We need to differentiate this with respect to x to see if we can find an expression for the derivative of y at various points. That will be the slope of the tangent to the curve. Then we want to see where that derivative might be infinite -- i.e., where the tangent is vertical.
It's not written as a function, but it can still be differentiated using the chain rule:
x2 + xy + y2 = 3
(2x) + (x dy/dx + y dx/dx) + (2y dy/dx) = 0
(I used parentheses to show the differentiation of each term in the original equation.)
2x + x dy/dx + y + 2y dy/dx = 0
2x + y = -x dy/dx - 2y dy/dx
2x + y = dy/dx (-x -2y)
-(2x + y)/(x + 2y) = dy/dx
We have the derivative of y, but it's defined partly in terms of y itself. That's OK. Let's go on...
So where would the slope be infinite? That would happen when x + 2y = 0, or y = -x/2
Let's plug that in for y in the original equation to find points where that's the case.
x2 + xy + y2 = 3
x2 + x(-x/2) + (-x/2)2 = 3
x2 - x2/2 + x2/4 = 3
3x2 / 4 = 3
x2 = 4
x = ±2
So we have two x values where the tangent might be vertical. Let's plug them into the equation and see what the y values are. First x = 2...
x2 + xy + y2 = 3
4 + 2y + y2 = 3
y2 + 2y + 1 = 0
(y + 1)2 = 0
y = -1
So at the point (2, -1) the tangent is vertical.
Now try x = -2...
x2 + xy + y2 = 3
4 - 2y + y2 = 3
y2 - 2y + 1 =0
(y - 1)2 = 0
y = 1
So at the point (-2, 1) the tangent is vertical.
A student states that Figure JKLM is congruent to Figure PQRS. Determine if the student is correct or has made an error. ;D
Answer:
Student has made an error
Step-by-step explanation:
If two figures are said to be congruent, this implies that area of both is same and both as exactly same or copy or each other.
But from the graph, it can be stated that height of figure JKLM is 4 units whereas that of other is 6 unit.
Hence explained !
Juan concludes that x? + 7x + 3 cannot be factored using integers.
is juan correct? how could juan improve his strategy?
I HOPE IT WILL HELP YOU. If it is right then plz tell me .
Name the property shown by the statement a + (b + 2) = (a + b) + 2
Answer:
The associative property
Step-by-step explanation:
In brief terms, the associative property states that when one has like operations, or an operation and its inverse, one can add parenthesis to the equation without changing the final answer. One can also change the place in which the parenthesis stands in this expression without altering the result. remember, an operation and its inverse refers to any operation and the operation that is done to undo the operation. The following is a list of such operations:
[tex]x^n=b[/tex] [tex]\sqrt[n]{b}=x[/tex]
[tex]a*b[/tex] [tex]a[/tex] ÷ [tex]b[/tex]
[tex]a+b[/tex] [tex]a-b[/tex]
PLEASE HELP ASAP!!! i dont understand :(
Answer:
hello,
Step-by-step explanation:
y=k(x-a')²+b'
focus is (a',1/(4k)+b')
2x²=-120y
==> y=-2/120x²
==> y=-1/60(x-0)²+0
focus= (0,-15)
Find the measure of the indicated angle.
Answer:
i think it the measured of the indicated angle is 55
Find the missing side of the triangle
I dont know the answer lol but imma say B
Help pls will give brainliest
Answer:
195.06
Step-by-step explanation:
area of circle = πr^2 = π8^2 = 64π
area of triangle = 1/2 x 4 x 3 = 6
area of shape = 64π-6 = 195.061929 = 195.06
BRAINLEST IF CORRECT!!!!!!!
Answer:[tex]\huge \boxed{x=180-26-90=64}[/tex]
Step-by-step explanation:
Answer:
Step-by-step explanation:
You have the angels 180, 26, 90(right angle) and x. So when you add them all up you should get 360 because there aren’t two straight lines. Only line makes a 180 angle. So...
180 + 26 + 90 + x = 360
296 + x = 360
x = 360 - 296
x = 64
If the mortgage interest rates increase, this would be an example of changing your external environment.
Answer:
Economic conditions
Step-by-step explanation:
If the mortgage interest rates increase, this would be an example of changing Economic conditions in a company's your external environment
Mortgage is the legal agreement/arrangement between a financial institution and a debtor wherein the Financial institution lends funds to the debtor at an interest rate, and also with the title of the property owned by the debtor.
once the debtor repays the mortgage he retains the full ownership of his property.
