Use implicit differentiation to find the slope of the tangent line to the curve 4 x^2 - 3 xy + 4 y^3 = -113 at the point ( -1,-3 ).

Answers

Answer 1
f'(x, y) = 8x -3xydy/dx +12y²dy/dx = 0
(12y² -3xy)dy/dx = -8x
dy/dx = -8x/[12y² -3xy]
dy/dx |(x=-1 , y=-3) : = -8(-1)/[12(-3)² - 3(-1)(-3)]
= 8/[108 -9]
=8/99

Related Questions

The height H(in feet) of a ball T seconds after it is hit can be modeled by the function H(t)=-16t^2+32t+7

Answers

H(t) = -16t^2 + 32t + 7
The 7 shows the height the ball was hit from
Setting H(t) = 0 and solving for t yields t= 2.2 seconds when it hits the ground

I need help with proofs

Answers

Proofs are often over-complicated in math class. They are basically a step by step way of doing an assignment. There can be ones that are done using only math equations, but there are also ones that you write out as you would an essay, and those are my personal favorite. In those, you basically write out moment by moment how you find out the answer to a given problem.

If a television is $117.00 and was marked down by 10% then what was the original price

Answers

$117.00(10%) = $117.00(0.10) = $11.70
$117.00 + $11.70 = $128.70

Thus, the original price for the television is: $128.70

The area of this triangle is 200ft what does x have to be height is 12 feet and base 5x feet

Answers

1/2(5x*12)= 200
5x*12=400
5x=33 1/3
x= 6 2/3

Answer:

x=6.67

Step-by-step explanation:

We are given that area of triangle is 200 square feet .

Height of triangle =12 feet

Base of triangle =5x feet

We have to find the value of x

We know that area of triangle with base b and height h

Area of triangle =[tex]\frac{1}{2}\times b\times h[/tex]

Substitute the values then we get

Area of triangle =[tex]\frac{1}{2}\times 5x\times 12 [/tex]

[tex]200=30 x[/tex]

[tex]x=\frac{200}{30}[/tex]

[tex]x=6.67[/tex]

Hence, x=6.67

What is the value of x?

A. 25 cm

B. 7 cm

C. 29 cm

D. 35 cm

Answers

Answer:

  29 cm

Step-by-step explanation:

The central triangle is isosceles, so the length if its right side (x) is the same as the length of its left side (29 cm).

  x = 29 cm

Ryan has read 30% of the pages of his book on monday if he read 45 pages how many pages does the book have

Answers

the answer is 1350 due to the fact that first you multiply 45 by 10 which is 450 and multiply it by 3
i hope this helps

Answer:

150

Step-by-step explanation:

30%=45

30%x3=90%

45x3=135

30%/3=10

45/3=15

10%=15

135+15=

150

what is the difference between 506 and 233

Answers

273 is the answer.
Hope it helps!
506 - 233 = 273
answer
the difference between 506 and 233 is 273

The amount of paint needed to cover the walls of a room varies jointly as the perimeter of the room and the height of the wall. if a room with a perimeter of 70 feet and 8-foot walls requires 5.6 quarts of paint, find the amount of paint needed to cover the walls of a room with a perimeter of 65 feet and 10-foot walls

Answers

the answer to the question is 6.5 quarts because according to this 1 quart will cover 1600 square feet

Given triangle JKL, sin 38 degree equals

Answers

Right triangle
sin(38) = cos(52)

answer
 cos(52)

hope it helps

Answer:

B. [tex]\text{cos}(52^{\circ})[/tex].

Step-by-step explanation:

We have been given a right triangle. We are asked to complete our given statement.

[tex]\text{sin}(38^{\circ})[/tex] equals ___.

We will use identity [tex]\text{sin}(x)=\text{cos}(90-x)[/tex] to solve our given problem.

[tex]\text{sin}(38^{\circ})=\text{cos}(90^{\circ}-38^{\circ})[/tex]

[tex]\text{sin}(38^{\circ})=\text{cos}(52^{\circ})[/tex]

Therefore, [tex]\text{sin}(38^{\circ})[/tex] equals [tex]\text{cos}(52^{\circ})[/tex].

Together, teammates pedro and ricky got 2671 base hits last season. pedro had 277 more hits than ricky. how many hits did each player​ have?

Answers

Final answer:

To find out how many hits each player had, we set up a system of equations and solve for the variables. Pedro had 2474 hits and Ricky had 1197 hits.

Explanation:

To solve this problem, we need to set up a system of equations. Let's represent the number of hits Pedro had as x and the number of hits Ricky had as y. We are given that their combined hits is 2671, so we can write the equation:

x + y = 2671

Additionally, we are given that Pedro had 277 more hits than Ricky. This can be represented as:

x = y + 277

We can now substitute the second equation into the first and solve for y:

y + 277 + y = 2671

2y = 2394

y = 1197

Now we can substitute the value of y back into the first equation to solve for x:

x + 1197 = 2671

x = 2474

Therefore, Pedro had 2474 hits and Ricky had 1197 hits.

