Find the equation of the tangent of x^2- xy + y^2 =7 at (-1, 2)
Answers
Answer:
It is 3y = 4x + 10
Step-by-step explanation:
Let's first get the slope of the curve.
[ slope is the derivative of the equation ]
[tex] {x}^{2} - xy + {y}^{2} = 7[/tex]
introduce dy/dx :
[tex] \frac{d}{dx} ( {x}^{2} - xy + {y}^{2} ) = \frac{d}{dx} (7) \\ \\ 2x - (y + \frac{dy}{dx} ) + 2y \frac{dy}{dx} = 0[/tex]
make dy/dx the subject:
[tex]2x - y - \frac{dy}{dx} + 2y \frac{dy}{dx} = 0 \\ \\ 2y \frac{dy}{dx} - \frac{dy}{dx} = y - 2x \\ \\ \frac{dy}{dx} (2y - 1) = y - 2x \\ \\ \frac{dy}{dx} = \frac{y - 2x}{2y - 1} [/tex]
At point (-1, 2):
[tex] \frac{dy}{dx} = \frac{2 - 2( - 1)}{2(2) - 1} \\ \\ slope = \frac{4}{3} [/tex]
but a tangent has the same slope as the curve:
[tex]y = mx + c[/tex]
m is the slope
c is the y-intercept
At (-1, 2):
[tex]2 = ( - 1 \times \frac{4}{3} ) + c \\ \\ c = 2 + \frac{4}{3} \\ \\ c = \frac{10}{3} [/tex]
equation:
[tex]y = \frac{4}{3} x + \frac{10}{3} \\ \\ { \boxed{3y = 4x + 10}}[/tex]
Answer:
Step-by-step explanation:
Here is an other way:
z=f(x,y)=x²-xy+y²-7=0
[tex]\dfrac{\partial f(x,y)}{\partial x} =2x-y\\\\\dfrac{\partial f(x,y)}{\partial y} =-x+2y\\\\\\\dfrac{dy}{dx} =-\dfrac{\dfrac{\partial f(x,y)}{\partial x} }{\dfrac{\partial f(x,y)}{\partial y}} =-\dfrac{2x-y}{-x+2y} \\\\(-1;2)\\Slope=-\dfrac{2*(-1)-2}{1+2*2} =\dfrac{4}{5} \\\\y-2=\frac{4}{5} (x+1)\\\\\\\boxed{y=\dfrac{4x}{5} +\dfrac{14}{5} }[/tex]
Related Questions
m∠ABC = (9x + 4)° and m∠DEF = (13x − 22)°. If ∠ABC and ∠DEF are supplementary, what is the measure of each angle?
Answers
Answer:
∠ABC measures 85° and ∠DEF measures 95°.
Step-by-step explanation:
We are given that ∠ABC and ∠DEF are supplementary. Then by definition:
[tex]\displaystyle m\angle ABC + m\angle DE F = 180^\circ[/tex]
Substitute:
[tex]\displaystyle \left(9x+4\right) + \left(13x-22\right) = 180[/tex]
Solve for x. Combine like terms:
[tex]22x -18 = 180[/tex]
Add:
[tex]\displaystyle 22x = 198[/tex]
And divide. Hence:
[tex]\displaystyle x = 9[/tex]
To find the measure of ∠ABC, substitute and evaluate:
[tex]\displaystyle \begin{aligned}m\angle ABC &= 9x + 4 \\ &= 9(9) + 4 \\ &= 81 + 4 \\ &= 85^\circ \end{aligned}[/tex]
And:
[tex]\displaystyle \begin{aligned}m\ngle DE F &= 13x - 22 \\ &= 13(9) - 22 \\ &= 117-22 \\&= 95^\circ \end{aligned}[/tex]
In conclusion, ∠ABC measures 85° and ∠DEF measures 95°.
50 yards of fabric for 18 flags Unit rate
Answers
0.36 ( hope this helps :)
2.6 a simplified fraction and the 6 is a repeating decimal
Answers
If your car gets 34 miles per gallon, how much does it cost to drive 420 miles when gasoline costs $3.30 per gallon?
