Answers
[tex]\text{Given that,}\\\\2(x^2+y^2)^2 = 25 (x^2-y^2)\\\\\implies 2\dfrac{d}{dx} (x^2 +y^2)^2 = 25 \dfrac{d}{dx} (x^2 -y^2)\\\\\implies 2 \cdot 2(x^2 +y^2) \dfrac{d}{dx}(x^2 +y^2) = 25\left[2x - 2y \dfrac{dy}{dx} \right]\\\\\implies (4x^2 +4y^2)\left(2x + 2y\dfrac{dy}{dx}\right) = 50x - 50y\dfrac{dy}{dx}\\\\\\\implies 8x^3+8x^2y \dfrac{dy}{dx} + 8xy^2 +8y^3\dfrac{dy}{dx} = 50x -50y \dfrac{dy}{dx}\\\\\\\implies 8x^2y \dfrac{dy}{dx} + 8y^3\dfrac{dy}{dx}+50y \dfrac{dy}{dx} = 50x -8x^3 -8xy^2\\\\[/tex]
[tex]\implies (8x^2y +8y^3 + 50y)\dfrac{dy}{dx} =50x -8x^3 -8xy^2\\\\\implies \dfrac{dy}{dx} = \dfrac{50x -8x^3 -8xy^2}{8x^2y+8y^3+50y}\\\\\implies \dfrac{dy}{dx}= \dfrac{25x-4x^3-4xy^2}{4x^2y+4y^3+25y}\\\\\\\implies \dfrac{dy}{dx} = \dfrac{x(25-4x^2-4y^2)}{y(4x^2 +4y^2 +25)}\\\\\\\text{Slope at}~~ (-3,-1)\\\\m=\dfrac{dy}{dx} = \dfrac{-3[25-4(-3)^2-4(-1)^2]}{(-1)[4(-3)^2 + 4(-1)^2+25]} = -\dfrac{45}{65} = -\dfrac 9{13}[/tex]
[tex]\text{Equation with given points,}\\\\y+1 = -\dfrac9{13}(x+3)\\\\\implies y = -\dfrac 9{13} x - \dfrac {27}{13} -1\\\\\implies y= -\dfrac 9{13} x - \dfrac{40}{13}\\\\\text{Hence the equation of this tangent line is now in a form of y= mx+b,}\\\\\text{where}~ m = -\dfrac 9{13}~ \text{and}~ b = -\dfrac{40}3[/tex]
Related Questions
Help pls!!!! Help PLs Help pls
Answers
Answer: mmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm
Step-by-step explanation:
Please Like!
HELP I'LL GIVE BRAINLY
Answers
Answer:
code is 4163
Step-by-step explanation:
x-35=27;x=64
-96=-8x;x=12
6=x/4 +2;x=16
76-3x=-29; x=31
code is 4163
Answer:
at least 8
Step-by-step explanation:
im from k12
112
121
124
137
147
156
173
189
Find the median revenue.
Answers
Answer:
142
Step-by-step explanation:
Median is the MID Number
Yoni has a ribbon that measures 5/3 yards. She wants to cut it into 3 equal pieces. What is the length of each piece of ribbon? 5\8 yards 5/6 yards 5/9 yards 5/3 yards
Answers
Answer:
Step-by-step explanation:
[tex]\frac{1}{3} * \frac{5}{3} = \frac{1 * 5}{3*3} = \frac{5}{9}[/tex]
The answer is 5/9 as you can see. 5/9 = 20 inches each.
1 yard = 36 inches
(5/9 * 36) = 5 * 4 = 20 inches.
Answer:
5/9
Step-by-step explanation:
I have a trick id like to teach here. Whenever you have a fraction being divided by a whole number, you can multiply the denominator by the diviser
So what I did was multiply the 3 by the diviser(3) and got 9
This left me with 5/9
lcm of 5,12 and 20????,
Answers
Answer: 60
Step-by-step explanation:
solve the inequality z + 9 > 6 z > ?
( Equations and Inequalities )
Answers
Answer:
You have to switch sides so the answer is x<z+9
Step-by-step explanation:
The table shows the relationship between r and s, where s is the independent variable.
