 will be added with 5 and we get 14, 1 will be given carry and 8 will be added by 4 and add the carry we get 13, 1 will be given carry and 1 will be added by 5 and add the carry we get 7
So, Computing the sum of $5.89 and $1.45 we get: $7.34
Which quotient is greater than 3?
42 ÷ 19
40 ÷ 18
38 ÷ 14
36 ÷ 11
Find the total surface area of the prism.
7 ft
8 ft
5 ft
5 ft
Answer:
The total surface area of triangular prism
A = 232 foot²
Step-by-step explanation:
Explanation:-
Given bases of prism 5 f t , 5 f t , 7 f t
The perimeter of the sum of the bases
P = 7 + 5 +5 = 17 f t
Lateral surface area =perimeter X height
= 1 7 × 8
= 136 f t²
Base area of the triangular prism = [tex]\frac{1}{2} h ( b_{1} + b_{2} ) = \frac{1}{2} 8 ( 5 +7) =48[/tex]
The total surface area of triangular prism
[tex]A = p h + 2 Base Area[/tex]
[tex]A = p h + 2 Base Area = 136 + 2 ( 4 8 ) = 232[/tex]
The total surface area of triangular prism
A = 232 foot²
What is the equation of the linear function represented by the table?
X Y
-5. 14
-2. 11
1. 8
4. 5
O y=-x+9
O y= -x+13
O y= x+13
O y=x+9
Answer:
the linear function is y= -x+9
44 divided by 8 fully
Answer:
The answer is 5.5
Step-by-step explanation:
Since you can't divide 44 from 8 evenly you have to look at it a new way by using haves. They have many amazing videos on this online that I recommend!
I have no idea on how to do this!!!!!
Answer:
the closest one it 3 months
Step-by-step explanation:
To find the simple interest, we multiply 15800 × 0.11 × 3 to get
the interest of 5214.00