Answers
Answer:
$40.76, if rounded then $40.80.
Step-by-step explanation:
you do 420 times 3.30 divided by 34
Solve 6x + ( 14x - 5 ) + ( 17 - 3x ) , - ( 2 - x ) -3 ( 6 + 8x ) -12, ( 4x - 9 ) + 8 ( 2x + 3 ) -7x
Answers
Answer:
Step-by-step explanation:
6x + ( 14x - 5 ) + ( 17 - 3x )
= 17x + 12
- ( 2 - x ) -3 ( 6 + 8x ) -12,
= -23x - 32
( 4x - 9 ) + 8 ( 2x + 3 ) -7x
= 13x +15
Evaluate the expression.
5 x -3 + 2
Answers
Answer:
5x-1
Step-by-step explanation:
solution
5x-3+2
or, 5x-1
More help Pls (am also giving away points).
Answers
Answer:
But where is the question???????
What effect does replacing x with x - 4 have on the graph for the functionſ (x)?
f(x) = |x – 6| + 2
Answers
Step-by-step explanation:
The graph is shifted 4 units left.
The graph is shifted 4 units right.
The graph is shifted 4 units up.
The graph is shifted 4 units down.
is the expression 5+3x/2 equal to the expression 4x
Answers
Answer:
No
Step-by-step explanation:
[5+3x] is an expression that cannot be added because 5 is a natural interger but 3x is an unknown
and therefore it cannot be divided by 2 to get 4
Better example :
if the question will give 4x , then
it should be [5x+3x]/2 = 8x/2 = 4x
it's obvious from the example I gave that 8x can be divided by 2 to give 4x
499 rounded to the nearest ten is
510
500
490
Answers
Answer:
500
Step-by-step explanation:
Since we are rounding to the tens place, that is the second value in the number 499. Remember these details when rounding;
4 and below round down5 and above round upSince we have a 9, we round up get and 500.
Best of Luck!
Answer:
499 rounded to the nearest tenth is 500.
Step-by-step explanation:
499 rounded to the nearest tenth is 500 because, every tenths place is + 10
the closest tenth 499 is closest to would be 500.
Hope this helped :)
the ratio of 3 less than k to 2 more than k
Answers
We will find that the ratio of 3 less than k to 2 more than k is:
(k - 3):(k + 2)
The ratio between two numbers A and B can be written as:
A:B
This is the ratio of A to B
and
B:A
Is the ratio of B to A.
Then for the ratio of 3 less than k to 2 more than k we have:
"3 less than k" is: k - 3
"2 more than k" is: k+ 2
Then the ratio is:
(k - 3):(k + 2)
if you want to learn more, you can read:
https://brainly.com/question/13419413
Find the midpoint of the segment with the given endpoints.
(-10.8) and (2.2)
Answers
Answer:
(-4,5)
Step-by-step explanation:
To find the x coordinate of the midpoint, add the x coordinate of the endpoints and divide by 2
(-10 +2)/2 = -8/2 = -4
To find the y coordinate of the midpoint, add the y coordinate of the endpoints and divide by 2
(8 +2)/2 = 10/2 = 5
(-4,5)
Answer:
(-4 , 5)
Step-by-step explanation:
(x₁ , y₁) = (-10 , 8) & (x₂ , y₂) = (2 , 2)
[tex]Midpoint = (\dfrac{x_{1}+x_{2}}{2},\dfrac{y_{1}+y_{2}}{2})\\\\[/tex]
[tex]=(\dfrac{-10+2}{2},\dfrac{8+2}{2})\\\\=(\dfrac{-8}{2},\dfrac{10}{2})\\\\=(-4 , 5)[/tex]
Seven of the algebra classes at a school have 23 students each. The eighth class has 25
students. What is the total number of students?
Answers
Answer: 186 students
Step-by-step explanation:
7x23+25= 186
It is given that the gradient of a straight line which passes through M(h,3) and N(-2,-9) is 2, calculate the value of h.
