Answers
[tex]~~~~~~\tan^{-1}(xy) = \sin^{-1}(4x+4y)\\\\\\\implies \dfrac d{dx} \left[ \tan^{-1}(xy)\right] = \dfrac d{dx} \sin^{-1}\left( 4x+4y\right)\\ \\\\\implies \dfrac{1}{1+(xy)^2} \left[ \dfrac{d}{dx} (xy)\right] = \dfrac{1}{\sqrt{1-(4x+4y)^2}} \cdot \dfrac{d}{dx}(4x+4y)\\\\\\\implies \dfrac{1}{1+x^2 y^2} \left(x\dfrac{dy}{dx}+y \right)=\dfrac{1}{\sqrt{1-(4x+4y)^2}} \left(4+ 4 \dfrac{dy}{dx} \right)\\\\\\\\[/tex]
[tex]\implies \left(\dfrac{x}{1+x^2y^2} \right) \dfrac{dy}{dx} + \dfrac{y}{1+x^2y^2}=\dfrac{1}{\sqrt{1-(4x+4y)^2}} \left(4+ 4 \dfrac{dy}{dx} \right)\\[/tex]
[tex]\\\\\implies 0 \cdot \dfrac{dy}{dx} +0 = \dfrac{1}{\sqrt{1 -0}} \left(4+4 \dfrac{dy}{dx} \right) ~~~~~~~~~;\left[ \text{at}~~ (0,0) \right]\\\\\\\implies 4+4 \dfrac{dy}{dx} = 0\\\\\\\implies \dfrac{dy}{dx} = -\dfrac 44\\\\\\\implies \dfrac{dy}{dx} = -1\\\\\text{So, the slope of the tangent line at (0,0) is}~ -1\\ \\\\\text{The equation of tangent line,}\\\\~~~~~~y-0 = -1(x-0)\\\\\implies y=-x[/tex]
Related Questions
9. Kate is randomly choosing a date in the month
of August. What is the probability that she
chooses a two-digit number or a prime number?
Answers
The probability that Kate chooses a two-digit number or a prime number randomly from the month of August is 7/31.
What is probability?Probability of an event is the ratio of number of favorable outcome to the total number of outcome of that event.
Kate is randomly choosing a date in the month of August. This date must be a two-digit number or a prime number.
Total days in August month is 31.Prime number data in this month is 11(2,3,5,7,11,13,17,19,23,29,31)Two-digit number data in this month is 21(10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31).The two digit prime numbers are 7(11,13,17,19,23,29,31). Thus, the probability is,
[tex]P=\dfrac{7}{31}[/tex]
Hence, the probability that Kate chooses a two-digit number or a prime number randomly from the month of August is 7/31.
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Find the amount you would pay for a jacket that costs $52 that is advertised at 25% off.
Answers
Answer:
39
Step-by-step explanation:
First find the discount
52 * 25%
52 * .25
13
Subtract that from the original amount
52-13
39
The price is 39 dollars
Quadrilateral QRST is dilated by a factor of 2 with the center of dilation at the origin. What are the coordinates of quadrilateral Q'R'S'T'?
A) Q' (4, 4), R' (-4, 4), S' (-4, -4), T' (4, -4)
B) Q' (-1, 1), R' (1, 1), S' (1, -1), T' (-1, -1)
C) Q' (-4, 4), R' (4, 4), S' (4, -4), T' (-4, -4)
D) Q' (-3, 3), R' (3, 3), S' (3, -3), T' (-3, -3)
Answers
Answer:
C) Q' (-4, 4), R' (4, 4), S' (4, -4), T' (-4, -4)
Step-by-step explanation:
Original:
Q = (-2, 2)
R = (2, 2)
S = (2, -2)
T = (-2, -2)
After multiplying each coordinate by 2:
Q' = (-4, 4)
R' = (4, 4)
S' = (4, -4)
T' = (-4, -4)
Find the value of n.
Answers
Answer:
45°
Step-by-step explanation:
sum of exterior angles = 360
n+n+n+n+90+90=360
4n+180=360
4n=180n=45
URGENT PLEASE HELP !
Answers
Answer:
8/4 Square Inches
Step-by-step explanation:
I think so
Michelle is rolling two six-sided dice, numbered one through six. What is the probability that the sum of her rolls is 5?
