4. Find an equation of the line that is tangent to the graph of 4x + 2xy^2 +44 = y^3 at the point (-3,2).

i need this asap.

Answers

Answer 1

Given:

The equation is:

[tex]4x+2xy^2+44=y^3[/tex]

To find:

The equation of the tangent on the given equation at point (-3,2).

Solution:

We have,

[tex]4x+2xy^2+44=y^3[/tex]

Differentiate with respect to x.

[tex]4(1)+2[x(2yy')+y^2(1)]+0=3y^2y'[/tex]

[tex]4+4xyy'+2y^2=3y^2y'[/tex]

[tex]4+2y^2=3y^2y'-4xyy'[/tex]

[tex]4+2y^2=(3y^2-4xy)y'[/tex]

Isolate y'.

[tex]\dfrac{4+2y^2}{3y^2-4xy}=y'[/tex]

Now, we need to find the value of the derivative at point (-3,2).

[tex]y'_{(-3,2)}=\dfrac{4+2(2)^2}{3(2)^2-4(-3)(2)}[/tex]

[tex]y'_{(-3,2)}=\dfrac{4+8}{12+24}[/tex]

[tex]y'_{(-3,2)}=\dfrac{12}{36}[/tex]

[tex]y'_{(-3,2)}=\dfrac{1}{3}[/tex]

It means the slope of the tangent line is [tex]\dfrac{1}{3}[/tex].

The equation of tangent line that passes through the point (-3,2) with slope [tex]\dfrac{1}{3}[/tex] is:

[tex]y-y_1=m(x-x_1)[/tex]

[tex]y-2=\dfrac{1}{3}(x-(-3))[/tex]

[tex]y-2=\dfrac{1}{3}x+1[/tex]

[tex]y=\dfrac{1}{3}x+1+2[/tex]

[tex]y=\dfrac{1}{3}x+3[/tex]

Therefore, the equation of tangent line is [tex]y=\dfrac{1}{3}x+3[/tex].


Related Questions

Help pls it is 7th grade math

Answers

Answer:

E

Step-by-step explanation:

Supplementary angles: angles that equal to 180

H + G = 180

H + F = 180

H and E are the same angle, but since they are not right angles, they do not equal 180

Emergency i will make brainly!! i need an answer cause its due today! And there are no options just solve

Answers

Answer:

cylinder

Step-by-step explanation:

A cylinder is generated by rotating a rectangle about one of its edges

Answer:

Cylinder

Step-by-step explanation:

A Cylinder is made by rotating one of a rectangles angles!! GoodLuck<33

What is the undefined value of 3b^2+13b+4/b+4 ?

O 4
O 0
O -3
O -4

Answers

Answer:

0

Step-by-step explanation:

when you divide anything by 0 it becomes undefined

I was a little confused on this problem

Answers

Answer:

Step-by-step explanation:

164.8+106.09=270.89

Solve for b.
-3b+2.5 = 4

Answers

Answer:

b = −0.5

Step-by-step explanation:

Let's solve your equation step-by-step.

−3b+2.5=4

Step 1: Subtract 2.5 from both sides.

−3b+2.5−2.5=4−2.5

−3b=1.5

Step 2: Divide both sides by -3.

-3b/-3 = 1.5/-3

The value of 'b' in the equation given is -0.5

Given the expression for which we could solve for the unknown:

-3b + 2.5 = 4

Subtract 2.5 from both sides

-3b = 4 - 2.5

-3b = 1.5

divide both sides by -3 to isolate b

-3b/-3 = 1.5/-3

b = -0.5

Therefore, the value of b in the equation given is -0.5

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Devin buys four shirts of equal price for a total of 36$ and teo pairs of shoes for equal price of $25.He has to pay 8% sales tax on his purchases devin decides instead to purchase five shirts and one pair of shoes.If the sales tax is 8% how much will devin pay for his ourchase

Answers

Answer:

$65.88

Step-by-step explanation:

Given data

Sales Tax= 8%

Cost of shirt= $36

Cost of shoe= $25

Total cost= 36+25

Total=$61

Let us find the amount of the Tax

=8/100*61

=0.08*61

=$4.88

Hence the amount paid is

=61+4.88

=$65.88

Find the 8th Term for the Geometric Sequence for which a1 - 3 and r = -2

Answers

Answer:

-384

Step-by-step explanation:

geometric sequence : every new element is generated by multiplying the previous element always with the same number r.

a(n) = a(n-1) * r

a(n) = a(1) * r^(n-1)

so, a(1) = 3, r = -2

a(8) = ?

a(8) = a(1) * r^7 = 3 * (-2)^7

a negative number to an uneven power is again a negative number.

so, (-2)^7 = -128

3 * -128 = -384 = a(8)

