Find the derivative of (3+tan X )( 4+3 Cos X)
The derivative of [tex]f(x) = (3 + \tan x)\cdot (4 + 3\cdot \cos x)[/tex] is [tex]f'(x) = \frac{4+3\cdot \cos x-9\cdot \sin x \cdot \cos^{2}x+3\cdot \sin^{2}x\cdot \cos x}{\cos^{2}x}[/tex].
In this question we shall use the following derivative rules:
Derivative of a sum of functions
[tex]\frac{d}{dt}(f(t) + g(t)) = \frac{df(t)}{dt} + \frac{dg(t)}{dt}[/tex] (1)
Derivative of a product of functions
[tex]\frac{d}{dt}(f(t)\cdot g(t)) = \frac{df(t)}{dt}\cdot g(t) + f(t)\cdot \frac{dg(t)}{dt}[/tex] (2)
Derivative of a constant
[tex]\frac{d}{dt}(k) = 0[/tex], [tex]\forall k \in \mathbb{R}[/tex] (3)
Derivative of a function multiplied by a constant
[tex]\frac{d}{dt}(c\cdot f(t)) = c\cdot \frac{df(t)}{dt}[/tex], [tex]\forall\, c\in \mathbb{R}[/tex] (4)
Derivative of the cosine function
[tex]\frac{d}{dt} \cos t = -\sin t[/tex] (5)
Derivative of the tangent function
[tex]\frac{d}{dt}\tan t = \sec^{2} t[/tex] (6)
Chain rule
[tex]\frac{d}{dt}f[u(t)] = \frac{df(u)}{du}\cdot \frac{du(t)}{dt}[/tex] (7)
Let be [tex]f(x) = (3 + \tan x)\cdot (4 + 3\cdot \cos x)[/tex], then the derivative of [tex]f(x)[/tex] is:
[tex]f'(x) = \sec^{2}x\cdot (4 + 3\cdot \cos x) + (3+\tan x)\cdot (-3\cdot \sin x)[/tex]
[tex]f'(x) = 4\cdot \sec^{2}x+3\cdot \sec x -9\cdot \sin x -3\cdot \sin x\cdot \tan x[/tex]
[tex]f'(x) = \frac{4+3\cdot \cos x}{\cos^{2}x} -\frac{9\cdot \sin x \cdot \cos x+3\cdot \sin^{2}x}{\cos x}[/tex]
[tex]f'(x) = \frac{4+3\cdot \cos x-9\cdot \sin x \cdot \cos^{2}x+3\cdot \sin^{2}x\cdot \cos x}{\cos^{2}x}[/tex]
The derivative of [tex]f(x) = (3 + \tan x)\cdot (4 + 3\cdot \cos x)[/tex] is [tex]f'(x) = \frac{4+3\cdot \cos x-9\cdot \sin x \cdot \cos^{2}x+3\cdot \sin^{2}x\cdot \cos x}{\cos^{2}x}[/tex].
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A spinner with sections Red, Blue, Yellow, and Green is spun 3 times. What is the
probability that it will land on yellow all 3 times?
Answer:
33.3%
Step-by-step explanation:
100 divided by 3 is 33.3
PLEASE HELP MEEEEE!!!!!
Answer:
Tan ∠E = 63/16 = 3.9375
Step-by-step explanation:
Tan ∠E = 63/16 = 3.9375
Answer:
Try 63/16 which is 4.0625
Step-by-step explanation:
Again im sorry if its incorrect. XD hope it helps tho. doing the rest o ur question noe .. tehe
Help!!!!!!!!!!!!!!!!!
Answer:
-64
Step-by-step explanation:
Calculate the pressure
300 Newtons ÷ 5 meters²
Answer:
60 pascals
Step-by-step explanation:
Answer:
60
Hope it helps
Please mark me as the brainliest
Thank you
PLEASE HELP ASAP I HAVE 10 MINUTES
Answer:
4, -3
Step-by-step explanation:
I believe it'd be 4, -3 due to the shape moving seven units downwards, though I've only messed with triangles so I may be wrong. Sorry if I am.
I need help with this.
Answer:
h
Step-by-step explanation
12 inches in 1 foot.
2.54 cm in 1 inch.
5x 12=60 inches
60 +4=64inches.
64 x 2.54=162.56 cm
Answer:
H. 162.56 cm
Step-by-step explanation:
12 inches in 1 foot.
2.54 cm in 1 inch.
5x 12=60 inches
60 +4=64inches.
64 x 2.54=162.56 cm
A person standing on level ground is 3020 feet away from the foot of a building. If the height of the building is 2534 feet, find the angle of elevation formed at the point where the person is standing to the nearest degree
Answer:
40°
Step-by-step explanation:
Base length, b = adjacent = 3020 feets
Height of building, h = opposite = 2534 feets
The angle of elevation formed :
Using the trigonometry relation:
Tan θ = opposite / Adjacent
Tan θ = 2534 / 3020
Tan θ = 0.8390728
θ = tan^-1(0.8390728)
θ = 39.999
= 40°
8. (03.04 MC)
What is the first step needed to solve
(4)x+6=–13 ?
