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
100 points please help
Factor 36x2 + 60x + 25.
(6 x + 5) 2
(12 x + 5)(3 x + 5)
(6 x + 5)(6 x - 5)
Answers
MUTUALLY OR NOT MUTUALLY EXCLUSIVE EVENTS?
Answers
Answer:
All are not mutually exclusive events
Mark bought two candy bars and a soda for $3.96. If each candy bar cost $1.10 how much did the soda cost?
Answers
Answer:
$1.76
Step-by-step explanation:
$1.10+$1.10 = $2.2
$3.96 - $2.2 = $1.76
PLEASE HELP ASAP!!! WITH EXPLANATION IF POSSIBLE!!!!!!!!!
Two chords PQ and ST of length 6cm and 10cm respectively of a circle are parallel to each other and are on opposite side of its center. If the distance between PQ and ST is 5cm. Find the radius of the circle
Answers
Answer:
Draw two parallel chords AB and CD of lengths 5 cm and 11 cm. Let the center of the circle be O. Join one end of each chord to the center.
Draw two perpendiculars OM and ON to AB and CD, respectively, which bisects the chords.
Two chords AB and CD of lengths 5 cm and 11 cm respectively of a circle are parallel to each other and are on opposite sides of its center. If the distance between AB and CD is 6 cm, find the radius of the circle.
Thus, MB = 2.5 cm and ND = 5.5 cm [The perpendicular drawn from the center of the circle to the chords bisects it.]
Let OM = x and ON = 6 - x
Consider ΔOMB
By Pythagoras theorem,
OM2 + MB2 = OB2
x2 + 2.52 = OB2
x2 + 6.25 = OB2..................(1)
Consider ΔOND
By Pythagoras theorem,
ON2 + ND2 = OD2
(6 - x)² + 5.52 = OD2
36 + x2 - 12x + 30.25 = OD2
x2 - 12x + 66.25 = OD2............... (2)
OB and OD are the radii of the circle. Therefore OB = OD.
Thus, OB2 = OD2
Equating (1) and (2) we get,
x2 + 6.25 = x2 - 12x + 66.25
12x = 60
x = 5
Substituting the value of x in (1),
OB2 = x2 + 6.25
OB2 = 52 + 6.25
OB2 = 31.25
OB = 5.59 (approx.)
Thus, we get the radius of the circle = 5.59 cm.
Select the correct answer.
What are the roots of this quadratic equation?
help
Answers
Answer:
A
Step-by-step explanation:
I took the test it was right
Explain the difference between yi and ŷi.
Answers
Answer:
Down:
Step-by-step explanation:
Terms in this set (23) The difference between the observed value of the dependent variable and the value predicted using the estimated regression equation; for the ith observation the ith residual is yi − ŷi. The analysis of variance table used to summarize the computations associated with the F test for significance.
Find the chance of having a face card if a card is drawn randomly from a deck of cards.
Answers
Answer:
3/13
Step-by-step explanation:
P(Choosing a Face card) =
12/52= 3/13
pls mark as brainliest
This is the same triangle you used for Question 2. Triangle ABC has angle measures as shown below. Using the information in the diagram, and the value of x that you calculated i Question 2, find the measure of Angle C. In your answer, give the measure of Angle C and explain how you calculated it.
Answers
Answer:
93
Step-by-step explanation:
So, you know the angles of a triangle added together is 180.
180-52-35=93
Which selection shows the correct order of points from least to greatest on the number line?
SUOSI
27 4 7 4
3 8 5 10 3
H
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0
2.
-1
A.
nim
4
5'
-
-
bu
4 7
3' 10
in
NICO
3
av
4
7
B.
4 2
5' 3'
7
3' 8' 10 de file upon two locou
2
4.
-
C.
4 7 7
5' 10' 8
3
3
4
2
7
7
D.
---
3
5'
3
10
8
Answers
Answer:
D.
Step-by-step explanation:
As is often the case with multiple choice questions, you only need to find part of a correct answer to be able to make the right choice.
The number line picture shows the left-most point has a value less than -1. That means the numerator of its negative fraction will be greater than the denominator. The only fraction like that on the list is -4/3, and the only answer choice with that listed first is choice D.