Learn more about Solving a system of equations here:

https://brainly.com/question/29050831

#SPJ12

What are the domain and range for the cube root function graphed below? Justify your answer in complete sentences.

Answers

whats the cube root function graphed below ?

Explain the error in each statement Three points have to be collinear

Answers

Three points do NOT HAVE to be collinear, but they can be.

Chloe draws three parallelograms. In each figure, she measures a pair of angles, as shown. What is a reasonable conjecture for Chloe to make by recognizing a pattern and using inductive reasoning?

a) In a parallelogram, consecutive angles are supplementary.
b) In a parallelogram, all angles are congruent.
c) In a parallelogram, all angles are supplementary.
d) In a parallelogram, consecutive angles are congruent.

Answers

The best answer is A) In a parallelogram, consecutive angles are supplementary.
Final answer:

The conjecture Chloe can make based on the given information is that in a parallelogram, consecutive angles are congruent.

Explanation:

Chloe's conjecture, based on the pattern she observed, would be that in a parallelogram, consecutive angles are congruent. To support this conjecture, we can explain that a parallelogram has opposite sides that are parallel, and therefore, the opposite angles are congruent. Since the consecutive angles are adjacent to these opposite angles, they must also be congruent.

Learn more about Parallelograms here:

https://brainly.com/question/32441125

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p(5)=-3+4(5) solve please

Answers

20+-3 is 17
First you do pemdas and multiply 4 and 5 first.
Then you add -3

Solve:
r/5 - 6 = -1

A) r = 1
B) r = 5
C) r = 10
D) r = 25

Answers

r/5 - 6 = -1

add 6 to both sides

r/5 = 5

multiply both sides by 5

r = 5 *5 = 25

r = 25

i believe its c?????

A student rolls a standard number cube. What is the probability the student rolled a 4, given that the number rolled was greater than or equal to 2?

Answers

<><> answer: B. 1/5 <><>

Are Abel Fields’s actions protected by the First Amendment?

Answers

According to a 2012 decision by the US Supreme Court, Abel Fields's actions are protected by the First Amendment.


In the fictitious case study scenario of Abel Fields, he claimed to have received a Purple Heart for wounds suffered in combat, when in fact he had never served in the military. He asserted his claim as a freedom of speech issue.


In a real-life decision by the US Supreme Court, United States v. Alvarez, the the Court struck down the Stolen Valor Act of 2005 (signed into law by President G.W. Bush in 2006). The law had criminalized false statements about having a military medal. By a 6-3 majority, the Supreme Court determined that the Stolen Valor Act was unconstitutional under the First Amendment's protection of free speech.

According to a 2012 decision by the US Supreme Court, Abel Fields's actions are protected by the First Amendment.

In which quadrant is θ located if cscθ is negative and tanθ is positive?

Answers

If cos is negative and tan is positive it's located in third quadrant (3)

Answer:

[tex]\theta[/tex] is located in 3rd Quadrant.

Step-by-step explanation:

We are given that [tex]cos\,\theta[/tex]  is negative  and [tex]tan\,\theta[/tex]  is positive

We have to find Quadrant in which [tex]\theta[/tex] is located.

We have 4 Quadrants.

In 1st Quadrant , All trigonometric ratios are positive.

In 2st Quadrant , sin and cosec are positive while others are negative.

In 3rd Quadrant , tan and cot are positive while others are negative.

In 4th Quadrant , cos and sec are positive while others are negative.

Therefore, According to given information [tex]\theta[/tex] located in 3rd Quadrant.

If f(x)=2−x12 and g(x)=x2−9, what is the domain of g(x)÷f(x)?

Answers

[tex]\bf \begin{cases} f(x)=2-x^{12}\\ g(x)=x^2-9\\ g(x)\div f(x)=\frac{g(x)}{f(x)} \end{cases}\implies \cfrac{x^2-9}{2-x^{12}}[/tex]

now, for a rational expression, the domain, or "values that x can safely take", applies to the denominator NOT becoming 0, because if the denominator is 0, then the rational turns to undefined.

now, what value of "x" makes this denominator turn to 0, let's check by setting it to 0 then.

[tex]\bf 2-x^{12}=0\implies 2=x^{12}\implies \pm\sqrt[12]{2}=x\\\\ -------------------------------\\\\ \cfrac{x^2-9}{2-x^{12}}\qquad \boxed{x=\pm \sqrt[12]{2}}\qquad \cfrac{x^2-9}{2-(\pm\sqrt[12]{2})^{12}}\implies \cfrac{x^2-9}{2-\boxed{2}}\implies \stackrel{und efined}{\cfrac{x^2-9}{0}}[/tex]

so, the domain is all real numbers EXCEPT that one.

9. Simplify the expression. 8 – 5(12x + 8) A) 36x + 24 B) –60x – 32 C) –60x + 16 D) –60x + 48

Answers

8 - 5(12x + 8)

8 - 60x - 40 

-60x + (8 - 40)

-60x - 32

hope that helps, God bless!