Simplify for me please
Need help ASAP rocky ! Help needed
Answer:
x/x∈R,x≤5 1/6
Step-by-step explanation:
Surveys were sent to a random sample of owners of all-wheel-drive (AWD) vehicles and to a random sample of owners of front-wheel-drive (FWD) vehicles. The proportion of owners who were satisfied with their vehicles was recorded for each sample. The sample proportions were used to construct the 95 percent confidence interval for a difference in population proportions (FWD minus AWD) for satisfied owners. The interval is given as (−0.01,0.12). A car company believes that the proportion of satisfied owners of AWD vehicles differs from the proportion of satisfied owners of FWD vehicles. Does the confidence interval provide evidence that this belief is plausible?
Answer:
No, the confidence interval does not provide evidence that this belief is plausible as the confidence interval range contains the null value (0)
Step-by-step explanation:
Given that the confidence interval for the mean difference of AWD and FWD vehicles is :
(−0.01,0.12)
When defining the hypothesis for mean difference :
H0 : μ1 - μ2 = 0
H1 : μ1 - μ2 ≠ 0
Using the confidence interval result, reject the Null if the confidence interval value at the given α - level does not contain 0 ; otherwise fail to reject the Null ;
Since the (−0.01,0.12) contains 0 ; then we fail to reject the Null and conclude that there is no statistically significant difference between the two groups
In the figure, AB¯¯¯¯¯∥CD¯¯¯¯¯ and m∠2=55°.
What is m∠8?
Enter your answer in the box.
°
Line a b parallel to line c d is cut by a transversal forming 8 angles. The angles formed when the transversal intersects with line A B clockwise starting from top left are angle 1, 2, 3, and 4. The angles formed where the transversal intersects line c d clockwise from top left are angle 5, 6, 7, and 8.
measure of angle E is 2 x degrees.
Answer:
m<8 = m<2, both are equal since they are alternate exterior angles.
m<2 = 55° given, so m<8 = 55°
Answered by GAUTHMATH
-4d - 5 = -1 answer for me pls
[tex]\\ \sf\longmapsto -4d-5=-1[/tex]
Cancel - from both sides[tex]\\ \sf\longmapsto -(4d+5)=-(1)[/tex]
[tex]\\ \sf\longmapsto 4d+5=1[/tex]
[tex]\\ \sf\longmapsto 4d=1-5[/tex]
[tex]\\ \sf\longmapsto 4d=-4[/tex]
[tex]\\ \sf\longmapsto d=\dfrac{-4}{4}[/tex]
[tex]\\ \sf\longmapsto d=-1[/tex]
Find m<DCV and m<VBD
Answer:
∠ DCV = ∠ VBD = 50°
Step-by-step explanation:
The inscribed angles DCV and VBD are half the measure of their intercepted arcs, that is
∠ DCV = [tex]\frac{1}{2}[/tex] DV = [tex]\frac{1}{2}[/tex] × 100° = 50°
∠ VBD = [tex]\frac{1}{2}[/tex] DV = [tex]\frac{1}{2}[/tex] × 100° = 50°
HELP ME PLEASE I NEED HELP
Consider the end behavior of the function g(x) = 4|x − 2| − 3.
As x approaches negative infinity, f(x) approaches POSITIVE OR NEGATIVE infinity.
As x approaches positive infinity, f(x) approaches POSITIVE OR NEGATIVE infinity.
Answer:
Step-by-step explanation:
This is a narrower-than-normal absolute value graph, which is a v-shaped graph. It's pointy part, the vertex, lies at (2, -3) and it opens upwards without bounds along both the positive and negative x axes. Therefore, as x approaches negative infinity, f(x) or y (same thing) approaches positive infinity. As x approaches positive infinity, f(x) approaches positive infinity.
Complete the table of values of y = 14 x + 1.
Answer:
-4,0
0,1
8,3
======
x: -4, 0, 8
f(x) = 1/4(x) + 1
Plug in x values into f(x)...
f(-4) = 0
f(0) = 1
f(8) = 3
SOMEONE HELP ME PLEASE
Answer:
1/4 * 2/3 = 2/12 = 1/6 = .1666 = 16.6%
Step-by-step explanation:
If m∠A = 43° and the measure of arc AB = 69°, then m∠B = ° (Blank 1). (Round your answer to one decimal place, if necessary.)
====================================================
Explanation:
If angle A is 43 degrees, then minor arc BC is 2*43 = 86 degrees according to the inscribed angle theorem. The central angle is twice that of the inscribed angle. Both of these angles subtend the same minor arc.
When I say "minor arc BC", I mean that we go from B to C along the shortest path. Any minor arc is always less than 180 degrees.
Since minor arc AB is 69 degrees, and minor arc BC is 86 degrees, this means arc ABC is arcAB+arcBC = 69+86 = 155 degrees
Let's say point D is some point on the circle that isn't between A and B, and it's not between B and C either. Refer to the diagram below. The diagram is to scale. The diagram your teacher provided is not to scale because arc ABC is way too big (it appears to be over 180 degrees). Hopefully the diagram below gives you a better sense of what's going on.