D. -4/3, -4/5, -2/3, 7/10, 7/8
D. -4/3, -4/5, -2/3, 7/10, 7/8
Step-by-step explanation:
# Brainliest Bunch
Kari and two of her friends are entering their senior year of high school. The tables below show the estimated expenses at three tied of schools they are considering. Complete the blanks in each table and use the information to help you answer questions 1-3
Answers
The expenses for the duration of the four years that Kari will use in the university is $68600.
How to calculate expenses?From the complete information, the expenses for the four years stay in the university will be calculated thus:
Tution = $8500
Room = $6700
Books = $1250
Miscellaneous expense = $700
Total = $17150
The expenses for the four years will be:
= $17150 × 4
= $68600
Learn more about expenses on:
https://brainly.com/question/14697297
=
EXPONENTS AND POLYNOMIALS
Factoring a quadratic by the ac-method
Factor by grouping (sometimes called the ac-method).
2
2x + 3x-9
-
First, choose a form with appropriate signs.
Then, fill in the blanks with numbers to be used for grouping.
Finally, show the factorization.
Answers
Answer:
5x-9
Step-by-step explanation:
Add 2x and 3x since they're like terms
5x-9
May anyone help me pls
Answers
Step-by-step explanation:
b is the smallest and then a , d, c, e
Question 6(1 point)
QS is a tangent to circle P. Find QS.
Answers
PR = 5 since it is also the radius.
So if you use the Pythagorean theorem, you get sqrt(13^2 - 5^2) = 12
what is the volume of this container 1ft 1ft 2ft
Answers
Answer:
Remember length times width times height when finding volume.
In non-terms of pi, the answer would be [tex]2[/tex] [tex]ft^2[/tex]
Answer:
Volume is 2ft
Step-by-step explanation:
Multiply the length x width once you find the answer for lengthxwidth.
Multiply the answer you got by height
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.
find the product of -5x^3y(4x-8y)
Answers
Answer:
-20x^4y + 40x^3y^2.
Step-by-step explanation:
-5x^3y(4x-8y)
= -5x^3y * 4x + -5x^3y * -8y
= -20x^4y + 40x^3y^2
What did is the total volume,in cubic feet of the shape below
Answers
Answer:
64ft^3 (The ^3 is meant to be cubed) 64 feet cubed.
Step-by-step explanation:
The picture has already split the two shapes.
*Remember Volume Formula: LWH or Length times Width times Height.*
The first shape is 4ft x 2ft x 2ft
The second shape is a little bit of a fuss but it's alright.
*Talking about the length of Shape no.2*
Since the second shape is longer than the first one (by length). You need to double it meaning: 4x2 or 4+4 = 8ft
The second shape is 8ft x 2ft x 3ft
First shape should have a volume of 16ft
Second shape should have a volume of 48ft
Now, you need to add the two volumes:
48ft + 16ft = 64ft cubed
Solve one half ÷ 8 = ___.
one seventh
one sixteenth
one twenthieth
one thirtieth
Answers
Answer:
one sixteenth
Step-by-step explanation:
I hope this helps! Have a lovely day!! :)
PLS HELPP- I NEED AN ANSWER ASAP BRAINLY WILL BE GIVEN~
Answers
You need a 40\% alcohol solution. On hand, you have a 150 mL of a 20% alcohol mixture. You also have 55% alcohol mixture. How much of the 55% mixture will you need to add to obtain the desired solution?
Answers
Answer:
You need to add 200 mL of the 55% to obtain the desired solution
Step-by-step explanation:
x=mixture you need to add
20% * 150 + 55% x = 40%(x + 150)
0.20 * 150 + 0.55x = 0.40(x + 150)
30+0.55x=60+0.40x
0.15x = 30
x=200 mL
At a track meet, Jacob and Daniel compete in the 220 m hurdles. Daniel finishes in of a minute. Jacob
finishes with of a minute remaining. Who ran the race in the faster time?
12
Answers
Daniels finishes in of the a min.
Jacob finishes with of a min remaining.
Question:
Who ran the race in faster time?