Which equation represents the relationship between r and s?
Answers
Answer:
burrito
Step-by-step explanation:
burrito
(2,170), (5,365) slope
Answers
Answer:
To find the slope given two points, use the slope formula. The slope formula is Y2-Y1/X2-X1. Substitute in the given points and solve.
365-170/5-2
195/3
65
The slope of the two points is 65.
Hope this helps! :)
In two or more complete sentences, describe the transformation(s) that take place on the parent function f(x) = 3x to obtain the graph of f(x) = 3-x + 1 - 5.
Answers
Answer:
Logarithmic functions are the inverses of exponential functions.The logarithmic function y=loga(x) is called the logarithmic function with base a .
When a constant c is added to the input of the parent function f(x)=loga(x), the result is a horizontal shift c units in the opposite direction of the sign on c. Our function is shifted 3 units to the right.
It is shifted 2 units vertical.(2 units down).
Answer:
Logarithmic functions are the inverses of exponential functions.The logarithmic function y=loga(x) is called the logarithmic function with base a .
When a constant c is added to the input of the parent function f(x)=loga(x), the result is a horizontal shift c units in the opposite direction of the sign on c. Our function is shifted 3 units to the right.
It is shifted 2 units vertical.(2 units down).
Step-by-step explanation:
I need help with this, i did part of it but i'm desperate
Answers
Answer:
Let's add more steps.
step 6: angle AEB measures 360 - 90 -90 - 70 - 39 = 71° Reason, AECF is a quadrangonal and three of its angle measures 90, 90, and (70+39)
step 7: angles AEB and ABE are congruent: reason triangle ABE is isosceles since AE is conruent to AB
step 8 Angle BAE measures 180 -71-71 = 38°: by difference from the sum of the internal angles.
step 9: Angle BAD measures 90 - BAE = 90 - 38 = 52° Reason angles BAD and BAE are complementary.
QED
What is the slope and y-intercept that represents this table?
Answers
Answer:
[tex]m=-2\ 000; q=17\ 000[/tex]
Step-by-step explanation:
First of all, whoever formatted that table is a criminal.
Now, slope first, it's the easiest: the slope in a table like that is the difference between two consecutive position: ie [tex]13\ 000 - 15\ 000[/tex] or [tex]11\ 000-13\ 000[/tex], being careful of subtracting the higher position (not value!) minus the lower, or right minus left. Your slope thus is [tex]-2 \ 000[/tex]. Intercept is found in two ways. One is writing the line in point slope form based on any two values and the slope we found, or since we're jumping integer to integer, you can look at the table in reverse and notice that if you go backwards (ie from 4 to 3 to 2 to 1) the value is increasing by 2000 every time. The intercept [tex]q[/tex]will be the value at 0, or 17 000
Which item produces the magnetic field in the electromagnet?
A-paperclips
B- a switch
C-paint brushes
D- a magnet
Answers
Answer:
Its ethier a switch or magnet
can someone help me with this i’ll give you 25 points
Answers
Answer:
Um.... Wouldn't angle 1 just be 180-17 which is 163. Angle 3 would be equal to angle 1 so also 163. Angle 4 and angle 2 are equal to 17.
Step-by-step explanation:
Answer:
angle1 = 163°
angle2 = given in diagram
angle 3 = alternating angle 1, so 163°
angle 4 = alternating angle 2, so 17°
Step-by-step explanation:
noticing that the two lines intercept each other at the centre, making angles going around that interception point add up to 360° (you can use this information to check the answers).
an angle on a straight line is always 180°, so given that angle2 is 17°, you can already do 180 - 17 to get an easy answer to angle 1 and 3.
Quadratic functions 30pt
Answers
Answer:
y= -x -3
Step-by-step explanation:
A perpendicular bisector of a line cuts through the line at its midpoint perpendicularly (90°).
Let's find the slope of the line segment.