Answers
Answer:
h = 4
Step-by-step explanation:
Calculate the slope m using the slope formula and equate to 2
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = M (h, 3 ) and (x₂, y₂ ) = N (- 2, - 9 )
m = [tex]\frac{-9-3}{-2-h}[/tex] = [tex]\frac{-12}{-2-h}[/tex] , then
[tex]\frac{-12}{-2-h}[/tex] = 2 ( multiply both sides by - 2 - h )
2(- 2 - h) = - 12 ( divide both sides by 2 )
- 2 - h = - 6 ( add 2 to both sides )
- h = - 4 ( multiply both sides by - 1 )
h = 4
Sum of the maximum and minimum values of y=2cos^2 x + 3sin^2 x + 5
Answers
To begin with, we can simplify y using the Pythagorean identity:
y = 2 cos²(x) + 3 sin²(x) + 5
y = 2 (cos²(x) + sin²(x)) + sin²(x) + 5
y = 2 + sin²(x) + 5
y = sin²(x) + 7
Next, we can further rewrite this using the half angle identity for sine:
y = (1 - cos(2x))/2 + 7
y = 15/2 - 1/2 cos(2x)
Now, since cos(x) is bounded between -1 and 1, we have
max(y) = 15/2 - 1/2×(-1) = 15/2 + 1/2 = 8
and
min(y) = 15/2 - 1/2×1 = 15/2 - 1/2 = 7
Then the sum of the maximum and minimum is 8 + 7 = 15.
help whhhahahahaha Helpppppppp
Answers
Answer:
320/420 = 4/3
Step-by-step explanation:
4/7= x /560
Cross multiply
7x = 2240
Divide by 7:
x=320
The school has 320 boys and 240 girls
I hope this helps u:)
Answer:
Problem(1): [tex]21[/tex]
Problem(2): Side length = [tex]\frac{1}{4}[/tex] Area = [tex]\frac{1}{16}[/tex]
Problem(3): Boys = [tex]320[/tex] Girls = [tex]240[/tex]
Step-by-step explanation:
(Notes steps are cut from this answer so that it isn't too long)
1. Problem (1)
One is given the following information:
[tex]x+\frac{1}{x}=5[/tex][tex](x-\frac{1}{x})^2[/tex]The most logical first step is to solve for the value of (x). One can solve for the numerical value of (x) with the first equation.
[tex]x+\frac{1}{x}=5[/tex]
Multiply the entire equation by (x),
[tex]x^2+1=5x[/tex]
Inverse operations put the equation in the general format of a quadratic equation. The general format of a quadratic equation is as follows,
[tex]ax^2+bx+c=0[/tex]
Put the given equation in this format,
[tex]x^2-5x+1=0[/tex]
Now use the quadratic formula to solve for the value of (x). The quadratic formula uses the coefficients of the terms in a quadratic equation to find the roots of the equation. The quadratic formula is as follows,
[tex]\frac{-b(+-)\sqrt{b^2-4ac}}{2a}[/tex]
Use the coefficients of the terms in the given quadratic equation in the formal, then simplify to solve for solutions of the given equation,
[tex]\frac{-(-5)(+-)\sqrt{(-5)^2-4(1)(1)}}{2(1)}[/tex]
Simplify,
[tex]\frac{-(-5)(+-)\sqrt{(-5)^2-4(1)(1)}}{2(1)}[/tex]
[tex]\frac{5(+-)\sqrt{21}}{2}[/tex]
Now substitute these values into the equation and simplify, even though there are two values of (x), there will only be one solution,
[tex]((\frac{5+\sqrt{21}}{2}-\frac{1}{\frac{5+\sqrt{21}}{2}})^2[/tex] [tex]((\frac{5-\sqrt{21}}{2}-\frac{1}{\frac{5-\sqrt{21}}{2}})^2[/tex]
[tex](\frac{5+\sqrt{21}}{2}-\frac{2}{5+\sqrt{21}})^2[/tex] [tex](\frac{5-\sqrt{21}}{2}-\frac{2}{5-\sqrt{21}})^2[/tex]
Convert to a common denominator,
[tex](\frac{5+\sqrt{21}}{2}*\frac{5+\sqrt{21}}{5+\sqrt{21}}-\frac{2}{5+\sqrt{21}}*\frac{2}{2})^2[/tex] [tex](\frac{5-\sqrt{21}}{2}*\frac{5-\sqrt{21}}{5-\sqrt{21}}-\frac{2}{5-\sqrt{21}}*\frac{2}{2})^2[/tex]