A. Subtract 13 from both sides
B. Divide both sides by 7
C. Add 5 to both sides
D. Multiply both sides by 4
Answer:
its a
Step-by-step explanation:
i did it
Answer:
A
Step-by-step explanation:
what does 9a^2 + 2b^2 if a=4 and b=7?
Answer:
242
Step-by-step explanation:
Answer:
242
Step-by-step explanation:
Given
9a² + 2b² ← substitute a = 4 and b = 7
= 9(4)² + 2(7)²
= 9(16) + 2(49)
= 144 + 98
= 242
Find the centroid of ABC if
A = (2, 2), B = (-1,0), and C = (8,4).
([?], [ ])
Answer:
The centroid of ABC is (3 , 2).
Step-by-step explanation:
The steps are :
[tex]centre = ( \frac{x1 + x2 + x3}{3} \: , \: \frac{y1 + y2 + y3}{3} )[/tex]
[tex]centre = ( \frac{2 + ( - 1) + 8}{3} \: , \: \frac{2 + 0 + 4}{3} )[/tex]
[tex]centre = ( \frac{9}{3} \: , \: \frac{6}{3} )[/tex]
[tex]centre = (3 \: , \: 2)[/tex]
Answer:
The centroid of ∆ABC is (3 , 2).
Step-by-step explanation:
Solution :
Here's the required formula to find the centroid of ∆ABC :
[tex]{\star{\footnotesize{\purple{\underline{ \boxed{\sf{\pink{Centroid = \bigg( \dfrac{x_1 + x_2 + x_3}{3} \: , \: \dfrac{y_1 + y_2 + y_3}{3} \bigg)}}}}}}}}[/tex]
Where :
[tex]\rightarrow\rm{x_1}[/tex] = 2[tex]\rightarrow\rm{x_2}[/tex] = -1[tex]\rightarrow\rm{x_3}[/tex] = 8[tex]\rightarrow\rm{y_1}[/tex] = 2[tex]\rightarrow\rm{y_2}[/tex] = 0[tex]\rightarrow\rm{y_3}[/tex] = 4Substituting all the given values in the formula to find the centroid of ∆ABC
[tex]{\implies{\small{\sf{Centroid = \bigg( \dfrac{x_1 + x_2 + x_3}{3} \: , \: \dfrac{y_1 + y_2 + y_3}{3} \bigg)}}}}[/tex]
[tex]{\implies{\small{\sf{Centroid = \bigg( \dfrac{2 + ( - 1) + 8}{3} \: , \: \dfrac{2 +0 + 4}{3} \bigg)}}}}[/tex]
[tex]{\implies{\small{\sf{Centroid = \bigg( \dfrac{2 - 1 + 8}{3} \: , \: \dfrac{2 +0 + 4}{3} \bigg)}}}}[/tex]
[tex]{\implies{\small{\sf{Centroid = \bigg( \dfrac{10 - 1}{3} \: , \: \dfrac{2 + 4}{3} \bigg)}}}}[/tex]
[tex]{\implies{\small{\sf{Centroid = \bigg( \dfrac{9}{3} \: , \: \dfrac{6}{3} \bigg)}}}}[/tex]
[tex]{\implies{\small{\sf{Centroid = \bigg( \cancel\dfrac{9}{3} \: , \: \cancel\dfrac{6}{3} \bigg)}}}}[/tex]
[tex]{\implies{\small{\sf{Centroid = \Big( 3\: , \: 2 \Big)}}}}[/tex]
[tex]\star{\underline{\boxed{\rm{\red{Centroid = \Big( 3\: , \: 2 \Big)}}}}}[/tex]
Hence, the centroid of ∆ABC is (3 , 2).
[tex]\rule{300}{1.5}[/tex]
If I live in the United States and I send 100 dollars to someone who lives in Mexico, how much are 100 dollars in Mexican money
I'm conscious
Answer:
2935 Mexican pesos
Step-by-step explanation:
First, it's worth noting that at current exchange rates, your $100 will equal upwards of 2,395 pesos in Mexico.
Does a rotation preserve congruence
Please help me find the area of this triangle!
Answer:
150
Step-by-step explanation:
1/2 multiply base times hieght
Answer:
150
Step-by-step explanation:
given in the pic above
in the pic its 15×10
i have written mistakely 15×12
Can someone do both plzzzz
Answer:
Answer to question 7: -2x+5y+9
Answer to question 8: 2x-6y+1
Answer:
7.) -2x + 5y + 9 ; 8.) 2x - 6y + 1
Step-by-step explanation:
7.)
7 + 2x + 5y - 4x + 2 ⇒ -2x + 5y + 9
2x - 4x ⇒ -2x
5y ⇒ 5y
7 + 2 ⇒ 9
8.)
-4y + 2x - 2y + 1 ⇒ 2x - 6y + 1
2x ⇒ 2x
-4y - 2y ⇒ -6y
1 ⇒ 1
The top of a ramp is 4 feet above the ground. The ramp makes a 21.3 degree angle with the ground. What is the length of the ramp
Answer:
Total ramp system length in feet: Includes the minimum number of 5′ x 5′ resting platforms and the 5′ x 5′ platform at the top of the ramp.
