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liraira [26]
3 years ago
7

Does anyone know what irrational numbers are and if so can you explain it to me???

Mathematics
1 answer:
Romashka [77]3 years ago
3 0

An irrational number cannot be expressed as a ratio between two numbers and it cannot be written as a simple fraction because there is not a finite number of numbers when written as a decimal. <u>Instead, the numbers in the decimal would go on forever, without repeating.  Ex) .7583947262.........    It doesn't repeat and goes on forever</u>

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Answer:

160

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What is X 7x - 3 = 11
BigorU [14]

Answer:

x=2

Step-by-step explanation:

7x - 3 = 11

Add 3 to each side

7x - 3+3 = 11+3

7x = 14

Divide by 7

7x/7 = 14/7

x = 2

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A basketball player has made 60 out of 125 attempts. How many shots is he likely to make in 500 attempts?
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Step-by-step explanation:

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3 years ago
The Cartesian coordinates of a point are given. (a) (−3, 3) (i) Find polar coordinates (r, θ) of the point, where r &gt; 0 and 0
irina [24]

Answer:

a) (-3, 3)

(i) Polar coordinates (r, θ) of the point, where r > 0 and 0 ≤ θ < 2π. (r, θ)

= (3√2, 0.75π)

(ii) Polar coordinates (r, θ) of the point, where r < 0 and 0 ≤ θ < 2π. (r, θ)

= (-3√2, 1.75π)

b) (4, 4√3)

(i) Polar coordinates (r, θ) of the point, where r > 0 and 0 ≤ θ < 2π. (r, θ)

= (8, 0.13π)

(ii) Polar coordinates (r, θ) of the point, where r < 0 and 0 ≤ θ < 2π. (r, θ)

= (-8, 1.13π)

Step-by-step explanation:

We know that polar coordinates are related to (x, y) coordinates through

x = r cos θ

y = r sin θ

And r = √[x² + y²]

a) For (-3, 3)

(i) x = -3, y = 3

r = √[x² + y²] = √[(-3)² + (3)²] = √18 = ±3√2

If r > 0, r = 3√2

x = r cos θ

-3 = 3√2 cos θ

cos θ = -3 ÷ 3√2 = -(1/√2)

y = r sin θ

3 = 3√2 sin θ

sin θ = 3 ÷ 3√2 = (1/√2)

Tan θ = (sin θ/cos θ) = -1

θ = 0.75π or 1.75π

Note that although, θ = 0.75π and 1.75π satisfy the tan θ equation, only the 0.75π satisfies the sin θ and cos θ equations.

So, (-3, 3) = (3√2, 0.75π)

(ii) When r < 0, r = -3√2

x = r cos θ

-3 = -3√2 cos θ

cos θ = -3 ÷ -3√2 = (1/√2)

y = r sin θ

3 = -3√2 sin θ

sin θ = 3 ÷ -3√2 = -(1/√2)

Tan θ = (sin θ/cos θ) = -1

θ = 0.75π or 1.75π

Note that although, θ = 0.75π and 1.75π satisfy the tan θ equation, only the 1.75π satisfies the sin θ and cos θ equations.

So, (-3, 3) = (-3√2, 1.75π)

b) For (4, 4√3)

(i) x = 4, y = 4√3

r = √[x² + y²] = √[(4)² + (4√3)²] = √64 = ±8

If r > 0, r = 8

x = r cos θ

4 = 8 cos θ

cos θ = 4 ÷ 8 = 0.50

y = r sin θ

4√3 = 8 sin θ

sin θ = 4√3 ÷ 8 = (√3)/2

Tan θ = (sin θ/cos θ) = (√3)/4

θ = 0.13π or 1.13π

Note that although, θ = 0.13π and 1.13π satisfy the tan θ equation, only the 0.13π satisfies the sin θ and cos θ equations.

So, (4, 4√3) = (8, 0.13π)

(ii) When r < 0, r = -8

x = r cos θ

4 = -8 cos θ

cos θ = 4 ÷ -8 = -0.50

y = r sin θ

4√3 = -8 sin θ

sin θ = 4√3 ÷ -8 = -(√3)/2

Tan θ = (sin θ/cos θ) = (√3)/4

θ = 0.13π or 1.13π

Note that although, θ = 0.13π and 1.13π satisfy the tan θ equation, only the 1.13π satisfies the sin θ and cos θ equations.

So, (4, 4√3) = (-8, 1.13π)

Hope this Helps!!!

8 0
3 years ago
What is the vertex form of y=2x^2-8x+1
bezimeni [28]

Answer:

2(x-2)^2-7

Step-by-step explanation:

y=2x^2-8x+1

When comparing to standard form of a parabola: ax^2+bx+c

  • a=2
  • b=-8
  • c=1

Vertex form of a parabola is: a(x-h)^2+k, which is what we are trying to convert this quadratic equation into.

To do so, we can start by finding "h" in the original vertex form of a parabola. This can be found by using: \frac{-b}{2a}.

Substitute in -8 for b and 2 for a.

\frac{-(-8)}{2(2)}

Simplify this fraction.

\frac{8}{4} \rightarrow2

\boxed{h=2}

The "h" value is 2. Now we can find the "k" value by substituting in 2 for x into the given quadratic equation.

y=2(2)^2-8(2)+1

Simplify.

y=-7

\boxed{k=-7}

We have the values of h and k for the original vertex form, so now we can plug these into the original vertex form. We already know a from the beginning (it is 2).

a(x-h)^2+k\\ \\ 2(x-2)^2-7

6 0
3 years ago
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