please explain how to do this one as well ...

Answer:

[tex]\displaystyle \frac{dy}{dx}\Big|_{(1, 1)}=0[/tex]

Step-by-step explanation:

We are given the equation:

[tex](x^2+y^2)^2=4x^2y[/tex]

And we want to find the slope of the tangent line at the point (1,1).

Recall that the slope of the tangent line to a point of a function is given by the function's derivative.  

Thus, find the derivative of the equation. Take the derivative of both sides with respect to x:

[tex]\displaystyle \frac{d}{dx}\left[(x^2+y^2)^2\right]=\frac{d}{dx}\left[4x^2y\right][/tex]

Let's do each side individually.

Left:

We can use the chain rule:

[tex](u(v(x))'=u'(v(x))\cdot v'(x)[/tex]

Let v(x) be x² + y² and u(x) is x². Thus, u'(x) is 2x. Therefore:

[tex]\displaystyle \frac{d}{dx}\left[(x^2+y^2)^2\right]=2\left(x^2+y^2\right)\left(\frac{d}{dx}\left[x^2+y^2\right]\right)[/tex]

Differentiate:

[tex]\displaystyle \frac{d}{dx}[(x^2+y^2)^2]=2(x^2+y^2)\left(2x+2y\frac{dy}{dx}\right)[/tex]

Factor. Therefore, our left side is:

[tex]\displaystyle 4(x^2+y^2)\left(x+y\frac{dy}{dx}\right)[/tex]

Right:

We have:

[tex]\displaystyle \frac{d}{dx}\left[4x^2y\right][/tex]

We can move the constant multiple outside:

[tex]\displaystyle =4\frac{d}{dx}\left[x^2y\right][/tex]

We will use the Product Rule:

[tex]\displaystyle =4\left(\frac{d}{dx}\left[x^2\right]y+x^2\frac{d}{dx}\left[y\right]\right)[/tex]

Differentiate:

[tex]\displaystyle =4\left(2xy+x^2\frac{dy}{dx}\right)[/tex]

Therefore, our entire equation is:

[tex]\displaystyle 4(x^2+y^2)\left(x+y\frac{dy}{dx}\right)=4\left(2xy+x^2\frac{dy}{dx}\right)[/tex]

To find the derivative at (1,1), substitute and evaluate dy/dx when x = 1 and y = 1. Hence:

[tex]\displaystyle 4((1)^2+(1)^2)\left((1)+(1)\frac{dy}{dx}\right)=4\left(2(1)(1)+(1)^2\frac{dy}{dx}\right)[/tex]

Evaluate:

[tex]\displaystyle 4((1)+(1))\left(1+\frac{dy}{dx}\right)=4\left(2+\frac{dy}{dx}\right)[/tex]

Further simplify:

[tex]\displaystyle 8\left(1+\frac{dy}{dx}\right)=8+4\frac{dy}{dx}[/tex]

Distribute:

[tex]\displaystyle 8+8\frac{dy}{dx}=8+4\frac{dy}{dx}[/tex]

Solve for dy/dx:

[tex]\displaystyle 4\frac{dy}{dx}=0\Rightarrow \frac{dy}{dx}=0[/tex]

Therefore, the slope of the tangent line at the point (1, 1) is 0.

Answer:

[tex]x = \frac{-r - 21}{2}[/tex]

Step-by-step explanation:

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other.  Remember to do the opposite of PEMDAS.

PEMDAS =

Parenthesis

Exponents (& Roots)

Multiplication

Division

Addition

Subtraction

First, subtract 6 from both sides:

2x + 6 (-6) = -r - 15 (-6)

2x = -r + (-15 - 6)

2x = -r + (-21)

2x = - r - 21

Next, divide 2 from both sides:

[tex]\frac{2x}{2} = \frac{-r - 21}{2}[/tex]

[tex]x = \frac{-r - 21}{2}[/tex]

~

Answer:

The Answer Is: m∠ABD = m∠ABC

Step-by-step explanation:

I just took the test

A line is a one-dimensional shape that is straight. The statement that must be true about the given condition is A, m∠ABD=m∠ABC.

A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely.

