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3 years ago

Please answer this correctly without making mistakes

Mathematics

1 answer:

LuckyWell [14K]3 years ago

8 0

Answer:

A=63.6 approximately

Step-by-step explanation:

P=14.28

p=1/4(2pi*r)

p=1/2pi*r

14.28=1/2pi*r

28.56=3.14*r

r=9...... approximately

A=1/4pi*r^2

A=0.25*3.14*81

A=63.6......approximately

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Need help to do this step by step please 3x2 - 2x=-1

sdas [7]

Answer:

Solving the expression $3x^2-2x=-1$ we get: $\mathbf{x=\frac{1+\sqrt{2}i }{3}\:or\:x=\frac{1-\sqrt{2}i }{3}}$

Step-by-step explanation:

We need to solve the expression: $3x^2-2x=-1$

This is a quadratic expression and it can be solved using quadratic formula

Solving:

$3x^2-2x=-1\\$

we can write it as:

$3x^2-2x+1=0$

The quadratic formula is: $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

where a = 3, b = -2 and c= 1

Putting values and solving:

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\x=\frac{-(-2)\pm\sqrt{(-2)^2-4(3)(1)}}{2(3)}\\x=\frac{2\pm\sqrt{4-12}}{2(3)}\\x=\frac{2\pm\sqrt{-8}}{6}\\We\:know\:that\:\sqrt{-1}=i\\x=\frac{2\pm\sqrt{8}\sqrt{-1} }{6} \\We\:know\:\sqrt{8}=\sqrt{2\times 2 \times 2}=\sqrt{2^2 \times 2}=2\sqrt{2} \\x=\frac{2\pm2\sqrt{2}i }{6}\\Now,\\x=\frac{2+2\sqrt{2}i }{6}\:or\:x=\frac{2-2\sqrt{2}i }{6}\\x=\frac{2(1+\sqrt{2}i) }{6}\:or\:x=\frac{2(1-\sqrt{2}i) }{6}\\x=\frac{1+\sqrt{2}i }{3}\:or\:x=\frac{1-\sqrt{2}i }{3}$

So, solving the expression $3x^2-2x=-1$ we get: $\mathbf{x=\frac{1+\sqrt{2}i }{3}\:or\:x=\frac{1-\sqrt{2}i }{3}}$

8 0

3 years ago

Imagine you have a job where you earn $700 each week after taxes. Your monthly living expenses include $725 for rent, $125 for u

Softa [21]

The monthly income is $844.

Given:

Weekly earning after taxes is $700
Monthly rent is $725
Monthly expense for utilities is $125

Monthly expense for cable/internet is $120

Monthly expense for cellphone is $35

Monthly expense for bus fare is $48

Minimum monthly payment of credit card debt is $78

Monthly expense for groceries is $600

Monthly expense for dining out and entertainment is $225

To find: The monthly income

The monthly income refers to the amount of money left over each month after paying all expenses.

Evaluating, we have,

The total monthly expense = $( $725 + 125 + 120 + 35 + 48 + 78 + 600 + 225$ )

That is, the total monthly expense is $1956.

It is given that weekly earning after taxes is $700. Since a month contains 4 weeks, we can say that monthly earning after taxes is $( $700 \times 4$ ), that is, $2800.

Then, monthly income is given by the difference between the monthly earnings and the monthly expenses. So, monthly income is $( $2800-1956$ ), that is, $844.