Step-by-step explanation:
hope this helps!
Find the value of x.
Answer:
Step-by-step explanation:
Remark
Since the chords of the circle are equal and non intersecting, The 2 bisecting perpendiculars are going to be equal.
Equation
5x = 7x - 8 Subtract 7x from both sides
5x - 7x = - 8
-2x = - 8 Divide by - 2
x = - 8/-2
x = 5
Yassar has purchased a $30,000 car for his business. The car depreciates at 30%
every year. {Depreciation means the value of the car decreases by that percent each
year).Calculate the value of the car to the nearest cent at the end of the 5th
year.
A. $5,042.10
B. $111.387.90
C. $21.000.00
D. $39,346.85
Answer:
A
Step-by-step explanation:
30% of 30000 is 9000, 30000-9000=21000 (1 year)
30% of 21000 is 6300, 21000-6300=14700 (2 years)
30% of 14700 is 4410, 14700-4410= 10290 (3 years)
30% of 10290 is 3087, 10290-3097= 7203 (4 years)
30% of 7203 is 2160.9, 7203-2160.9= 5042.1 (5 years)
Posted the next question!
Answer:
angle 3 and angle 2 are complementary angle.
Help me with this pls 10 points
Answer:
48
Step-by-step explanation:
Add 84+48 to get 132. subtract 180 the total to the 132 to get 48.
Answer:
its not 10 points its says 8
Step-by-step explanation:
What is the area of the shaded region?
Answer:
15x^2-24x+9
Step-by-step explanation:
help me pls and show work 8th grade math
Answer:
Find the slope this way Hanna,
Step-by-step explanation:
slope = m
m = (y2-y1) / (x2-x1)
you are given the two points
P1 = (-2,-6) in the form (x1,y1)
P2 = (2,2) in the form (x2,y2)
plug those into the slope formula above
m = (2-(-6) ) / (2 - (-2) )
m = (2 +6) / (2+2)
m = 8 / 4
m = 2
if you need more explanation just leave a comment, it will show up and I'll come look at your question
In the year 2000, the number of bunnies in a certain forest was 320. Since that year the number of bunnies in that forest has increased at a rate of 16% per year. Write a function, f(x), that models the number of bunnies x year after the year 2000.
Answer:
f(x)=320(1.16)^x
Step-by-step explanation:
This is an exponential equation with an initial population at x=0 of 320 (because 1.16^0=1, and 320*1=320) After the first year, there are 371 bunnies. After two years, there are 431, etc etc.
Answer:
f(x)=320(1.16)^x
This is an exponential equation with an initial population at x=0 of 320 (because 1.16^0=1, and 320*1=320) After the first year, there are 371 bunnies. After two years, there are 431, etc etc.
Use the information in the figure. Find mZD. 106 D Drawing not to scale 37° 53
Answer: Its B
Step-by-step explanation: Hope this was helpful I am not to sure this is the right answer but let me know if it is
HELP DUE IN 10 MINS! Kayla decided to try parasailing. She was strapped into a parachute towed by a boat. An 800 foot line connected her parachute to the boat, which was at a 32 degree angle of depression below her. How high above the water was Kayla? Round to the nearest foot.
feet=??
Answer:
424 ft
Step-by-step explanation:
Answer:
424 feet is the answer rrrr
Help plzzzzzzzzzzzzzzzzzzzz
Answer:
B
Step-by-step explanation:
Y is the total cost, 22x is how many tickets bought, and 10 is the parking cost
Simplify (3x + 2)(4x - 7). Write your answer in standard form.
Answer:
noninvasive I will not pay any fee in full and the other fees for my undergraduate degree
80% or 7/9 which is greater
Answer:
80% is greater
Step-by-step explanation:
Answer:
The number 80% is greater than 7/9
Step-by-step explanation:
You have a balance of $4,600 on your credit card. The interest rate is 12% (1% per month). The late payment fee is $40.
You miss a payment. What are your fees plus interest for the month?
Answer:
$86
Step-by-step explanation:
first you gotta find the interest
4,600 * 1% = 46
so the interest is $46
then you add the interest and late fees together to get the payment for the month
46 + 40 = $86
your total cost is $86
The fess plus interest of the month will be $86 after missing a payment.
Given:
Balance = $4600
Interest rate = 0.01
Step 1: Calculate the interest for the month.
Interest for the month = Balance × Monthly Interest Rate
Substituting the value back to the formula
Interest for the month= $4,600 × 0.01
= $46
Step 2: Add the late payment fee.
Late payment fee = $40
Step 3: Total fees plus interest for the month.
Total = Interest for the month + Late payment fee
Total = $46 + $40
Total = $86
So, fees plus interest for the month when you miss a payment amount to $86.
Learn more about interest here:
https://brainly.com/question/28272078
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Find the difference using fraction bars or a paper and pencil. Write your answer in simplest form. 7/10 - 1/2 help asap!! im on a test
Step-by-step explanation:
7/10 - 1/2 = 7/10 - 5/10 = 2/10
Answer:
4/4
Step-by-step explanation: