1. Translate: A number divided into 4 2. Translate: The sum of 2/3 and a number 3. Translate: Drew is "n" years younger than Joe who is 9 years old

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:

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:

all work is pictured and shown

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:

[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.

4,383  I hope I got that right, Hope it helps!

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 .

Answer:

9 1/3

Step-by-step explanation:

4 2/3 ÷ 1/2

Write the mixed number as an improper fraction

(3 * 4 +2)/3 = 14/3

14/3 ÷1/2

Copy dot flip

14/3 * 2/1

28/3

Divide 28 by 3

9 with 1 left over

Put the left over part on top of the denominator

9 1/3

Answer: who knows what the answers is bruh

Step-by-step explanation:

Answer:

-4 and -5

Step-by-step explanation:

- 13/3 is equal to -4.3 so this is why i think this but it maybe wrong.

Answer:

20.85 ft

Step-by-step explanation:

first convert 7 in to ft than add 9 to it

10×5×9.583 = 479.15ft that's how much carpet he needs for his room

500-479.15= 20.85ft left for the rest of his house

p-9/3 = 2

p-9 = 2×3

p-9 = 6

p = 6+9

... Hope this will help...

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

Find out more at: https://brainly.com/question/18271653

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.

To solve more questions on momentum, visit the link below-

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Answer:

The difference is 85 ft.

Step-by-step explanation:

Elevation 1: 50 ft

Elevation 2: -35 ft

Difference = Elevation 1 - Elevation 2

Difference = 50 - (-35)

I can simplify this expression, as subtracting a negative number is the same as adding a positive number:

Difference = 50 + 35

Difference = 85

Answer: The difference is 85 ft.

Answer:

False

Step-by-step explanation:

-(-21) is positive 21 since there are 2 negative signs, and -21 is negative, therefore they are not the same.

Hope this helps!

Answer:

False. It is equal to 21.

Step-by-step explanation:

-(21) would equal -21

However,

- (- 21) equals 21

The two negatives "cancel" each other out.

Answer: False. It is equal to 21.

Answer: The midpoint  is MZ midpoint = (0.5,1)

Step-by-step explanation:

[tex]MP= (\frac{x_1+x_2}{2}),(\frac{y_1+y_2}{2} ) \\MP= (\frac{-4+3}{2}),(\frac{-1+3}{2} )\\MP= (\frac{-1}{2}),(\frac{2}{2} ) \\\\MP= (-0.5 ,1)[/tex]

Answer:

the 2nd one

Step-by-step explanation:

look at it again its simple

Answer:

0.15

Step-by-step explanation:

longerrrrrrrrrrrrr

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

196

Step-by-step explanation:

12*8=96+100=196

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.

Learn more about the square root visit:

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Answer:

1/4n - 3

Step-by-step explanation:

1/4 of a number means multiplying 1/4 to n. So we can write 1/4n. Now we write the subtract 3 portion. 1/4n - 3.

The expression n = 1/4n - 3 shows that Emily's number can be obtained by adding 3 to one-fourth of her number.

Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.

Emily's number can be represented as:

n

One-fourth of Emily's number can be represented as:

1/4n

Subtracting 3 from one-fourth of Emily's number gives us:

1/4n - 3

Therefore, the expression that represents Emily's number is:

n = 1/4n - 3

This expression shows that Emily's number can be obtained by adding 3 to one-fourth of her number.

Learn more about the algebraic expression here :

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Answer:

m is represented as the slope

Step-by-step explanation:

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:

number 5 is 22

Step-by-step explanation:

it is 10.63

Step-by-step explanation:

Used a calculator