[tex](\frac{(5+\sqrt{21})^2-4}{2(5+\sqrt{21})})^2[/tex] [tex](\frac{(5-\sqrt{21})^2-4}{2(5-\sqrt{21})})^2[/tex]
Simplify,
[tex](\frac{25+10\sqrt{21}+21-4}{10+2\sqrt{21}})^2[/tex] [tex](\frac{25-10\sqrt{21}+21-4}{10-2\sqrt{21}})^2[/tex]
[tex](\frac{42+10\sqrt{21}}{10+2\sqrt{21}})^2[/tex] [tex](\frac{42-10\sqrt{21}}{10-2\sqrt{21}})^2[/tex]
[tex]\frac{1764+840\sqrt{21}+2100}{100+40\sqrt{21}+84}[/tex] [tex]\frac{1764-840\sqrt{21}+2100}{100-40\sqrt{21}+84}[/tex]
[tex]\frac{3864+840\sqrt{21}}{184+40\sqrt{21}}[/tex] [tex]\frac{3864-840\sqrt{21}}{184-40\sqrt{21}}[/tex]
[tex]21[/tex]
2. Problem (2)
All four sides of a square are congruent (have the same measure), thus dividing the perimeter of a square by (4) will yield the side length of the square,
[tex]Perimeter\ of\ the\ square: 4\\Side\ length: \frac{1}{4}[/tex]
The area is the two-dimensional space that a figure takes up, in the case of a square, the area is the side length times itself:
[tex]A=(\frac{1}{4})^2=\frac{1}{16}[/tex]
3. Problem (3)
Let (x) represent the amount by which the ratio of boys to girls was scaled down. Assuming that these are the only two genders in the school, one can state that the sum ratio coefficients times the scaling value for both boys and girls, will equal the total number of people in the school. Thus, one can form the following equation and solve it with inverse operations and simplification,
[tex]boys + girl = total\ students\\4x + 3x = 560\\7x = 560\\x = 80[/tex]
Now substitute this into the expression for the two genders in this scenario, respectively, to solve for the actual number of students of that gender,
Boys, Girls,
[tex]4(x)[/tex] [tex]3(x)[/tex]
[tex]4(80)[/tex] [tex]3(80)[/tex]
[tex]320[/tex] [tex]240[/tex]
Is the expression 2•4 equal to the expression 8x? Explain your answer
Answers
9514 1404 393
Answer:
no
Step-by-step explanation:
The expression 2·4 has the value 8.
The expression 8x has the value 8x, which is only equal to 8 when x=1. In general, x may have any value, so the expressions are not equal.
the round trip distance between City X and City Y is 647 miles. A national park is between City X and City Y, and is 27 miles from City X. Find the round trip distance between the national park and city Y. Justify your answer.
Answers
The round trip distance between the national park and city Y is 593 miles.
Given:
Round trip distance from City X and City Y = 647 milesDistance between City X and national park = 27 milesTo find :
The round trip distance between the national park and city Y
Solution:
According to the question, the round trip distance between City X and City Y is 647 miles.
Let the distance from City X to City Y = d
Let the distance from City Y to City X = d
[tex]d+d=647 miles\\2d=647 miles\\d=\frac{647miles}{2}=323.5 miles[/tex]
Distance from City X to City Y = 323.5 miles
Distance of City X from national park = 27 miles
From the figure, the distance of the national park from the City Y = d -27 miles:
[tex]= 323.5 miles - 27 miles = 296.5 miles[/tex]
The distance from national park to City Y = 296.5 miles
When we will be going on the round trip between the national park and city Y we will be first traveling 296.5 miles from the national park to the City Y and then 296.5 miles from City Y to the national park.