The Process:
Let us see the denominators. The least common multiple (LCM) of 4 and 12 is 12.
Let us draw the diagram that represents a minute.
12 units represent in one minute.
Daniels finishes in of the a min.
or 9 of 12 units.
Jacob finishes with of a min remaining, or 5 of 12 units. This means Jacob finishes in or 7 of 12 units, that is
And now we conclude who ran the race in a faster time.
Daniels:
Jacobs:
Because Jacob took the race in a shorter time, he was who ran the race in a faster time.
- - - - - - - - - -
Quick Steps
Daniels: in of the a min.
Jacob: in of the a min.
Jacob's time is shorter, so he's the fastest.
- - - - - - - - - -
Calculate the speed
Recall
Daniels:
Jacob:
Thus, Jacob's speed proved greater than Daniels's speed.
B
ca
(3y +9)°
1149
4yº
D C
А
1.
o
Answers
(3y + 9) + (4y) = 114
7y+9 =114 (combine like terms)
7y= 105 (Subtract 9 from both sides)
Y=15 (divide 7 from both sides)
4 x 15=60 (substitute 15 for Y)
Find the next two numbers in the sequence 5,2,-1,…
Answers
Answer:
The answer is (-4) and (-7).
Step-by-step explanation:
Given;a₁ = 5a₂ = 2a₃ = (-1)To Find;a₄ = ?a₅ = ?Formula;aₙ = a + (n – 1) × dNow, for common difference (d)
d = a₂ – a₁ = 2 – 5 = -3
d = a₃ – a₂ = (-1) – 2 = -3
Here, common difference is same everywhere.
So, for fourth term or n = 4
aₙ = a + (n – 1) × d
a₄ = 5 + (4 – 1) × (-3)
a₄ = 5 + 3 × (-3)
a₄ = 5 – 9
a₄ = -4
Then, for fifth term or n = 5
a₅ = 5 + (5 – 1) × (-3)
a₅ = 5 + 4 × (-3)
a₅ = 5 – 12
a₅ = -7
Thus, The fourth term is (-4) and fifth term is (-7).
log7(49)=2 in exponential form
Answers
Answer:
49 = 7²
Step-by-step explanation:
A logarithm is an exponent. The base of the logarithm is the base of the exponent. The base to that exponent is the argument of the log function.
__
The logarithm (exponent) is 2. The base is 7. The argument of the log function is 49. In exponential form, this is written ...
7² = 49
Write the equation for the function graphed attached
f(x)=
Answers
Answer:
here
Step-by-step explanation:
Question 11
1 pts
A baby was 6 lb 8 oz at birth. At one month old, she weighed 9 lb 2 oz. How much weight did the
baby gain in the first month?
Answers
Answer:
2 lb and 4oz
Step-by-step explanation:
because if you do 9lb 2oz minus 6lb 8oz you get 2 lb 4oz
Write the given expression as a single trigonometric function.
2 sine (StartFraction 3 pi Over 8 EndFraction) cosine (StartFraction 3 pi Over 8 EndFraction)
Sine (StartFraction 3 pi Over 16 EndFraction)
2 sine (StartFraction 3 pi Over 16 EndFraction)
Sine (StartFraction 3 pi Over 4 EndFraction)
2 sine (StartFraction 3 pi Over 4 EndFraction)
Answers
Answer:
sin(3pi/4)
Step-by-step explanation:
I got it right on edg
Answer:
The answer is letter c
Step-by-step explanation:
Is it possible that all solutions of a homogeneous system of ten linear equations in twelve variables are multiples of one fixed nonzero solution
Answers
The answer is no, because the Rank Theorem tells us that rank A + dim Nul A = 12 . Since the rank can be at most 10, the null space has to have dimension at least two.
11. Reduce 48/72 to its lowest terms.
A. 6/9
B.2/3
c. 24/36
D. 30/54
Answers
Answer:
its A my friend because: 48/2=24. 72/2=36
24/2=12. 36/2=18
12/2=6. 18/2=9
Bill is A yr old. Write a simplified expression for his daughter's age if Bill's daughter is 28 yr younger than he is.
Bill's daughter is _____yr old?