Answers
Answer:
13.8888888889% or 0.1388888888889
Step-by-step explanation:
Place these 5 possible results of 6 over the total number of possible outcomes for rolling 2 fair 6-sided dice to obtain 5/(6×6) or 5/36 equal to 0.1388888888889 or 13.8888888889% Probability
:) :) :) :) :) :) :)
I need some help. i dont know what to do, and its very hard for my smol brain
Answers
Check the picture below.
[tex]\begin{cases} (12x)+(5x-10)+\theta =180\\ ~\hfill \theta +16x = 180 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{\Large 180}}{(12x)+(5x-10)+\theta}~~ = ~~\stackrel{\textit{\Large 180}}{\theta +16x}\implies 17x-10+\theta =\theta +16x \\\\\\ 17x-10=16x\implies 17x=16x+10\implies \boxed{x=10} \\\\[-0.35em] ~\dotfill\\\\ \theta +16x = 180\implies \theta +16(10)=180\implies \theta +160=180\implies \stackrel{\measuredangle C}{\theta} =20[/tex]
Over the next 3 days Mrs. Messer would like to write 27 thank you cards. How many cards will she need to write each day in order to finish in time?
Answers
Answer:
9 Cards
Step-by-step explanation:
9 Cards a day equals 27 cards in 3 days
Answer:
9 CARDS
Step-by-step explanation:
(9) ~\(-_-)/~
Write the equation for function g(x)
Answers
Answer:
g(x) = (x + 2)^2 + 1
Step-by-step explanation:
From the graph/image that you have provided said translated shift of
f(x) -> g(x)
f(x) = x^2 , g(x) = a(x -h)^2 +k
h is shift right/left
k is shift up/down.
It appears that the shift is left 2 and up 1.
h = -2 and k = 1
g(x) = (x - (-2))^2 +1
g(x) = (x + 2)^2 + 1
Find the following given f(x) = 10x- + 9.
a. f(4)
b. f(- 6)
c. f(0)
D. F(1/5)
Answers
Answer:
c
Step-by-step explanation:
c
The area of a rectangular pool is given by the expression, h^2+11h+28. Which of the following represents the length and width of the pool, in terms of h?
A) (h+2)(h+14)
B) (h+1)(h+28)
C) (h+4)(h+28)
Answers
I think of a number,divide it by 4 then subtract 3. Give your answer in algebraic notation.
Correct answer automatically gets brainliest :)
Answers
(*make sure to write the division in fraction form as shown for algebraic notation)
The diagram shows figures that are parallelograms and figures that are rectangles.
Select the four attributes that all parallelograms and all rectangles have in common.
Answers
Step-by-step explanation:
Venn diagram shows the figures that are parallelograms and the figures that are rectangles
Hope its help thanks
A shopkeeper sold 12 bags on the first day. The number became four times
every subsequent day. Find the total number of bags sold in seven days.
48
84
65,532
65,535
Answers
The total number of the bags sold by the shopkeeper will be 65532.
What is number series?The sequence formed by using the numbers is termed as the number series.So in this question from day one to day seven each day the sold items are multiplied by 4.
So the mathematical expression will be given as:
[tex]=(12\times 4^0)+(12\times 4^1)+(12\times 4^2)+(12\times 4^3)+(12\times 4^4)+(12\times 4^5)+(12\times 4^6)[/tex]
[tex]=12+48+192+768+3072+12288+49152\\\\=65532[/tex]
Hence the total number of the bags sold by the shopkeeper will be 65532.
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the length of the side sqaure A is 50% OF THE LENGTH OF THE SIDE SQUARE b
Answers
Let's say the side length of square A is x, which means the side length of square B is 2x.
Then, the area of square A can be written as , and the area of square B can be written as .
There's no diagram here with shaded region, so I'll just find the area of square A as a percentage of the area of square B:
= 1/4 = 25%
So, the answer is 25% (note this is the answer to the question: "express the area of square A as a percentage of the area of square B; there is no diagram showing me where the shaded area is, so I cannot answer the original question
How do we find coterminal angles for
degrees? Radians?
Answers
Answer:
To find coterminal angles, add or subtract 360 degrees of the terminal angle as many times possible.
To find radians, use this formula:
Degrees × π/180°
Coterminal angles point in the same exact direction.
In degree mode, you can add on 360 degrees to get a coterminal angle.
Example: 90 degrees is coterminal to 450 degrees because 90+360 = 450. Both angles 90 and 450 point directly north.
You can also subtract 360 from the angle to get a coterminal counterpart.
