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3 years ago

Find the exact circumference of a circle with the given radius.

2 answers:

7 0

I don't see an answer choice for this question. The equation for circumference is 2 $\pi$ r
You should get 2pi(3.5)=21.99

olya-2409 [2.1K]3 years ago

6 0

None of the answers are "exact" if you use 3.14 for pi.

That 3.14 is an approx. to pi.

If you want an exact answer, include "pi" in your answer, not a numerical value:

C = 2pi*r becomes C = 2pi(3.5 cm) = 7pi cm, or 7 $\pi$ cm

You might be interested in

List all possible rational roots. Then use synthetic division to confirm which rational roots exist:

Kisachek [45]

Answer:

$\boxed{(1) \, x = \, \pm \dfrac{1}{2}, \pm 1, \pm2, \pm \dfrac{5}{2}, \pm 5, \pm 10; (2) \, x = -2}$

Step-by-step explanation:

2x³+ 6x² - x - 10 = 0

(1) Possible roots

The Rational Roots Theorem states that, if a polynomial has any rational roots, they will have the form p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.

$\text{Possible rational root} = \dfrac{ p }{ q } = \dfrac{\text{factor of constant term}}{\text{factor of leading coefficient}}$

In your function, the constant term is -10 and the leading coefficient is 2, so

$\text{Possible root} = \dfrac{\text{factor of 10}}{\text{factor of 2}}$

Factors of 10 = ±1, ±2, ±5, ±10

Factors of 2 = ±1, ±2

$\text{Possible roots are } \large \boxed{\mathbf{x = \pm \dfrac{1}{2}, \pm 1, \pm2, \pm \dfrac{5}{2}, \pm 5, \pm 10}}$

(2) Synthetic division

Rather than work through all 12 possibilities, I will do one that works.

$\begin{array}{r|rrrr}-2 & 2 & 6 & -1 & -10\\& & -4& -4 & 10\\& 2 & 2& -5 & 0\\\end{array}$

So, x = -2 is a root, and the quotient is 2x² + 2x - 5.

(3) Check for other rational roots

2x² + 2x - 5 = 0

D = b² - 4ac =2²- 4(2)(-5) = 4 + 40 = 44

√44 = 2√11, which is irrational.

Since irrational roots come in pairs, the cubic equation has two real, irrational roots and one rational root at x = -2.

6 0

4 years ago

34.7% of city employees ride the bus to work. Last year, 5.2% of city employees rode the bus to work. What is the relative chang

DaniilM [7]

Answer:

$5.67\%$

Step-by-step explanation:

The relative change is defined by the following equation:

$Relative\hspace{3}change=\frac{x-x_r_e_f_e_r_e_n_c_e}{x_r_e_f_e_r_e_n_c_e}$ (1)

Where:

$x=Value\hspace{3}of\hspace{3}indicator\hspace{3}in\hspace{3}period\hspace{3}2$

$x_r_e_f_e_r_e_n_c_e=Value\hspace{3}of\hspace{3}indicator\hspace{3}in\hspace{3}period\hspace{3}1$

With this in mind, let's replace the values in the equation (1):

$Relative\hspace{3}change=\frac{34.7-5.2}{5.2}=\frac{29.5}{5.2}=5.673076923\approx5.67\%$

4 0

3 years ago

The mean score on a physics test was 75 points. Amy’s score was 67 points, which was 2 standard deviations below the mean. What

Norma-Jean [14]

Answer:

Its 16

Step-by-step explanation:

i had the same question and this was the answer on the unit test

7 0

2 years ago

Write the log equation as an exponential equation. You do not need to solve for x.

aliya0001 [1]

9514 1404 393

Answer:

x^2 -5x +14 = 10^(2x +4)

Step-by-step explanation:

The relationship is ...

log(a) = b ⇔ a = 10^b

Using this with a=x^2-5x+14 and b=2x+4, we have ...

x^2 -5x +14 = 10^(2x +4)

_____

Additional comments

In plain text, the exponent needs parentheses, because superscript formatting is not available to tell what is and isn't part of the exponent.

The base of "log" is assumed to be 10 in high school algebra. In the larger world, "log" is often used in place of "ln" to mean the logarithm to base 'e'.

The one solution is approximately x = −1.32505947996.

8 0

3 years ago

Which would it be? 1. 2143.57 2. 17,148.59 3. 1607.68

Vadim26 [7]

It’s 17,148,59 I believe pls mark me :)

5 0

3 years ago