Answers
So, here we need to differentiate tan³[tex](\theta)[/tex], wr.t.[tex]\theta[/tex], but let's recall some identities which will be very useful in this question :
[tex]{\boxed{\bf{\dfrac{d}{dx}\{\tan (x)\}=\sec^{2}(x)}}}[/tex][tex]{\boxed{\bf{\dfrac{d}{dx}(x^n)=nx^{n-1}}}}[/tex][tex]{\boxed{\bf{\sec^{2}(\theta)=\tan^{2}(\theta)+1}}}[/tex]Coming back on the question, consider :
[tex]{:\implies \quad \sf \dfrac{d}{d\theta}\{\tan^{3}(\theta)\}}[/tex]
[tex]{:\implies \quad \sf 3\tan^{3-1}(\theta)\dfrac{d}{d\theta}\{\tan (\theta)\}}[/tex]
[tex]{:\implies \quad \sf 3\tan^{2}(\theta)\sec^{2}(\theta)}[/tex]
Using the identity ;
[tex]{:\implies \quad \sf 3\tan^{2}(\theta)\{1+\tan^{2}(\theta)\}}[/tex]
[tex]{:\implies \quad \sf 3\tan^{2}(\theta)+3tan^{4}(\theta)}[/tex]
[tex]{:\implies \quad \sf 3\tan^{4}(\theta)+3\{\sec^{2}(\theta)-1\}}[/tex]
[tex]{:\implies \quad \boxed{\bf 3\tan^{4}(\theta)+3\sec^{2}(\theta)-3}}[/tex]
Hence, Proved
Related Questions
Nancy bought a new rectangular rug for her kitchen. The rug measures 2 feet by 2 feet. What is the area of the rug?
A. 4 3/4
B. 5 1/2
C. 5 3/4
D. 9 1/2
Answers
Answer: 5.5 or 5 1/2.
Step-by-step explanation:
Solve all this
1) 2x-8=11x-10
2)6x-6=3x+1
3)1/2x+4=1/3x+1
4)-2/5x+1/3=1/2x+1/4
5)5/3x2=1/2x-2/3
Answers
Answer: hii :)
1. 2x-8=11x-10 = 2/9
2. 6x-6=3x+1 = 7/3
3. 1/2x+4=1/3x+1 = -18
4. -2/5x+1/3=1/2x+1/4 = 5/54
5. I dont know the answer to <3
Step-by-step explanation:
Hopefully this helps you,
Sorry for being late on the question.
- Matthew
Find the mean, median, and mode of the data set. Round to the hundredths, if necessary. 29,300 24,350 32,400 15,100 14,200 21,950 27,450 29,400 15,200 35,050 16,050 11,500 13,050 11,500 11,600 11,100 21,450
Answers
The mean of the data is 20038.24, the median is 16050 while the number with the highest frequency is 11500
Mean, median, and mode of a datasetMean are known as averages, median is the middle value after rearrangement while the mode is the value with the highest frequency
Calculate the mean
Mean = sum of data/sample size
Given the data
29300, 24350, 32400, 15100, 14200, 21950, 27450, 29400, 15200, 35050, 16050, 11500, 13050, 11500, 11600, 11100, 21450
The mean of the data is 20038.24
For the median being the value at the middle, the median is 16050 while the number with the highest frequency is 11500
Learn more on mean, median and mode here: https://brainly.com/question/14532771
An employer pays you penny the first day you work and doubles your wages each day after that: Find your total earnings after working 7 days a week for (a) One week (b) Two weeks (c) Three weeks (d) Four weeks
Answers
a) answer is 64 pennies
b) answer is 8 192 pennies
c) answer is 1 048 576 pennies
d) answer is 134 217 728 pennies
What is the mode of the data represented in this line plot? Enter your answer in the box. A dot plot on a number line. The number line ranges from 5 to 11. The number 5 has 2 marks above it. The number 6 has 4 marks above it. The number 7 has 3 marks above it. The number 8 has 6 marks above it. The number 9 has 2 marks above it. The number 10 has 4 marks above it. The number 11 has 2 marks above it.
Answers
The mode of the data in the line plot is the data with the highest number of marks
The mode of the data is 8
How to determine the mode?From the line plot, we have the following frequency table:
Number Frequency
5 2 marks
6 4 marks.
7 3 marks
8 6 marks
9 2 marks
10 4 marks
11 2 marks
The number with the highest mark is 9
Hence, the mode of the data is 8
Read more about mode at:
https://brainly.com/question/14532771
Answer: The mode is 8
Step-by-step explanation: Mode means the number that shows up must in the graph and since 8 is the highest that goes the mode is 8. Also I did the k12 quiz.
8 less than the product of 3 and j
Answers
Answer:
3j - 8
Step-by-step explanation:
8 less than the product of 3 and j
3×j - 8
3j - 8
The slope of a line is -1/3. Find the slope of a line that is perpendicular to this line.