Example: Given the angle 700, it is coterminal to 340 since 700-360 = 340
This process of adding or subtracting 360 can be done as many times as you like.
------------------------------
For radian mode, you'll add or subtract 2pi radians to get a coterminal angle. This is because 2pi radians = 360 degrees by definition.
Examples:
pi is coterminal to 3pi because pi+2pi = 3pi, both point directly westpi/4 is coterminal to 9pi/4 because pi/4 + 2pi = pi/4 + 8pi/4 = 9pi/421pi/4 is coterminal to 13pi/4 because 21pi/4 - 2pi = 21pi/4 - 8pi/4 = 13pi/4which function corresponds to the graph below? help pleaseee!
Answers
Answer:
A
Step-by-step explanation:
It is A because the negative in front of the 4 shows the curve was REFLECTED over the x-axis. The +1/2 in the parenthesis with the x shows the curve was translated (shifted or slid) to the LEFT 1/2 unit and the +3 at the end of the equation shows the whole thing was translated/shifted/slid UP 3 units. These transformations all together make the equation in A match the curve given.
What can the read infer most likely happened to Jun Do's mother?
a. She was forced to become a singer.
b. She left because she was tired of living in the countryside.
She was taken away
without her consent.
d. She left because she no longer loved Jun Do's father.
C.
Answers
maria worked as a florist and worked 12 hours last week and earned $96 at that rate how much will she earn this weekend if she works 14 hours
Answers
Answer:
Maria earned 112 dollars
Step-by-step explanation:
divided 96 by 12 then once you have that, multiply your answer by 14
What is the exact value of x?
5 ⋅ 8^4x = 376
x=4log75.2/log8
x=4log8/log75.2
x=log75.2/4log8
x=log8/4log75.2
Answers
Answer:
[tex]x=\dfrac{\log(75.2)}{4\log(8)}[/tex]
Step-by-step explanation:
[tex]\begin{aligned}5 \cdot 8^{4x} & =376\\8^{4x} & = \dfrac{376}{5}\\8^{4x} & =75.2\end{aligned}[/tex]
Taking logs of both sides:
[tex]\implies \log(8)^{4x}=\log(75.2)[/tex]
Using the power log rule [tex]\log_a(x)^n=n\log_a(x)[/tex] :
[tex]\implies 4x\log(8)=\log(75.2)[/tex]
Solving for x:
[tex]\begin{aligned}\implies 4x\log(8) & =\log(75.2)\\\\ 4x & =\dfrac{\log(75.2)}{\log(8)}\\\\x & =\dfrac{\log(75.2)}{4\log(8)}\\\end{aligned}[/tex]
Which fraction below represents a repeating decimal?
A.1/2
B.1/5
C.1/8
D.1/9
Answers
Answer:
1/9
Step-by-step explanation:
lol
Answer:
1/9
Step-by-step explanation:
Your welcome
How do you find A to C?
Answers
Answer:
7√3
Step-by-step explanation:
Pythagorean Theorem
a² + b² = c²
7² + b² = 14²
b² = 14² - 7²
b² = 196 - 49
b = √147
7√3
BRAINLIEST please if this helped!Answer:
[tex]AC = 12.12[/tex]
Step-by-step explanation:
Step 1: Determine side AC
[tex]Pythagorean\ theorem[/tex] → [tex]a^2 + b^2 = c^2[/tex]
[tex](AC)^2 + (CB)^2 = (AB)^2[/tex]
[tex](AC)^2 + (7)^2 = (14)^2[/tex]
[tex](AC)^2 + 49 = 196[/tex]
Step 2: Subtract 49 from both sides
[tex](AC)^2 + 49 - 49 = 196- 49[/tex]
[tex](AC)^2 = 147[/tex]
Step 3: Square root both sides
[tex]\sqrt{(AC)^2} = \sqrt{147}[/tex]
[tex]AC = 12.12[/tex]
Answer: [tex]AC = 12.12[/tex]
3cot^(2 )x-1=0
Pls Help
Answers
Answer:
[tex]x=\frac{\pi }{6} ,\frac{7\pi }{6}[/tex]
Step-by-step explanation:
[tex]3*cot^2x-1=0\\\\3*cot^2x=1\\\\cot^2x=\frac{1}{3} \\\\cot(x)=\sqrt{\frac{1}{3} } \\\\cot(x)=\frac{1}{\sqrt{3} } \\\\\frac{1}{tan(x)}=\frac{1}{\sqrt{3} } \\\\tan(x)=\sqrt{3} \\[/tex]
x=tan^-1([tex]\sqrt{3}[/tex])
It has to be in Quadrant 1 [tex]\frac{+}{+} =+[/tex] or 3 [tex]\frac{-}{-}=+[/tex] for positive.
