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2 years ago

Find the area of a circle with a circumference of 31.5 units

Mathematics

1 answer:

Westkost [7]2 years ago

6 0

Answer:

79 units²

Step-by-step explanation:

The area of a circle is found by using the formula A = π x r². Since we are not given the radius we can use the formula r = C / (2π). Substituting in the given values, we get r = 31.5/(2π). 2 times pi is 6.283185307. 31.5 divided by this will get you 5.013380707. Now, put that value in for r in the area equation. A = π x 5.013380707². Pi times 5.013380707² equals 78.96074613. This can be rounded to 79. (Or 80 if you need to the nearest whole number.)

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2x2 – 5x + 67 = 0<br> What would be your first step in completing the square for the equation above?

7nadin3 [17]

Answer:

The first step is to divide all the terms by the coefficient of $x^{2}$ which is 2.

The solutions to the quadratic equation $2x^2\:-\:5x\:+\:67\:=\:0$ are:

$x=\frac{5}{4}+i\frac{\sqrt{511}}{4},\:x=\frac{5}{4}-i\frac{\sqrt{511}}{4}$

Step-by-step explanation:

Considering the equation

$2x^2\:-\:5x\:+\:67\:=\:0$

The first step is to divide all the terms by the coefficient of $x^{2}$ which is 2.

$\frac{2x^2-5x}{2}=\frac{-67}{2}$

$x^2-\frac{5x}{2}=-\frac{67}{2}$

Lets now solve the equation by completeing the remaining steps

Write equation in the form: $x^2+2ax+a^2=\left(x+a\right)^2$

Solving for $a$ ,

$2ax=-\frac{5}{2}x$

$a=-\frac{5}{4}$

$\mathrm{Add\:}a^2=\left(-\frac{5}{4}\right)^2\mathrm{\:to\:both\:sides}$

$x^2-\frac{5x}{2}+\left(-\frac{5}{4}\right)^2=-\frac{67}{2}+\left(-\frac{5}{4}\right)^2$

$x^2-\frac{5x}{2}+\left(-\frac{5}{4}\right)^2=-\frac{511}{16}$

Completing the square

$\left(x-\frac{5}{4}\right)^2=-\frac{511}{16}$

Since, you had required to know the first step in completing the square for the equation above, I hope you have got the point, but let me quickly solve the remaining solution.

For $f^2\left(x\right)=a$ the solution are $f\left(x\right)=\sqrt{a},\:-\sqrt{a}$

Solving

$x-\frac{5}{4}=\sqrt{-\frac{511}{16}}$

$x-\frac{5}{4}=\sqrt{-1}\sqrt{\frac{511}{16}}$

$x-\frac{5}{4}=i\sqrt{\frac{511}{16}}$ ∵ Applying imaginary number rule $\sqrt{-1}=i$

$x-\frac{5}{4}=i\frac{\sqrt{511}}{\sqrt{16}}$

$-\frac{5}{4}=i\frac{\sqrt{511}}{4}$

$x=\frac{5}{4}+i\frac{\sqrt{511}}{4}$

Similarly, solving

$x-\frac{5}{4}=-\sqrt{-\frac{511}{16}}$

$x-\frac{5}{4}=-i\frac{\sqrt{511}}{4}$ ∵ Applying imaginary number rule $\sqrt{-1}=i$

$x=\frac{5}{4}-i\frac{\sqrt{511}}{4}$

Therefore, the solutions to the quadratic equation are:

$x=\frac{5}{4}+i\frac{\sqrt{511}}{4},\:x=\frac{5}{4}-i\frac{\sqrt{511}}{4}$

4 0

2 years ago

Which expressions are polynomials? select each correct answer

Zielflug [23.3K]

Note:
A polynomial of order n is of the form
$f(x)=a_{n}x^{n}+a_{n-1}x^{n-1} + \, ..., \, +a_{1}x+a_{0}$
where the a's are constants.

Consider the given expressions.
x/5 + 2 Not a polynomial
35x² It is a polynomial of order 2
7x⁷ - x⁵ It is a polynomial of order 7
4x + √(x-1) It is not a polynomial

Answer:
The polynomials are
35x²
7x⁷ - x⁵

8 0

2 years ago

A student solved this problem and said the answer is 1 3/4 quarts. Gary mixed 1/4 quart of plain milk and 2/3 quart of chocolate

levacccp [35]

Gary is wrong. the answer is 11/12.

1/4 + 2/3= n
1/4= 3/12
2/3= 8/12
3/12+8/12= 11/12 .
So, the answer cannot be 1 & 3/4.

6 0

2 years ago

The measure of an angle is 32.6º. What is the measure of its supplementary angle?

dalvyx [7]

Answer:

147.4°

Step-by-step explanation:

Supplementary angles sum to 180° , then

supplementary angle = 180° - 32.6° = 147.4°

8 0

2 years ago

Read 2 more answers

The Salami and More Deli sells a 5-foot submarine sandwich for parties. It weighs 8 pounds. Assuming that the weight per foot is

laiz [17]

Answer:

7.5 feet long

Step-by-step explanation:

if I had one, 5 foot sandwich, I would have 8 pounds. if I had 2.5 more foot of sandwich I would have 4 more pounds ( because 2.5 feet is half of 5 feet which means we would have to divide 8 pounds by 2). which means I have 8 pounds and 4 pounds, which equals 12 pounds. I also have 5 feet and 2.5 feet of sandwich which is equal to 7.5 feet. since it's asking the length of a 12 pound sandwich, your answer is 7.5 feet long.

5 0

1 year ago