1) As you know, the area of a square is A = x , where for this problem, A is area in feet and x is the length of a side, in feet. If the length of a side is changing at a rate of 6 feet/minute when the length of a side is 4 feet, at what rate is the area changing?

[tex]\sf{\dfrac{a^x}{log(a)} }[/tex]

[tex]\sf{\dfrac{a^x}{ln(a)} }[/tex]

[tex]\sf{Let\ y=\dfrac{a^x}{ln(a)} }[/tex]

[tex]\sf{=\dfrac{d}{dx}\bigg[\dfrac{a^x}{ln(a)} \bigg] }[/tex]

[tex]\sf{=\dfrac{1}{ln(a)}.\dfrac{d}{dx}(a^x) }[/tex]

[tex]\sf{=\dfrac{ln(a)a^x}{ln(a)} }[/tex]

[tex]\boxed{\sf{=a^x}}[/tex]

→ [tex]\sf{[a.b(x)+c.d(x)]'=a.b'(x)+c.d'(x)}[/tex]

→ [tex]\sf{(a^x)'=ln(a).a^x}[/tex]

Answer:

a^x.

Step-by-step explanation:

y = a^x / log a

Assuming the log is to the base e:

y = (1/ log a) * a^x

Derivative of a^x:

Let u = a^x

log u = log a^x

log u = x log a

1/u * du/dx = log a

du/dx =  = u * log a

y = (1 / log a) * u

so  dy/du = 1/log a

and dy/dx = dy/du * du/dx

=  (1/log a )* log a u

= u

= a^x.

Answer:

x = -50/9    

General Formulas and Concepts:

Pre-Algebra

Step-by-step explanation:

Step 1: Define equation

3x - 8 - 12x = 42

Step 2: Solve for x

Answer:

Step-by-step explanation:

Let the original width be x

Then the original length = x + 11

Area = x * (x + 11)

If you decrease each side by 7 you get

Area 1 = (x - 7)(x + 4)

So area - area1 =

x (x + 11) -98 = (x - 7)(x + 4)                  Remove the brackets

x^2 + 11x - 98 = x^2 - 7x + 4x - 28      Combine the like terms

x^2 + 11x - 98 = x^2 - 3x - 28              Add 98 to both sides

x^2 + 11x = x^2 - 3x + 70                     Cancel the x^2

11x = -3x + 70                                       Add 3x to both sides

14x = 70                                               Divide by 14

x = 70 / 14

x = 5

=====================

Original conditions

Answer width = 5

Length = 16

If you check this, you will get totally bizarre answers. Don't check it. It gives negative results. You can do this in math, but not in the real world.

Answer:

y = (7/3)x - 9

Step-by-step explanation:

1. Convert given equation to y=mx+b form --> y = (7/3)x - 5/3

2. Equation of new line --> y = (7/3)x + b

3. Plug in given values --> 5 = (7/3)(6) + b

4. Solve for b --> b = 5 - 14    b = -9

5. New line --> y = (7/3)x - 9

Answer:

I got 90

Please correct me If I am wrong Please and Thank You

Step-by-step explanation:

Combine like terms 70 and 10 which will be 60

and Combine like terms  and you get 30

Then you add 60+30= 90

Answer: 60=30

Step-by-step explanation:

70-10= -40=10

  60  =    30

Answer:

6 wrong.

Step-by-step explanation:

25 questions  76% 25*0.76=19 so he got 6 wrong.

Hope this helps plz hit the crown :D

Answer:

he got 19 correct and 6 incorrect

Step-by-step explanation:

Answer:

Y=90

X=180

Step-by-step explanation:

Answer: b

Step-by-step explanation:

Answer:

D (-3, 1)

Step-by-step explanation:

Answer:

See below

Step-by-step explanation:

If we want to reflect across x-axis, we'll change the y-coordinate of the        co-ordinate to it's opposite (If it's negative, it will become positive and vice versa) while the x-coordinate will remain the same.

[tex]\rule[225]{225}{2}[/tex]

Hope this helped!