[tex]x=\frac{\pi }{6} ,\frac{7\pi }{6}[/tex]
Unless that incorrect due to tan(x) range is [tex]-\frac{\pi }{2} \leq x\leq \frac{\pi }{2}[/tex]. Then the only answer is [tex]x=\frac{\pi }{6}[/tex]
What is the value of this expression? [(9+5) x (4-2)] X (5-1) A 108 B112 C148 D336
Answers
Answer:
B
Step-by-step explanation:
Scarlett is designing a package for a candy her company makes. She has cut several cardboard equilateral triangles, squares, rectangles, and regular pentagons to try out her ideas for the package. Which 3-D figure and combination of shapes can Scarlett use?
Equilateral triangle prism with two equilateral triangles and three rectangles
Pentagonal prism with one pentagon and five rectangles
Rectangular prism with four rectangles
Square prism with four squares
Answers
To create a 3D figure, Scarlett can use two equilateral triangles and three rectangles, which leads to an equilateral triangle prism.
What is a prism?This is a solid or 3D figure that has two faces made up of polygons.
How to create different prisms?Square prism: Six squares.Rectangular prism: Two squares and four rectangles.Pentagonal prism: Two pentagons and five rectangles.Equilteral triangle prism: Two equilateral triangles and three rectangles.Learn more about geometrical figures in: https://brainly.com/question/2778048
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Answer: The answer is Equilateral triangle prism with two equilateral triangles and three rectangles
Step-by-step explanation:
I took the test
Oh and I am good like that.
REASONING The table shows the weights (in pounds) and the prescribed dosages (in milligrams) of medicine for six patients.
Weight (lb), x Dosage (mg), y
94 72
119 90
135 103
150 115
185 140
202 156
a. Find an equation of the line of best fit. Round the slope and the $y$ -intercept to the nearest tenth, if necessary.
y=
Identify the correlation coefficient. Round your answer to the nearest thousandths.
Interpret the correlation coefficient.
b. Interpret the slope of the line of best fit.
c. A patient who weighs 140 pounds is prescribed 135 milligrams of medicine. How does this affect the line of best fit? Explain.
Answers
The equation of the line of best fit in the table given regarding the weights will be y = 0.77x - 1.1
How to illustrate the table?From the information given, the equation of the line of best fit in the table given regarding the weights is given and the correlation coefficient is 0.99.
The relationship is strongly positive as it's close to 1. The slope of the best fit gives the change in dosage for for an increase in the weight of the patient.
When a patient who weighs 140 pounds is prescribed 135 milligrams of medicine, it affects the line of best fit as it increases the intercept but decreases the slope.
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A room is 3m high and has a volume of 60m3 calculate area of floor of the room
Answers
[tex]height = 3m[/tex]
[tex]volume = 60 {m}^{3} [/tex]
to find:the area of the room.
solution:[tex]l \times w \times h = 60[/tex]
[tex]l \times w \times 3 = 60[/tex]
[tex]l \times w = 20 {m}^{2} [/tex]
therefore, the area of the room is 20 square meters.
What are the solutions to the quadratic equation 4x2 = 64?
x = −16 and x = 16
x = −8 and x = 8
x = −4 and x = 4
x = −2 and x = 2
Answers
Answer:
x = −4 and x = 4
Step-by-step explanation:
if you do divide its all the opposite 8÷64=8 4×2=8 8×32=4 or 8÷-2=-4
A table has a length of 9 and a width of 4. What is the perimeter?
Answers
Answer:
26
Step-by-step explanation:
Assume the table is a rectangle.
A rectangle has 2 sides with the length of the length and 2 sides with the length of the width.
perimeter = sum of the lengths of the sides
perimeter = 9 + 9 + 4 + 4
perimeter = 26
Answer:
26
Step-by-step explanation:
Assuming the table is rectangular...
Rectangles = 4 sides
2 sides = 9
Other 2 sides = 4
Perimeter = adding up the sides
9+9+4+4=26
Ax+By=C
Use integers for A,B, and C
y+5=4(x-2)
Answers
y + 5 = 4x - 8
y = 4x - 3
-4x + y = - 3
-1(-4x + y = - 3)
4x - y = 3