Because arc ABC = 155 degrees, this means the remaining part of the circle, arc ADC, is 360-(arc ABC) = 360-155 = 205 degrees
Inscribed angle B subtends arc ADC. So we'll use the inscribed angle theorem again, but this time go in reverse from before. We'll cut that 205 degree angle in half to get 205/2 = 102.5 degrees which is the measure of angle B. This value is exact. In this case, we don't need to apply any rounding.
What is the equation of a line, in slope-intercept form, that has a slope of 3 and contains the point (0,5)?
Is the answer option c?
Answer:
Discrete
Step-by-step explanation:
A set can simply be defined as a list of values. There are many different types of sets, some are intervals, others are enumerated numbers. Often, a set composed of values that are listed is referred to as a discrete set. Discrete sets can be a list of information, or "isolated points". Knowing this information, the most logical answer to fill in the blank is "discrete".
"If a set is made up of isolated points and can be written as a list, it is called a discrete set."
[tex]\frac{1}{3-6y} + \frac{1}{y} = \frac{1}{6\\}[/tex]
Answer:
y = 11 + √ 73/ 4 , 11 − √ 73 /4
Step-by-step explanation:
Can u help solve this problem
Answer:
45in³
Step-by-step explanation:
6 x 5 x 3 = 90/2 = 45in³
rút gọn M=[ căn x -2/x-1- căn x +2/x+2 căn x+ 1] nhân x bình-2x+1/2 với x>0 x khác 1
Answer:
Step-by-step explanation:
kiro and lito were assigned the same book to read for a class. kiro started reading on Saturday, and he's reading 20 pages a day. Lito didn't start until Sunday, but he is reading 25 pages a day. How many days will it take Lito to catch up to kiro and how many pages will they have each read?
what system of equations represents this situation and how do you solve it?
Where is the blue dot on the number line ?
Answer:
-1.13
Step-by-step explanation:
the gape between two points is 0.01 so the required answer is -1.13
Beaker A contains 1 liter which is 15 percent oil and the rest is vinegar, thoroughly mixed up. Beaker B contains 2 liters which is 55 percent oil and the rest vinegar, completely mixed up. Half of the contents of B are poured into A, then completely mixed up. How much oil should now be added to A to produce a mixture which is 60 percent oil
Answer:
Add 1.25 litres of oil.
Step-by-step explanation:
Contents in beaker A implies;
15% of oil in 1 litre = 0.15 litres of oil
So that, there are 0.15 litres of oil and 0.85 litres of vinegar in beaker A.
Contents in beaker B implies:
55% of oil in 2 litres = 1.1 litres of oil
So that, thee are 1.1 litres of oil and 0.9 litres of vinegar in beaker B.
Half of contents of B poured into A implies that beaker A now contains:
0.15 litres + 0.55 litres = 0.7 litres of oil
0.85 litres + 0.45 litres = 1.3 litres of vinegar
The percentage of oil in A now = [tex]\frac{0.7}{2}[/tex] x 100%
= 35%
To increase the percentage of oil to 60%, then:
0.7 litres + 1.25 litres = 1.95 litres of oil
But the new total litres of the content in beaker A = 3.25 litres
So that;
[tex]\frac{1.95}{3.25}[/tex] x 100% = 60%
Therefore, to produce a mixture which is 60% oil, add 1.25 litres of oil.
Which of the following lists of ordered pairs is a function? A. (2,5), (3, 6), (6, 9) B. (-1,2), (2, 3), (3, 1), (2,5) C. (1,2), (4,0), (3,5),(4,3) D. (2,5), (3, 6), (2, 1)
Answer:
A. (2,5), (3,6), (6,9)
Step-by-step explanation:
In order to be a function, all inputs (x values) must go to only one output (y value). List A is the only list that obeys this rule. Therefore, List A is a function.
A box contains 4 red cubes, 3 blue cubes, 2 green cubes, and 1 yellow cube. You pick two cubes at random, replacing each after you pick. Find the probability of picking a blue and then a red.
A.3/25
B.9/100
C.3/4
D.4/25
Answer:
Step-by-step explanation:
There are 10 cubes all together.
You want blue and then red with replacement.
Blue
P(B then red) = 3/10 * 4/10 = 12 / 100
12/100 reduces to 3/25
The answer is A
Answer:
A?
Step-by-step explanation:
I WILL GIVE BRAINLIEST IF TWO PEOPLE ANSWER! PLEASE PUT WHAT X IS, AND PLEASE PUT THE REASONS OF HOW YOU DID IT, FOR INSTANCE, SUBSTITUTION, OR ALTERNATE INTERIOR ANGLES
Answer:
14°
Step-by-step explanation:
4x + 32 + 64 = 180 => x = 14 (°)
