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4 years ago

Prove that 5x^3+4x-2=0 has exactly one solution

1 answer:

3 0

$5x^3+4x-2=0\\\\
(5x^3+4x-2)'=15x^2+4\\\\
15x^2+4=0\\
15x^2=-4\\
x^2=-\dfrac{4}{15}\\
x\in\emptyset 
$

The derivative of $5x^3+4x-2$ is positive for all real numbers, which means the function is increasing in its all domain and therefore there is only one intersection with the x-axis ⇒ one solution.

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3 years ago

the perimeter of a rectangle is 56 m. if the width were doubled and the length were increased by 8 m, then the perimeter would b

Natasha2012 [34]

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Define x and y:
----------------------------------------------------------------
Let the length be x.
Let the width be y.

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Formula:
----------------------------------------------------------------
Perimeter = 2(Length + Width)

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Construct equations and solve for x and y:
----------------------------------------------------------------
2x + 2y = 56 ---------------------- (1)
2(x+8) + 4y = 82 -----------------------(2)

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From equation 1:
----------------------------------------------------------------
2x + 2y = 56
x + y = 28
x = 28 - y

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From equation 2:
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2(x+8) + 4y = 82
2x + 16 + 4y = 82
2x + 4y = 66
x + 2y = 33

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Substitute x = 28 - y into equation 2:
----------------------------------------------------------------
x + 2y = 33
(28 - y) + 2y = 33
28 - y + 2y = 33
y = 5

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Substitute y = 5 into equation 1:
----------------------------------------------------------------
x = 28 - y
x = 28 - 5
x = 23

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Find Length and Width
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Length = x = 23 m
Width = y = 5m

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Answer: Length = 23m and Width = 5m
----------------------------------------------------------------

3 0

3 years ago

A sauce recipe uses 4 cans of tomatoes in every 2/12 quarts. How many cans of tomatoes are used in each quart of the sauce?

My name is Ann [436]

4/12 quarts
hope this helps

7 0

3 years ago

Three sets have 5, 10, 15 elements, respectively. How many elements can their union and intersection have?

Degger [83]

Answer:

$Union = 15$

Step-by-step explanation:

Given

$n(A) = 5; n(B) = 10; n(C) = 15$

Solving (a): Possible union elements

This is the represented by element with the largest number of the sets

i.e.

$Union = 15$

Solving (b): Possible intersection elements

This is the represented by element with the least number of the sets

i.e.

$Intersection = 5$

6 0

3 years ago

What is the solution for the system of equations? Use the elimination method to solve. 2x+y=20 -5y=-6x+12

egoroff_w [7]

Given Equations :

✿ 2x + y = 20 ------------------ [1]

✿ 6x - 5y = 12 ----------------- [2]

Multiplying Equation [1] with 5, We get :

⇒ 5(2x + y) = 5(20)

⇒ 10x + 5y = 100 -------------- [3]

Adding Equations [2] and [3], We get :

⇒ (10x + 5y) + (6x - 5y) = 100 + 12

⇒ 16x = 112

⇒ x = 7

Substituting x = 7 in Equation [1], We get :

⇒ 2(7) + y = 20

⇒ 14 + y = 20

⇒ y = 20 - 14

⇒ y = 7

So, The Solution for the Given System of Equations is : (x , y) = (7 , 7)

3 0

3 years ago