Answer:

50%

Step-by-step explanation:

Most people assume the toss of a coin is always a 50/50 probability, with a 50 percent chance it lands on heads, and a 50 percent chance it lands on tails

Answer:

100%

Step-by-step explanation:

There is a 50% chance of getting heads, and 50% chance of getting tails.

If these two options are added together, you get 100%. There are only two options on a coin flip anyways, so the probability of getting heads or tails would be 100%.

Answer:

two-thirds plus five=five and two-thirds

Step-by-step explanation:

Answer:

I think this is right 5 is x=30

Step-by-step explanation:

4 is a because 2x=6 can simple to x=3

and 5 is x=30

Answer:

It's undefined. x=4

Step-by-step explanation:

Answer:

x=5

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

Answer:

115

Step-by-step explanation:

Answer:

A. [tex] PR = 80.6 yd [/tex]

B. Perimeter = 190.6 yd

Step-by-step explanation:

A. Distance between P(10, 50) and R(80, 10):

[tex] PR = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]

[tex] PR = \sqrt{(80 - 10)^2 + (10 - 50)^2} [/tex]

[tex] PR = \sqrt{(70)^2 + (-40)^2} [/tex]

[tex] PR = \sqrt{4,900 + 1,600} [/tex]

[tex] PR = \sqrt{6,500} [/tex]

[tex] PR = 80.6 yd [/tex] (nearest tenth)

B. Distance around the park = Perimeter = PR + PQ + QR

PR = 80.6 yd

PQ = |50 - 10| = 40 yd

QR = |80 - 10| = 70 yd

Perimeter = 80.6 + 40 + 70

Perimeter = 190.6 yd

Answer:

1

Step-by-step explanation:

Answer:

see below

Step-by-step explanation:

[tex]e(x)=\frac{1}{5}x\\\\e(5)= \frac{1}{5}*5\\\\\boxed{e(5)=1}[/tex]

Hope this helps.

Answer:d

Step-by-step explanation: tufryvztgv

Answer:

Yes. |8|+|-7| = 15

Step-by-step explanation:

the absolute cancels out the -, so it would mean that -7 is now positive 7, so yes it'd be 15

9514 1404 393

Answer:

  $170

Step-by-step explanation:

If the price of a pair of Jordans is the same as the price of two shirts, the total purchase has a value equivalent to that of 3 Jordans.

  pair of Jordans = $510/3 = $170

Answer:

$170

Step-by-step explanation:

Answer:

An apple costs £0.25

A banana costs £0.34

Step-by-step explanation:

Answer: OMG that is sad why did you hide the the cheating tabs

Step-by-step explanation:

Answer:

Girl why did u cheat in the first place???

Step-by-step explanation:

Cheating is not going to get u into college or get you a scholorship. Its just a road to lies and people not trusting u. You should take this moment and reflect. Also, STUDY

sorry that happened but tbh, if u cheated then u kinda deserved that

NOT BEING MEAN

have a great day and LEARN

Answer:

yupyup

Step-by-step explanation:

been having it for years now

Answer:

3x^3+2x^2+2x+5

Step-by-step explanation:

The answer is A

Answer:

i think its -10

Step-by-step explanation:

hope im not wrong

Answer:

5 1/6 ÷ 4 2/3 = 31/28

3 3/4 ÷ 1 2/8 = 3

4 2/4 ÷ 2 1/4 = 2

5 2/5 ÷ 1 4/5 = 3

4 2/8 ÷ 3 2/4 = 17/4

3 3/9 ÷ 2 4/12 = 10/7

7 1/2 ÷ 3 3/5 = 25/12

6 2/8 ÷ 3 1/3 = 15/8

Explanation:

5 1/6 ÷ 4 2/3 = 31/6 ÷ 14/3 = (31/14) / (6/3) = (31/14) / 2 [when you divide by a certain number you multiply that number by the denominator] = 31/28

5 1/6 ÷ 4 2/3 = 31/6 ÷ 14/3 = 31/6 × 3/14