Answers
Answer: 3
Step-by-step explanation:
Perpendicular lines have slopes that are negative reciprocals of each other.
Answer:
Slope = 3
Step-by-step explanation:
The question is asking us to find the slope of the line that is perpendicular to the line whose slope is -1/3.
Main idea: Perpendicular lines have slopes that are opposite reciprocals.
So our task boils down to finding the opposite reciprocal of -1/3.
First, we change the sign from negative to positive. We get 1/3.
Then, we turn the number over. We get 3.
Therefore, the slope is 3.
Please solve the whole page
Answers
Answer:
1. 3/20
2. 76/4
3. 16
4. 1/8
5. 11/1
6. 2.5/1
7. 13/1
8. 255/1
9. 20, 140, 240
10. 3.5, 17.5, 31.5
11. 12
12. 2
A local restaurant uses a computer to randomly select an appetizer and accompanying sauce. The table below shows all the
possible outcomes when ordering
What is the probability of receiving chicken or ribs and getting a red sauce?
Answers
Answer:
B 1/5
Step-by-step explanation:
there is 20 combinations
4 of the twenty are ribs or chicken with a red sauce
4/20 = 1/5
Please I really need help
Answers
Answer:
NM = 17, LY = 5, m<NLY = 53.13 degrees, m<NMY = 28.07 degrees
Step-by-step explanation:
To solve for NM, you just use the Pythagorean theorem,
[tex]8^{2} + 15^{2} = x^{2}[/tex]
64 + 225 = [tex]x^{2}[/tex]
289 = [tex]x^{2}[/tex]
[tex]17 = x[/tex]
To solve for LY, you can use geometric mean,
[tex]\frac{10}{y} = \frac{15+y}{10}\\\\100 = 15y + y^{2} \\y^{2} +15y - 100 = 0\\(y+20)(y-5) = 0\\y= 5[/tex]
To solve for the other angles, use the inverse.
Sin-1, = 8/10
= 53.13
Other angle =
Tan-1 = 8/15
= 28.07
Hope this helps, I put a lot of time into this :)
if i make 8.50 an hr and i work 30 hours a week 5 days a week how much would i make in a month?
Answers
Find the missing coordinate (?, -1) for 3x -4y=11
Answers
Answer:
[tex]\frac{7}{3}[/tex]
Step-by-step explanation:
Substitute -1 in place of y in the equation:
[tex]3x -4(-1)=11\\3x=7\\x=\frac{7}{3}[/tex]
Answer:
(7/3, -1)
Step-by-step explanation:
3x -4y=11
Let y = -1
3x -4(-1) = 11
3x +4 =11
Subtract 4 from each side
3x+4-4 = 11-4
3x = 7
Divide each side by 3
3x/3 = 7/3
x = 7/3
2x+2=4 solve for x please help me solve this problem
Answers
Answer:
x = 1
Step-by-step explanation:
First subtract 2 on both sides.
2x + 2 -2 = 4 - 2
2x = 2
Divide by 2 on both sides
2x/2 = 2/2
x = 1
Answer:
x=1
Step-by-step explanation:
cause it do 2 multiplied by 1 is 2 plus 2 is 4
What is the circumference in centimeters, of the circle?
Use 3.14 for TT
Answers
Step-by-step explanation:
the full question please
Help picture below problem 8
Answers
Answer:
C. never
Step-by-step explanation:
A trapezoid has exactly one pair of opposite sides parallel.
A parallelogram has exactly two pairs of opposite sides parallel.
A trapezoid is never a parallelogram.
A battery for an underwater drone is in the shape of a square prism is designed to draw in
searates that is then used to produce energy. The base of the battery has soe lengths of 15 centimeters and the heght of the
bertery is 10 centimeters. Find the volume of the battery.
Answers
Answer:
2250 cm^3
Step-by-step explanation:
Volume of sq prism - Base x Base x Height
15 x 15 x 10 = 2250
How do you solve this? I don't understand
Answers
Answer:
x=4 (Vertical angles have to be equal to each other! If one side is 46 then the side vertical to it is 46!) **Plug number in for x to verify once again!**
Step-by-step explanation:
You need to understand vertical angles!!
Vertical Angles must be congruent and equal to each other!
You need to do:
10x+6=46
Subtract 6 from both sides
10x=40
Do 40 divided by 10
x=4
To verify: plug 4 for x which should be 40 added to 6 is 46!
The sum of two numbers is 21. Their product is 108. What are the two numbers?
Answers
Answer:
9 and 21
Step-by-step explanation:
First we can write the factors of 108:
1,108
2,54
3,36
4,27
6,18
9,12 - these 2 numbers add up to 21 so these 2 numbers is our answer.
