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aniked [119]
2 years ago
6

Charlie drove for 45 minutes to go from Town X to Town Y, which are 54 miles apart. How fast were they going in miles per hour?

Mathematics
2 answers:
n200080 [17]2 years ago
5 0

Answerprobably 70

Step-by-step explanation:

Because hours

Setler [38]2 years ago
3 0
70 hope it helps have a nice day
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Use differentiation rules to find the values of a and b that make the function f(x) = ( x 2 if x ≤ 2, ax3 + bx if x > 2 diffe
Maurinko [17]

Answer:

The values of a and b are  a=\frac{1}{4} and b = 1

Step-by-step explanation:

* <em>Lets explain how to solve the equation</em>

  f(x) =  {x²                x  ≤ 2

            {ax³ + bx     x > 2  

* We need to find the values of a , b that make the function

 differentiable at x = 2

- <em>At first for f(x) to be continuous at x = 2, substitute x by two in the</em>

<em>  the two expressions and equate them</em>

∵ f(x) = x² at x ≤ 2 and f(x) = ax³ + bx at x > 2

∴ f(2) = (2)² = 4 ⇒ (1)

∴ f(2) = a(2)³ + b(2)

∴ f(2) = 8a + 2b ⇒ (2)

- Equate (1) and (2)

∴ 8a + 2b = 4 ⇒ (3)

* <em>For f(x) to be differentiable when x = 2, the function must be </em>

<em>  continuous when x = 2 and the one-sided derivatives must be </em>

<em>  equal when x = 2</em>

# <u>Remember</u>: If f(x)=ax^{b} , then f'(x)=abx^{b-1}

 If f(x)=ax , then f'(x)=a

 If f(x)=a , then f'(x)=0

∵ f(x) = x²

∴ f'(x) = 2x

- Substitute x by 2

∴ f'(2) = 2(2) = 4

∴ f'(2) = 4 ⇒ (4)

∵ f(x) = ax³ + bx

∴ f'(x) = 3ax² + b

- substitute x by 2

∴ f'(2) = 3a(2)² + b

∴ f'(2) = 12a + b ⇒ (5)

- Equate (4) and (5)

∴ 12a + b = 4 ⇒ (6)

* Now we have system of equations

 8a + 2b = 4 ⇒ (3)

 12a + b = 4 ⇒ (6)

- Multiply equation (6) by -2 to eliminate b

∴ -24 a - 2b = -8 ⇒ (7)

- Add equations (3) and (7)

∴ -16a = -4

- Divide both sides by -16

∴ a = \frac{1}{4}

- substitute the value of a in equation (6)

∴ 12(\frac{1}{4})+b=4

∴ 3 + b = 4

- Subtract 3 from both sides

∴ b = 1

* The values of a and b are  a=\frac{1}{4} and b = 1

5 0
3 years ago
A grandmother deposited $4,000 in an account that pays 5% per year compounded annually when her granddaughter was born. What wil
Leya [2.2K]
A = P (1 + r/n)^nt
A = 4000(1 + 0.05/1)^(13)(1)
A = $7542.59
4 0
3 years ago
(7,-4);
olga_2 [115]

Literally just plug it in

6(7) + 5(-4) - 42 = 0

42 -20 -42 = 0

-20 = 0

Not a solution.

8 0
3 years ago
Quick anyone know the answer to this?
nata0808 [166]
The top question is B. 30, because you have to set 7y-30 equal to 4y+60 since both lengths are the same.
4 0
3 years ago
You are making a lot of cookies and buy 12 bags of chocolate chips, which are $1.89 per bag
Liono4ka [1.6K]

Answer:

$22.68

Step-by-step explanation:

5 0
3 years ago
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