\boxed{ slope = \frac{y _{1} - y_2 }{x_1 - x_2} }slope=x1−x2y1−y2
Slope of line segment
= \frac{4 - ( - 8)}{5 - ( - 7)}=5−(−7)4−(−8)
= \frac{4 + 8}{5 + 7}=5+74+8
= \frac{12}{12}=1212
= 1
The product of the slopes of 2 perpendicular lines is -1.
Let the slope of the perpendicular bisector be m.
m(1)= -1
m= -1
y= -x +c
To find the value of c, substitute a pair of coordinates in which the line passes through into the above equation.
Since the perpendicular bisector cuts through the midpoint of the line segment, let's find the coordinates of this midpoint.
\boxed{midpoint = ( \frac{x _{1} + x _2}{2} , \frac{y_1 + y_2}{2} )}midpoint=(2x1+x2,2y1+y2)
Midpoint of line segment
= ( \frac{5 - 7}{2} , \frac{4 - 8}{2} )=(25−7,24−8)
= ( \frac{ - 2}{2} , \frac{ - 4}{2} )=(2−2,2−4)
= (-1, -2)
y= -x +c
When x= -1, y= -2,
-2= -(-1) +c
-2= 1 +c
c= -2 -1
c= -3
Thus, the equation of the perpendicular bisector is y= -x -3.
answer this pleaseEeeeeeee
Answers
Answer:
no solution ?
Step-by-step explanation:
Answer:
Infinitely many solutions because the system of equations are the exact same.
please help ill mark brainliest
Answers
Answer:
x=3
Step-by-step explanation:
6(x+5)=4(x+9)
6x+30=4x+36
2x+30=36
2x=6
x=3
Put these fractions in order from least to greatest:
Answers
Answer:
1/4, 3/8, 2/3
Step-by-step explanation:
3/8 is more than 25% (1/4) but is less than 66% (2/3) making the order 1/4 3/8 2/3.
Answer:
The answer is the 3rd option. (1/4, 3/8, 2/3)
Step-by-step explanation:
All u have to do is find a common denominator for all 3 fractions.
The common denominator in this problem would be 24
So lets convert all the fractions with a denominator of 24.
1/4 = 6/24
3/8 = 9/24
2/3 = 16/24
Since we now converted the fractions with a common denominator, we can deduce the order from least to greatest.
6/24, 9/24, then 16/24
In other words, the answer is the 3rd option. (1/4, 2/8, and 2/4)
Hope this helps! :0
૮ ・ﻌ・ა
Find x given the prism has a surface area of 286 in². Explain your thoughts
Answers
Answer:
h
=
3
r
=
4
h
=
2
r
=
6
h
=
4
l
=
4
w
=
4
Step-by-step explanation:
Rewrite the expression with rational exponents.
Answers
Answer:
([tex]\sqrt[5]{x}[/tex])^7
Step-by-step explanation:
to cancel out the radical you do the exponent inside and divide it by the out side one so it will be 7/5 so make it x to the expontent of 7/5 and to do rational exponets it will be (^5radicalx)^7
i was doing this task in math and I came across this: x-12x=0.88x . can someone plz explain why is this equal to this? I understand it's simplified, but how?
Answers
1x-12x=0.88x
1x-12x=0.88x
11x=0.88x
-11x=0.88x-0.88x
-11.88x=0x
-11.88x=0
Isolate x
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Use the quadratic formula to solve the equation.
X^2 - 7x – 6 = 0
Answers
Step-by-step explanation:
[tex]x = \frac{ - b + - \sqrt{ {b}^{2} - 4ac} }{2a} [/tex]
a=1.
b=-7
c=-6
x=
[tex] \frac{ - ( - 7) + \sqrt{ (- 7)^{2} - 4(1)( - 6)} }{2(1)} [/tex]
OR
[tex] \frac{ - ( - 7) - \sqrt{ (- 7) ^{2} - 4(1)( - 6)} }{2(1)} [/tex]
Therefore x= 7,772
OR
x=-0,772
What do we call these types of fractions?
1/2 and 5/10
Answers
Answer:
Proper Fractions.
Step-by-step explanation:
These are Proper Fractions because the numerator (1 and 5) is lower than the denominator (5 and 10).