Answer:
12 and 9
First, divide 108 by a relatively low number, 12[tex]108 / 12 = 9[/tex]
Now that we have 9, multiply 9 by 12[tex]9 * 12 = 108[/tex]
This is one method that proves the statement true. I call the method mirroring. This method consists of finding the lowest numbers a large number is divisible by, then flipping the problem to a multiplication problem.________________________________________________________
What have we learned?We learned alternative ways to find the sum and product of a number using a similar method.
Questions related to the topic? Ask me in the comments box.
PLEASE HELPPPPPPPPPPPPPPPPPPPPPPPPPPP
Consider this dilation.
(a) Is the image of the dilation a reduction or an enlargement of the original figure? Explain.
(b) What is the scale factor? Explain and show your work.
ANSWER BOTH PARTS YOU MAY GET EXTRA POINTS!
Answers
Answer:
reductionscale factor 1/2Step-by-step explanation:
The usual English meanings of the words "reduction" and "enlargement" apply to geometrical figures.
(a)Figure A'B'C'D' is smaller than figure ABCD, so represents a reduction.
__
(b)Every coordinate of every image point is half as far from the origin in A'B'C'D' as in the original figure ABCD. For example, the x-coordinate of C' is 2, and the x-coordinae of C is 4. The dilation factor is the ratio of these values:
k = Cx'/Cx = 2/4 = 1/2
The scale factor is 1/2.
How do I find the mean of these numbers?
Answers
Answer:
how to find the mean: add all your values together then divide them by how many numbers u added
example:
5,7,9,9,10
add= 40
divide by 5, we have 5 values = 8
A drug prescription of 45 pills costs $427. 95. If each pill contains 3 mg of medication, what is the cost per milligrams?
Answers
Total milligrams
45(3)135mgCOST PER MG:-
TOTAL COST/total Mg427.95/1353.17$/pillsAnswer:
$3.17
Step-by-step explanation:
1 pill = 3 mg
⇒ 45 pills = 45 × 3 = 135 mg
45 pills = $427.95
⇒ 135 mg = $427.95
⇒ 1 mg = $427.95 ÷ 135 = $3.17
if a number is added by 2 the answer is10 find the number
Answers
Explanation:
Just do the reverse of addition. 10-2=8
Melanie is designing a new board game, and is trying to figure out all the possible outcomes. How many different possible outcomes are there if she rolls a fair die in the shape of a pyramid that has four sides labeled 1 to 4 and spins a spinner with 5 equal-sized sections labeled Monday, Tuesday, Wednesday, Thursday, Friday?
Answers
Answer:
20 possible outcomes
Step-by-step explanation:
5 equal-sized sections x 4 sides of the die = 20
A mother decides to teach her son about a letter each day of the week. She will choose a letter from the name of the day. For example, on Saturday she
might teach about the letter S or the letter U, but not the letter M.
Sunday
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday
What letters are CANT BE TAUGHT using this method? (There are 11.)
ОА
OB
Ос
OD
ОЕ
OF
OH
01
Answers
Answer:
01 she can teach alphabet using seven days name but not numbers.
-
The expression (3 - 7i)^2 equivalent to
Answers
Answer:
-40-42i
Step-by-step explanation:
9-42i+49i^2=9-42i-49=-40-42i
The function f(x)=(2)(1.0)+x(0.5)2+x models the concentration of pineapple when 2 gallons of pineapple juice are added to x gallons of another juice. Find the concentration of pineapple when 2 gallons of pineapple juice are added to 3 gallons of the other juice. Give the answer as a percent but do not include the percent sign (%).
Answers
The concentration of pineapple when 2 gallons of pineapple juice are added to 3 gallons of the other juice is 5.75
Functions and valuesGiven the functions that model the concentration of pineapple when 2 gallons of pineapple juice are added to x gallons of another juice as:
f(x)=(2)(1.0)+x(0.5)²+x
If the concentration of pineapple when 2 gallons of pineapple juice are added to 3 gallons of the other juice, then;
f(3) = (2)(1.0)+3(0.5)²+3
f(3) = 2.0 + 3.75
f(3) = 5.75
Hence the concentration of pineapple when 2 gallons of pineapple juice are added to 3 gallons of the other juice is 5.75
Learn more on functions here: https://brainly.com/question/2833285
A video has 25 thumbs up. What integer represents its score in points?
Answers
Answer:
25 points
Hope this helps!
Find a polynomial f(x) of degree 5 that has the following zeros -1,4,2,0,3
Answers
Answer:
Given that f(x) contains the discrete points of{(0, 3), (1, 4), (2, 0), (3, 1), (4, 2)}, the value of (f of)(0) is5.
Is this adjacent, vertical, linear, or complimentary?
Answers
Adjacent angles share a common side. Think of two neighboring adjacent apartments that share a common wall.
Select all possible values for x in the equation
Answers
Answer:
x = ∛375
Step-by-step explanation:
This expression can be written in multiple ways:
x³ = 375
x = ∛375
x = 5∛15
Seems like x = ∛375 is the only correct answer choice.
Hope this helps!