WHATS THE VOUME WILL MARK BRAINLIST GOD BLESS

Answers

Height = 15

Length = 8

Width = 5

V = lwh/3

V = 15*8*5/3

V = 200




Solve for y:
x + 2y = -8

y=-1/2x+4
y=-1/2x-4
y=-2x - 4
y=1/2x-4

Answers

Answer:

x + 2y = -8 = y = -4 - 1/2x

y= -1/2x + 4 =  y = 4

y= -1/2x - 4 = y = -4

y=-2x - 4 = y = -4

y=1/2x-4 = y = -4

Step-by-step explanation:

(x + 2y = -8 = y = -4 - 1/2x)

[tex]x+2y=-8\\2y=-8-x\\y=-4-\frac{1}{2}x\\[/tex]

Dan and Joe are responsible for cutting the grass on the local high school soccer field. Joe cuts a diagonal line through the field, as shown in the diagram below, and says that each person is responsible for cutting the grass on one side of the line. Dan says that this is not fair because he will have to cut more grass than Joe. Is Dan correct? Why or why not?​

Answers

Answer:

Step-by-step explanation:

The figure shows the graphs of the functions y = f(x) and y = g(x). The four indicated points all have integer coordinates. y = f(x) y = g(x) If g(x) = k f(x), what is the value of k? I am not sure how to do this.​ k = -3

Answers

Answer:

k = -3

Step-by-step explanation:

f(x) = -2x+1

g(x) = 6x - 3

=> g(x) = k.f(x)

6x - 3 = k(-2x+1)

k = (6x-3)/(-2x+1)

= 3(2x-1)/-1(2x-1)

k = 3/(-1) = -3

The value of k for the given function will be k = -3.

What is a function?

In mathematics, a function is a relation between a set of inputs and a set of possible outputs with the property that each input is related to exactly one output. A function can be thought of as a machine that takes an input, performs a certain operation on it, and produces an output.

Formally, a function is defined as a set of ordered pairs (x, y) such that each value of x is associated with exactly one value of y. The set of all possible inputs to a function is called its domain, while the set of all possible outputs is called its range.

The given functions are,

f(x) = -2x+1

g(x) = 6x - 3

The value of k will be calculated as,

g(x) = k.f(x)

6x - 3 = k(-2x+1)

k = (6x-3)/(-2x+1)

k= 3(2x-1)/-1(2x-1)

k = 3/(-1) = -3

To know more about function follow

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Solve for the missing side

Answers

Step-by-step explanation:

12²=a²+9²

144=a²+81

a²=144-81

a²=63

a=√63

a=7.94

There are 48 cars in the parking lot 16 are blue. What fraction of parked cars are blue? *

Answers

Answer:

16/48

Step-by-step explanation:

GIVING BRAINIEST IF CORRECT!!!!!

On Monday the temperature was 31º F. By Thursday it went down to –8º F.
How much did the temperature drop?

Answers

Answer:

39 F

Step-by-step explanation:

32 - (-8) is 39 F. The answer is 39 farhenheit

Answer:

39 F

Step-by-step explanation:

the answer is 39 yan lang po sana makatulong hehehehe

Ravi worked 6 days for a total of 64.2 hours. If he worked the same number of hours each day, how many hours did he work in a day

Answers

Answer:

10.7 hours per day

Step-by-step Explanation:

The total is 64.2.

If Ravi worked for 6 days and worked the same amount of hours each day then you do:

64.2 hours ÷ 6 days = 10.7 per day

Hope this helps!-Finny

Profit P(x), is the difference between revenue, R(x), and cost, C(x), so P(x) = R(x) - C(x). Which expression represents P(x), if R(x) = 2x⁴ – 3x³ +2x– 1 and C(x) = x⁴ – x² + 2x +3?​

Answers

Answer:

x⁴-3x³+x²-4

Step-by-step explanation:

I know cuz i worked it out, and it's really hard to explain, so just trust me.

please help me! and please do not guess or just say something to take points bc i will make sure your account gets deleted. thank you!! 20 points for answering

Answers

Answer:

1. 3.

Step-by-step explanation:

The answer to tx2x365 is 730t so when you solve the others you also get 730t

I just wanna answer the answer is 1.3

Can someone help me pls!!

Answers

Answer:

x=1

Step-by-step explanation:

I need help ASAP! 20 point
I’m the xy-plane, a line has a slope of 6 and passed through the point (0,8). Which of the following is an equation of this line?

Answers

Answer:

A)  y = 6x + 8

Step-by-step explanation:

What is the value of x on a triangle with sides 13cm and 5cm?

