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lukranit [14]
4 years ago
12

Question number 8. Prove that 3 + √5 is an irrational number.​

Mathematics
1 answer:
Marina86 [1]4 years ago
7 0

Answer :

Let's assume the opposite of the statement i.e., 3 + √5 is a rational number.

\\  \sf \: 3 +  \sqrt{5}  =  \frac{a}{b}   \\  \\   \qquad \: \tiny \sf{(where \:  \: a \:  \: and \:  \: b \:  \: are \:  \: integers \:  \: and \:  \: b \:  \neq \: 0)} \\

\\  \sf \:  \sqrt{5}  =  \frac{a}{b}  - 3 =  \frac{a - 3b}{b}  \\

Since, a, b and 3 are integers. So,

\\ \sf \:  \frac{p - 3b}{b}  \\  \\  \qquad \tiny \sf{ \: (is \:  \: a \:  \: rational \:  \: number \:) } \\

Here, it contradicts that √5 is an irrational number.

because of the wrong assumption that 3 + √5 is a rational number.

\\

Hence, 3 + √5 is an irrational number.

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In the united states the speed limit signs are in Miles per hour. Unfortunately, your speedometer only reads in km/hour. How man
ohaa [14]

Hello,

1mph = 1.60934kph

70 x 1.60934 = 112.6538

Answer:

70mph = 112.6538kph

8 0
3 years ago
Jada solved the equation Negative StartFraction 4 over 9 EndFraction = StartFraction x over 108 EndFraction for x using the step
GalinKa [24]

Answer:

Jada should have multiplied both sides of the equation by 108.

Step-by-step explanation:

The question is incomplete. Find the complete question in the comment section.

Given the equation -4/9 = x/108, in order to determine Jada's error, we need to solve in our own way as shown:

Step 1: Multiply both sides of the equation by -9/4 as shown:

-4/9 × -9/4 = x/108 × -9/4

-36/-36 = -9x/432

1 = -9x/432

1 = -x/48

Cross multiplying

48 = -x

x = -48

It can also be solved like this:

Given -4/9 = x/108

Multiply both sides by 108 to have:

-4/9 * 108 = x/108 * 108

-4/9 * 108 = 108x/108

-432/9 = x

x = -48

Jada should have simply follow the second calculation by multiplying both sides of the equation by 108 as shown.

7 0
3 years ago
What is the ratio of the volume of Cylinder A to the volume of Cylinder B?
erastovalidia [21]

Answer:

The ratio of volume of Cylinder A to the volume of Cylinder B is 18:25.

Step-by-step explanation:

Dimension of cylinder A,

Radius is 3 units and height is 4 units.

Dimension of cylinder B,

Radius is 5 units and height is 2 units.                          

The volume of a cylinder is given by :

V=\pi r^2 h

For cylinder A to B,

\dfrac{V_A}{V_B}=(\dfrac{r_A}{r_B})^2\times \dfrac{h_A}{h_B}\\\\\dfrac{V_A}{V_B}=(\dfrac{3}{5})^2\times \dfrac{4}{2}\\\\\dfrac{V_A}{V_B}= \dfrac{18}{25}

So, the ratio of volume of Cylinder A to the volume of Cylinder B is 18:25.

3 0
3 years ago
- f(x) = 3x3 – 21ײ – 54x<br>Zero<br>Multiplicity<br>Effect​
xenn [34]

Answer:

x = 9 or x = 0 or x = -2

Step-by-step explanation:

Solve for x:

3 x^3 - 21 x^2 - 54 x = 0

The left hand side factors into a product with four terms:

3 x (x - 9) (x + 2) = 0

Divide both sides by 3:

x (x - 9) (x + 2) = 0

Split into three equations:

x - 9 = 0 or x = 0 or x + 2 = 0

Add 9 to both sides:

x = 9 or x = 0 or x + 2 = 0

Subtract 2 from both sides:

Answer:  x = 9 or x = 0 or x = -2

3 0
3 years ago
How do you interpret expressions that represent a quantity in terms of its context?
natali 33 [55]
Interpret parts of an expression, such as terms, factors, and coefficients. Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r)n as the product of P and a factor not depending on P. Use the structure of an expression to identify ways to rewrite it.
3 0
3 years ago
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