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muminat
2 years ago
7

The sum of three consecutive numbers is 51. What are the three numbers

Mathematics
1 answer:
bixtya [17]2 years ago
6 0

Answer: 16,17,18

Step-by-step explanation: 16,17,18 are consecutive numbers and when you add them up the equal 51

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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
Rosie did the following problem. (7-1) 2 ÷ 6 + 4 · 3 6 2 ÷ 6 + 4 · 3 36 ÷ 6 + 4 · 3 6 + 4 · 3 10 · 3 30 Which statement best des
Travka [436]
Answer: Rosie is incorrect because she needs to do the exponent before subtracting.
4 0
2 years ago
Decrease 119kg by 2/7
slava [35]

Answer:

51

Step-by-step explanation:

1-2/7 = 3/7

119 x 3/7 = 51

8 0
2 years ago
Urgent please help quick!!!
Radda [10]

Answer:

x=-1\\y=-1

Step-by-step explanation:

5x+5y=-10\\3x-7y=4

Let's solve the first equation for either x or y. I'll do it for x.

5x+5y=-10

Begin by subtracting 5y.

5x=-5y-10

Now divide by 5.

x=\frac{-5y}{5}-\frac{10}{5}

Simplify:

x=-y-2

Now substitute x in the second equation for this value.

3x-7y=4\\3(-y-2)-7y=4

Distribute;

-3y-6-7y=4

Add 6

-3y-7y=4+6

Combine like terms;

-10y=10

Divide by -10.

y=\frac{10}{-10}\\ y=-1

-----------------------------------------------------------------------------------------------------------

Take this value of y and replace it in the first equation to find the value of x.

5x+5y=-10\\5x+5(-1)=-10\\5x-5=-10\\5x=-10+5\\5x=-5\\x=\frac{-5}{5}\\ x=-1

5 0
2 years ago
Select three ratios that are equivalent to <br> 4:3 <br> Choose 3 answers:
postnew [5]
Ratios equivalent to 4:3 would be 8:6 16:12 and 24:18
6 0
3 years ago
Read 2 more answers
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