Can someone help me with his I will mark u brilliant
Answers
Answer: 1260 books
Step-by-step explanation:
2/5=0.4
19000x0.4=7600
12500x0.4=5000
7600+5000=12600
1/10=0.1
12600x0.1 = 1260
/Answer:
1,260 books (or C)
Step-by-step explanation:
1. 2/5 of fiction (12,500) are out, so 5,000 are out
2. 2/5 of non-fiction (19,000) are out, so 7,600 are out
3. Total books checked out are 12,600
4. 1/10 of checked out books are due this week, so 1,260 books (10%)
help please asappppppppp
Answers
Answer:
First Equation: 6a-23
Second Equation: 5a-20
Step-by-step explanation:
So, I think you want me to answer part 2...
For the first equation, we can see that the denominator stays the exact same, meaning the numerator will also not change.
For the second equation, we can see the denominator changed from a-3 to 5a-15. The denominator was simply multiplied by 5. Since the denominator was multiplied by five we must multiply the numerator by five as well.
5(a-4)
5a-20
Hope this helps :)
The amount of money, y, pizzeria J makes by
selling x pizzas can be modeled by the equation
y = 14x. The relationship of the amount of money
pizzeria W makes is shown in the following graph.
Which pizzeria makes more money per pizza?
Answers
Answer:
Pizzeria J
Step-by-step explanation:
Pizzeria J makes
y = 14x
Let x = 1, for 1 pizza. Then,
y = 14 × 1
y = 14
At pizzeria J, 1 pizza costs $14.
In the equation y = 14x, the slope, 14, is the cost per pizza.
Now we find the slope of the graph for pizzeria W.
The x-axis is the number of pizzas.
For x = 1, y = 11.
The slope is 11, so the price per pizza is $11.
Answer: Pizzeria J
5.4-0.25 I'm so confused
Answers
Answer:
5.15
Step-by-step explanation:
Answer:
5.15
Step-by-step explanation:
5.4 = 5.40
5.40
- 0.25
= 5.15
because 0.40 - 0.25 = 0.15
Okie help help math math math math
Answers
Answer: 33
Step-by-step explanation: In the problem, you are given the figure with the following:
2x+3 and 3x+12
Method: Lets set this into an equation. Remember that straight lines add up to 180°.
2x+3+3x+12=180° Combine like terms.
5x+15=180°
5x=165°
x=33°
You can always plug in 33° in the expression that was set to make sure it does give you 180°.
Hope this helps.
Answer:
33
Step-by-step explanation:
A dolphin dives down into the ocean and resurfaces along a path that is modeled by x^2- 8x + 4y = 0, where the distances are in feet. How many feet is the dolphin from its starting point along the
water's surface?
8 feet
6 feet
4 feet
O feet
please guys i need help
Answers
Answer:
6ft
Step-by-step explanation:
The Dolphin is 8 feet apart from starting point along the water surface.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
Equation: x²- 8x + 4y = 0
Now, solving for variable 'y' we get
y= (8x - x²) /4
y= 2x - x²/4
So, the Dolphin is 8 feet apart from starting point along the water surface.
Learn more about Equation here:
https://brainly.com/question/29657983
#SPJ2
The quotient of a number and negative eight is five-eighths. Find the number.
Answers
Answer:
-64/5
Step-by-step explanation:
Basically, the word "quotient" means the answer to a division problem. Therefore, its a division problem, so you have to work backwards with multiplication. -8 times a number is 5/8, so the other number is going to be negative.
The number is -64/5
Answer:
n = -5
Step-by-step explanation:
Form this quotient, representing the number by n: n / (-8) = 5/8.
Solve this equation for n by multiplying both sides by 8: -n = 5. Then n = -5
A shuffled deck of cards is placed facedown on the table. It contains 7
hearts, 8 diamonds, 6 clubs and 3 spades. What is the probability that the top two cards are one of the clubs followed by one of the heartS?
Answers
Answer:
3/23 x 5/23 = 15/529 = 2.84%
Answer:
First find the total of 7 hearts, 8 diamonds, 6 clubs and 6 spades which is 24 altogether. Therefore we are talking about 4 types of cards. I therefore think the probability will be 2/24
