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Paraphin [41]
2 years ago
12

The Leibnitz notation for the chain rule is

Mathematics
1 answer:
tankabanditka [31]2 years ago
6 0

For this derivative, you could set

\boxed{u = x^2 - 4x}

Then

y = \sin(x^2-4x) = \sin(u)

so that

\boxed{\dfrac{\mathrm dy}{\mathrm du} = \cos(u)}

and

\boxed{\dfrac{\mathrm du}{\mathrm dx} = 2x - 4}

Then the chain rule gives

\dfrac{\mathrm dy}{\mathrm dx} = \dfrac{\mathrm dy}{\mathrm du}\dfrac{\mathrm du}{\mathrm dx} \\\\ \dfrac{\mathrm dy}{\mathrm dx} = \cos(u)(2x-4) \\\\ \boxed{\dfrac{\mathrm dy}{\mathrm dx} = (2x-4)\cos(x^2-4x)}

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Victoria recently switched to a new electric company. If she uses between 0 and 400 kilowatt-hours (kWh) of electricity per mont
Gekata [30.6K]

Answer:

see the explanation

Step-by-step explanation:

<em><u>The question is </u></em>

Identify the domain and the range, using words and inequalities

Let

x -----> the number of kilowatt-hours (kWh) of electricity per month

y ----> the price per month

we know that

Part 1) For the value of x between 0 kWh and 400 kWh

0\ kWh \leq x < 400\ kWh

The price is equal to

y=\$30

therefore

The domain is the interval ------> [0,400)

The domain is all real numbers greater than or equal to 0 kWh  and less than 400 kWh

The range is ($30)

The range is equal to $30

Part 2) For the value of x equal to 400 kWh or more per month

x\geq 400\ kWh

The domain is the interval -----> [400, infinite)

The domain is all real numbers greater than or equal to 400 kWh

The price is

y=0.097x

<em>Find the range</em>

For x=400 kWh

y=0.097(400)=\$38.8

so

y\geq \$38.8

The range is the interval -----> [38.8, infinite)

7 0
3 years ago
The Martinez family went to play and paid $13 for 1 adult and 4 children. The Hernandez family went to the same place and paid $
andrey2020 [161]

Answer: the price for an adult ticket is $3

Step-by-step explanation:

Let x represent the price of one adult ticket.

Let y represent the price of one child ticket.

The Martinez family went to play and paid $13 for 1 adult and 4 children. This means that

x + 4y = 13 - - - - - - - - - - -1

The Hernandez family went to the same place and paid $14 for 3 adults and 2 children. This means that

3x + 2y = 14 - - - -- - - - - - - -2

Multiplying equation 1 by 3 and equation 3 by 1, it becomes

3x + 12y = 39

3x + 2y = 14

Subtracting, it becomes

10y = 25

y = 25/10 = 2.5

Substituting y = 2.5 into equation 1, it becomes

x + 4 × 2.5 = 13

x + 10 = 13

x = 13 - 10

x = 3

6 0
2 years ago
4^338^37 / 4^158^21 A. 4^18 8^16 B. 8^48 16^58 C. 16^18 64^16 4^18 8^58
Rainbow [258]
If the problem is supposed to read (4^33*8^37)/(4^15*8^21), then...

(4^33*8^37)/(4^15*8^21) = (4^33/4^15)*(8^37/8^21)
(4^33*8^37)/(4^15*8^21) = 4^(33-15)*8^(37-21)
(4^33*8^37)/(4^15*8^21) = 4^18*8^16

Answer: Choice A) 4^18*8^16

6 0
3 years ago
(MIDDLE SCHOOL MATH) what is the answer for b)?
lesya692 [45]

Answer:

because it easily displays all of the info

7 0
3 years ago
Read 2 more answers
How do i find the value of x?
inn [45]

Answer:h

2x+1+3x+8./2=. 17

5x+9. = 17 x2

5x+9= 34

-9. -9

5x=25

Divide by 5

X=5

Step-by-step explanation:

4 0
3 years ago
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