Answers

Answer:

12

Step-by-step explanation:

what is the value of x? you ask.

use the pythogoras Theorem =

C^2 = a^2 + b^2

169= 25 + x^2

144 = x^2

√144 = the answer is 12

please help

Select all the correct answers.
Which expressions are equivalent to the given expression?

Answers

It's (A).

................................

The above expression can be rewritten as

log(10) x^5 + log(10) 20 - log(10) 10

= log(10) [(20x^5)/10]

= log(10) (2x^5)

QUICK HURRY PLEASE Liam gave his friends a puzzle. He said he had two numbers that were not between -1 and 1. However, when the
numbers were multiplied, the result was always less than either of the numbers.
If Liam's puzzle is true, which of the following statements is true?

A- Both numbers must be positive

B- Both numbers must be negative

C- At least one number will be negative

D- One number will be positive, and one will be negative

Answers

Answer:

D

Step-by-step explanation:

One number will be positive, and one will be negative

Answer:

The answer is option D

Step-by-step explanation:

multiplication of numbers having opposite signs will result in a number having negative sign .

What is the missing reason in the proof ?

Answers

Answer:

A

Step-by-step explanation:

The reflexive property of congruence basically says that a segment is congruent with itself. B and C are related to angles so do not apply here.


Kalo randomly surveyed 25 students at his school and found that 19 of them have at least one sibling. Based on these data, how many of the 125 students at his
school would be expected to have at least one sibling?

Answers

Answer:

95 students

Step-by-step explanation:

25 students -- 19 have sibling

1 student -- (19/25)

125 students -- (19/25) * 125 = 95

Therefore, 95 students out of 125 are expected to have at least one sibling.

Thenks and mark me brainliest :))

Answer:

95

Step-by-step explanation:

Calculate the experimental probability of choosing a student who has at least one sibling:  It is 19/25, or 0.56.

If 125 students are selected, this probability applies.  Multiply 125 by 0.56:

0.56(125 students) = 95

95 students could be expected to report having at least one sibling.

Prove quadrilateral WXYZ is a rhombus.

Answers

Answer:

To prove a quadrilateral is a rhombus, here are three approaches:

Show that the shape is a parallelogram with equal length sides; Show that the shape is a parallelogram with equal length sides; Show that the shape's diagonals are each others' perpendicular bisectors; orShow that the shape is a parallelogram with equal length sides; Show that the shape's diagonals are each others' perpendicular bisectors; orShow that the shape's diagonals bisect both pairs of opposite angles.

At a location 30m from the base of a flagpole, the angle of elevation is 34 degrees. Determine the height of the flagpole to the nearest meter.

Answers

Answer:

20.2 m

Step-by-step explanation:

At a location 30m from the base of a flagpole, the angle of elevation is 34 degrees. Determine the height of the flagpole to the nearest meter.

We solve this question using the Trigonometric function of Tangent

tan θ = Opposite/Adjacent

θ = 34°

Adjacent =30m

Opposite = Height of the flag pole = x

Hence

tan 34 = x/30

Cross Multiply

tan 34 × 30m

= 20.235255505 m

Approximately = 20.2 m

Hence, the height of the flag pole to the nearest meter = 20.2m

A bag of marbles contains 1 red marble and 2 blue marbles. After a marble is chosen, it is replaced. Na'Tasha draws two from the bag 2 times.
What is the probability that the red marble is chosen both times?

1/9
1/3
1/2
1/4

Answers

The answer is 1/9 because if you add them all up it’s 9

Find the length of the missing side, given the information below.
PLEASE HELP I NEED THIS

Answers

Answer:

x = 2

UV = 9 ft

VW = 6 ft

WU = 5 ft

Step-by-step explanation:

The perimeter of a figure can be represented as the sum of lengths of all of its sides. In this case we can write:

P = UV + VW + WU

Now, we can substitute the values which we have:

20 = 4x + 1 + 8 - x + 2x + 1

We can combine like terms...

20 = 5x + 10

5x = 10

x = 2

Since UV is represented by 4x + 1, we can substitute in x to find its length.

UV = 4x + 1

UV = 4(2) + 1

UV = 6 + 1

UV = 9

We can do the same for the other two sides:

VW = 8 - x

VW = 8 - 2

VW = 6

WU = 2x + 1

WU = 2(2) + 1

WU = 4 + 1

WU = 5

Pls answer quick i need it for a timed assignment

Answers

Answer:

No solution

One solution

One solution

Step-by-step explanation:

Step-by-step explanation:

1.) no solutions

2.) one solution

3.)one solution

PLEASE HELP
I WILL GIVE YOU BRAINLIEST

Create the equation that represents the table

Answers

Answer:

I think the answer is Quadratic.

Step-by-step explanation:

Sorry if I'm wrong

A quadratic equation
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