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sattari [20]
3 years ago
14

(a)Use differentiation to find the minimum value of f(x)= 3x^2 - 5x + 10 and the value(s) of x for which this minimum occurs.

Mathematics
1 answer:
elena-14-01-66 [18.8K]3 years ago
3 0

Hi there!

Begin by differentiating f(x) using the power rule:

dy/dx = nxⁿ⁻¹

Therefore:

f(x) = 3x² - 5x + 10

f'(x) = 6x - 5

Set this equation equal to 0 to find the x-intercept:

0 = 6x - 5

5 = 6x

x = 5/6, which is where the graph goes from NEGATIVE to POSITIVE, so there is a MINIMUM at this value.

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Mrrafil [7]
Let the length of the rectangle is x. units , accordingly :

2.(x+3) = x×3.

2x + 6 = 3x.

x = 6 units is the answer :)
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3 years ago
Mr. Jamison will stain the deck in his backyard. The deck has an area of 752.4 square feet. If the deck is 33 feet long, how wid
Art [367]

area = L x W

752.4 = 33 x w

 w = 752.4 / 33 = 22.8


width = 22.8 feet

8 0
3 years ago
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Help!![tex]Janet is buying a $28 necklace. The store reduces the price by 20% and then applies a $2 off coupon. How much will sh
Nataliya [291]
$20.40

Hope this helps! ^_^
6 0
3 years ago
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A sequence can be generated by using fn = 2f(n-1)+1, where f1 = 4 and n is a whole number greater than 1. What are the first fou
hoa [83]

Answer:

<em>{9,19,39,79}</em>

Step-by-step explanation:

<u>Recursive Sequences</u>

The recursive sequence can be identified because each term is given as a function of one or more of the previous terms. Being n an integer greater than 1, then:

f(n) = 2f(n-1)+1

f(1) = 4

To find the first four terms of the sequence, we set n to the values {2,3,4,5}

  • For n=2

f(2) = 2f(1)+1

Since f(1)=4:

f(2) = 2*4+1

f(2) = 9

  • For n=3

f(3) = 2f(2)+1

Since f(2)=9:

f(3) = 2*9+1

f(3) = 19

  • For n=4

f(4) = 2f(3)+1

Since f(3)=19:

f(4) = 2*19+1

f(4) = 39

  • For n=5

f(5) = 2f(4)+1

Since f(4)=39:

f(5) = 2*39+1

f(5) = 79

4 0
3 years ago
Can 12m, 35m and 37m make a right triangle
antoniya [11.8K]

Answer:

YES

Step-by-step explanation:

Explanation:

If this is a right triangle we can then substitute the sides of the triangle (12 and 35) and the hypotenuse (37) into the Pythagoras Theorem and the two sides of the equation will be equal. If this is not a right triangle the two sides of the equation will not be equal.

The Pythagoras Theorem is  

a

2

+

b

2

=

c

2

Substituting we get:

12

2

+

35

2

=

37

2

12

⋅

12

+

35

⋅

35

=

37

⋅

37

144

+

1225

=

1369

1369

=

1369

Because these are equal this is a right triangle.

3 0
3 years ago
Read 2 more answers
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