So, the round trip distance between the national park and city Y:
[tex]296.5 miles + 296.5 miles = 593 miles[/tex]
So the round trip distance between the national park and city Y is 593 miles.
Learn more about- Round trip Distance
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3(m+1)+1>7 what is m?
Answers
3m +4 > 7
3m > 3
m is 1
The coordinates of point T are (0,6). The midpoint of ST is (3, -4). Find the coordinates of point S
Answers
Answer:
S = (-8, 0 )
Step-by-step explanation:
how much time will it take for a bug to travel 5 meters if it is traveling 1 m/s
Answers
Answer:
5
Step-by-step explanation:
divide the distance by the rate of speed
5/1=5
Answer:
5 seconds.
Step-by-step explanation:
Convert 6 kilograms into pounds. Round your answer to the nearest tenth.
Answers
[tex]\boxed{\sf 1kg=2.205lbs}[/tex]
[tex]\\ \sf\longmapsto 6kg[/tex]
[tex]\\ \sf\longmapsto 6(2.205)[/tex]
[tex]\\ \sf\longmapsto 13.23lbs[/tex]
If 1 kg is equivalent to 2.2 pounds…. therefore 6 kg would be 6 x 2.2 which gives you 13.2
4,540,597 to the nearest million
Answers
Answer:
Hi, there! The correct Answer Is Below
4,540,597 Would Round To 5,000,000
Step-by-step explanation:
If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up. Example: 38 rounded to the nearest ten is 40. ...
If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down. Example: 33 rounded to the nearest ten is 30.
________________________________________________________
-Darkspirit-
Answer:
Step-by-step explanation:
The hundred thousands digit is 5 so it is 5,000,000.
Given that g(x) = x°, find each of the following.
a) g(1)
b) g(-2)
c) g(-x)
d) g(3y)
e) g(1 + h)
Answers
Describe how to use a random number generator to simulate the following performances
a) A basketball player has the ability to make 40% of his shots and takes 25 shots in one game.
b) A basketball player has the ability to make 75.2% of her free throw shots and she takes 8 free throws in a game.
Answers
Answer:
random number generators return numbers from 0 to 1...
a) generate 25 random numbers if the number x is ≤ .4 he makes the shot
otherwise he misses
a) generate 8 random numbers if the number x is ≤ .752 she makes the shot otherwise it is a miss
otherwise he misses
Step-by-step explanation:
15 = [tex]\frac{5}{3}[/tex] (x + 12)
Answers
Answer:
x = -3
Step-by-step explanation:
15 = 5/3 (x + 12)
Multiply each side by 3/5 to clear the fraction
3/5 *15 =3/5 *5/3 (x + 12)
9 = x+12
Subtract 12 from each side
9-12 = x+12-12
-3 =x
Answer:
15 = 5/3(x + 12)
Using distributive law
15 = 5x/3 + 20
15 = 5x + 60/3
15 × 3 = 5x + 60
45 = 5x + 60
45 - 60 = 5x
-15 = 5x
-15/5 = x
-3 = x
There are 16 tablespoons in 1 cup. How many tablespoons of cornstarch would Chery need to make the green slimerecipe 15 time?
Answers
16 xs 15 = 240
please vote me brainliest! :)
a die is rolled find the probability of rolling a multipul of 5
Answers
Answer:
1/6
Step-by-step explanation:
It's 1/6 because the only multiple of 5 in a die is 5, so it will be 1/6.
help me with this plsssssssss ps that is a 2
Answers
Answer:
14...
plz mark me brailiest
Pamella late for school 10% of time. Richard late for 15% of the time.
a) What percentage are they both late?
b) What is the probability only one of them is late?
Answers
Answer:
a) 25%
10%+15% = 25%
b) doesn't have any idea