Given that a horizontal line has points D, B, C. A line extends vertically from point B to point A. Also, Ray BA bisects ∠DBC. Therefore, the diagram for the given condition can be made as shown below.

Thus, the statement that must be true is m∠ABD = m∠ABC. This is because ∠DBC is a straight line, therefore, its measure will be 180°. And since Ray BA bisects ∠DBC. Therefore, the measure of m∠ABD = m∠ABC = 90°.

Hence, the statement that must be true about the given condition is A, m∠ABD = m∠ABC.

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Answer:

There will be 14 and 1/4 GROUPS of 4 toys created by 57 toys

Step-by-step explanation:

57 toys divided into groups of 4 toys.

57/4= 14.25 or 14 1/4 GROUPs

Answer:

88.796

Step-by-step explanation:

you multiply them...

it is 10.63

Step-by-step explanation:

Used a calculator

Answer:

the 2nd one

Step-by-step explanation:

look at it again its simple

Answer:

The answer is

Step-by-step explanation:

The midpoint M of two endpoints of a line segment can be found by using the formula

[tex]M = ( \frac{x1 + x2}{2} , \: \frac{y1 + y2}{2} )[/tex]

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

(12,-7) and (-6,15)

The midpoint is

[tex]M = ( \frac{12 - 6}{2} , \: \frac{ - 7 + 15}{2} ) \\ = ( \frac{6}{2} \: , \: \frac{8}{2} )[/tex]

We have the final answer as

Hope this helps you

Answer:

all work is pictured and shown

Answer: who knows what the answers is bruh

Step-by-step explanation:

The variable x represent the number of months in which he runs.

A linear equation is in the form:

y = mx + b

where y, x are variables, m is the rate of change (slope) and b is the y intercept.

Given that Sean one-half mile on his first run and adds two miles a month to his run. It is given by the equation f(x)= 0.5 + 2x

The variable x represent the number of months in which he runs.

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The equation for the vertical line that goes through point M(−2, 6) is x = -2.

The equation of a straight line is:

y = mx + b;

y, x are variables, m is the slope of the line and b is the y intercept.

The slope of a vertical is undefined. Since the line passes through the point M(−2, 6), hence the equation of the vertical line is:

x = -2

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Answer:

[tex]\frac{1}{3}[/tex] x³ + 5x + c

Step-by-step explanation:

Using the power rule

∫ a[tex]x^{n}[/tex] dx = [tex]\frac{a}{n+1}[/tex] [tex]x^{n+1}[/tex]

Thus

∫ x² + 5 dx

= [tex]\frac{1}{3}[/tex] x³ + 5x + c ← c is the constant of integration

Answer:

its the last one i believe

Step-by-step explanation:

because u have to get m by its self so

you divide 5 square from both sides and boom

Answer:

because the are not the same measurement nor the right placement

Step-by-step explanation:

The sides of figure B appear narrower than the sides of figure A.

We need to explain why Figure B is not the image of Figure A after a rotation using centre P.

A rotation is a type of transformation that takes each point in a figure and rotates it a certain number of degrees around a given point.

Now,

The reason why figure B is not the image of figure A after a rotation using centre P includes

1) The angle of rotation is measured as 180 - 45 = 135°, while the angle of rotation of the base is (90 - 26) + (90 - 71) = 83°

2) Rotation of a figure is a rigid transformation, such that the dimensions of the sides of the pre-image and the sides of the image should be equal after the rotation, however, the sides of figure B appear narrower than the sides of figure A.

Therefore, the sides of figure B appear narrower than the sides of figure A.

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Answer:

x= 12 y= 9

Step-by-step explanation:

x+29=3x+5

-x

29=2x+5

-5

2x=24

/2 /2

x=12

12+29=41

180-41= 139+5= 144÷16=9

Danny was closest to the surface of the water.

Here,

Darcy and Danny were diving on a trip in the Bahamas.

When they stopped to look at a school of fish, Darcy was [tex]\sqrt{78}[/tex] feet below the surface of the water and Danny was 17/2 feet below the surface.

What is square root?

A square root of a number x is a number y such that [tex]y2 = x[/tex].

Now,

Darcy was [tex]\sqrt{78}[/tex] feet below the surface of the water.