A woman 5 ft tall walks at the rate of 3.5 ft/sec away from a streetlight that is 12 ft above the ground. at what rate is the tip of her shadow moving? at what rate is her shadow lengthening? ⇒

Answers

Refer to the diagram shown below.

The woman walks at a rate of 3.5 ft/s away from the streetlight. Therefore
[tex] \frac{da}{dt} =3.5 \, ft/s[/tex]

The length of the shadow changes at the rate
[tex] \frac{dx}{dt} [/tex]

Because triangles ACE and BCD are similar  (AAA), therefore
[tex] \frac{AC}{BC}= \frac{AE}{BD} \\\\ \frac{a+x}{x} = \frac{12}{5} [/tex]
12x = 5a + 5x
7x = 5a

Therefore
[tex] \frac{dx}{dt} = \frac{5}{7} \frac{da}{dt} = \frac{5}{7} (3.5 \, ft/s) = 2.5 \, ft/s[/tex]

Answer: 2.5 ft/s

The rate at which her shadow is lengthening is 2.5ft/sec

Triangular altitude theorem:

To get the rate of her shadow lengthening, we will use the similarity theorem of a triangle.

Find the triangle attached. From the triangle;

[tex]\frac{EA}{AC} =\frac{DB}{BC}[/tex]

Substitute the sides as given in the diagram:

[tex]\frac{12}{x+a} =\frac{5}{x}\\12x = 5(x+a)\\ 12x=5x+5a\\7x = 5a[/tex]

Differentiate both sides with respect to t

[tex]7\frac{dx}{dt} = 5\frac{da}{dt} \\7\frac{dx}{dt}=5(3.5)\\7\frac{dx}{dt}=17.5\\\frac{dx}{dt} = 2.5ft/sec[/tex]

The rate at which her shadow is lengthening is 2.5ft/sec

Learn more on similar triangles here: https://brainly.com/question/2644832

In the southern hemisphere about ________ percent of the surface is land. 55 .019 19 1.9 78

Answers

それでも、日本人の食生活も急速に変化してきています。

6% of 124 =
7.44
0.744
74.4
744
If you could explain would be great

Answers

To turn a percentage into a decimal, divide it by a hundred. So, 6% --> 6/100 which is 0.06.  To find a percentage of a number, multiply the number by the percent in decimal form. In this case, 124 x 0.06. The answer is 7.44. So 6% of 124 is 7.44

Suppose a cup of coffee at the campus coffee shop is $2.50 and a cup of hot tea is $1.25. suppose a student's beverage budget is $20 per week. if you were going to write an algebraic expression of this budget line of the form coffee = a + b tea. b would be

Answers

B = $1.25
I don't fully understand what the question is going for.

five times the sum of a number and 27 is greater than or equal to six times the sum of the number and 26 what is the solution to set of the problem

Answers

5(n + 27) >= 6(n + 26)

5n + 135 >= 6n + 156

-n >= 21

n <= -21

Study the Proof Given.

List the reasons for Items 2,3, & 4.

Right the number and then the answer.

Question 1 options:

Answers

2. Definition of midpoint
3. Given
4. Transitive property

joy is planning to purchase a sweater that costs 30$ dollars at her local department store. The sweaters are on sale for for 20% off.

Which steps are needed to find the sale price of the sweater in words?

Answers

First we calculate 20% of the price:

20% of 30$ is 0.2*30$=6$.

Then we subtract 6$ (that is 20% of the price) from 30$, and get 24$.

Thus, the sale price is 24$

Answer:24

Step-by-step explanation:

Match the inequality to the graph of its solution.
a. n/4 ≤ -1
b. -10 ≥ -100
c. 5x ≥ 20

Answers

B. -10x>= -100 is for the first graph.
A. n/4<= -1 is for the second song
Hope this helps

Answer:

its B

Step-by-step explanation:

John concludes that, since (x - 5) is a factor of the polynomial x2 - 25, if he performed the long division (x2 - 25) ÷ (x - 5), the remainder would be zero. This is an example of ___________ reasoning(x2 - 25)

Answers

John concludes that, since (x - 5) is a factor of the polynomial x2 - 25, if he performed the long division (x2 - 25) ÷ (x - 5), the remainder would be zero. This is an example of deductive reasoning(x2 - 25).

Answer:

Deductive reasoning

Step-by-step explanation:

Given : John concludes that, since (x-5) is a factor of the polynomial [tex]x^2-25[/tex], if he performed the long division [tex](x^2-25)\div (x-5)[/tex], the remainder would be zero.  

To find : This is an example of ___________ reasoning [tex]x^2-25[/tex]?

Solution :

The above situation make conclusion when we know the fact that (x-5)

is the factor as the factor of polynomial divide it completely.

Therefore, This is the example of deductive reasoning.

Deductive reasoning is the process by which a person makes conclusions based on previously known facts.

How long will it take you to bike a distance of 108 miles at a speed of 24 miles per hour ?

Answers

Just divide 108 by 24 and you'll figure out how many hours.



(Also, if you don't want to do it the answer is 4.5 (4 hours and 30 minutes)

:D
4 and a half hours (4 hours & 30 minutes)
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