⇒[tex]\sqrt{78} = 8.83[/tex]

Danny was 17/2 feet below the surface.

[tex]\frac{17}{2} = 8.5[/tex]

Clearly,  [tex]8.5 < 8.85[/tex]

Hence, Danny was closest to the surface of the water.

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Answer: c

Step-by-step explanation:

On solving for [v], we get v = p/m.

Momentum is defined as the product of mass and velocity of a body. Mathematically, we can write vector as -

p = mv

It is a vector quantity. In a three dimensional coordinate, the momentum vector can be resolved as -

[p] = p[x] a[x] + p[y] a[y] + p[z] a[z]

[p] = m {v[x] a[x] + v[y] a[y] + v[z] a[z]}

Given is the momentum of an object whose formula is p=mv.

We have the formula for momentum as -

p = mv

We can solve for [v] as -

p = mv

Divide by [m] on both sides, we get -

p/m = mv/m

v = p/m

Therefore, on solving for [v], we get v = p/m.

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Given :

Peter velocity , P = 30 mph .

Mitchell velocity , M = 40 mph .

Mitchell leaves 15 min later .

To Find :

If they drive along the same route how long will it take Mitchell to catch Peter.

Solution :

Distance covered by Peter in 15 min .

[tex]D = 30\times \dfrac{15}{60}=7.5\ miles[/tex]

Let , time taken is x .

So , distance covered b them is equal :

[tex]7.5+30\times x=40\times x\\\\x=\dfrac{7.5}{10}=0.75\ hours\\\\x=0.75\times 60\ min\\\\x=45\ min[/tex]

Therefore , time taken by them is 45 minutes .

Hence , this is the required solution .

p-9/3 = 2

p-9 = 2×3

p-9 = 6

p = 6+9

... Hope this will help...

Answer:

1

Step-by-step explanation:

12-4x-10-3+(8x-5x)

collect like terms

12-4x-10-3+(3x)

remove the parenthesis

12-4x-10-3+3x= 1

Answer:

10x² - 9x - 13

Step-by-step explanation:

6x² - (4x + 10) - 3 + (4x² - 5x)

~Remove parenthesis

6x² - 4x + 10 - 3 + 4x² - 5x

~Combine like terms

10x² - 9x - 13

Best of Luck!

Answer:

x=85/11

Step-by-step explanation:

[tex]\frac{x}{5}= \frac{17}{11} \\\\5*\frac{x}{5} =\frac{17}{11} \\\\x=\frac{85}{11}[/tex]

Answer:

0.15

Step-by-step explanation:

longerrrrrrrrrrrrr

Answer:

D) The slope of the line is undefined

Step-by-step explanation:

A vertical line will have an undefined slope, because it does not run horizontally.

To find the slope, you calculate it with rise over run, however, a vertical line will not run horizontally, meaning the run is 0.

And, dividing anything by 0 will get you an undefined answer.

So, D is correct. the slope of the line is undefined

Answer:

the slope of the line is undefined

Step-by-step explanation:

i just took test

Answer:

[tex]x=7[/tex]

Step-by-step explanation:

So we have the function:

[tex]w(x)=3x-7[/tex]

And we want to find x when w(x) is 14.

So, substitute 14 for w(x):

[tex]14=3x-7[/tex]

Add 7 to both sides. The right cancels:

[tex]21=3x[/tex]

Divide both sides by 3:

[tex]x=7[/tex]

So, the value of x is 7.

The correct answer is the first option.

Answer:

number 5 is 22

Step-by-step explanation:

Answer:

reflection

Step-by-step explanation:

this is a reflection off y=-x

Answer:

Step-by-step explanation:

You could use a calculator or you could perform long division to find the remainder of 15/266.  There is no integer quotient, other than 0 (zero).  That means 15 is the remainder.

Supposing you were dealing with 266/15 (which is really a different problem).  This division produces an integer quotient and a remainder:

266

------- = 17 r. 11

 15

Double-check to ensure that you've copied this problem down correctly.

Answer:

Add 9 to both sides of the equation.

p=12r+9

Step-by-step explanation:

The answer is 21.

Have a good day!