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3 years ago

8

Find the center and radius of the circle whose equation is given below: x2 + (y − 3)2 = 16.

1 answer:

Lana71 [14]3 years ago

7 0

Answer:The circle equation image

image

Compare to the standard form of circle image

Where (h,k ) is center and r is radius of circle.

Center (0,3) radius = 4.

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The city of Anvil is currently home to 21000 people, and the population has been growing at a continuous rate of 4% per year. Th

Yanka [14]

Answer:

They'll reach the same population in approximately 113.24 years.

Step-by-step explanation:

Since both population grows at an exponential rate, then their population over the years can be found as:

$\text{population}(t) = \text{population}(0)*(1 + \frac{r}{100})^t$

For the city of Anvil:

$\text{population anvil}(t) = 21000*(1.04)^t$

For the city of Brinker:

$\text{population brinker}(t) = 7000*(1.05)^t$

We need to find the value of "t" that satisfies:

$\text{population brinker}(t) = \text{population anvil}(t)\\21000*(1.04)^t = 7000*(1.05)^t\\ln[21000*(1.04)^t] = ln[7000*(1.05)^t]\\ln(21000) + t*ln(1.04) = ln(7000) + t*ln(1.05)\\9.952 + t*0.039 = 8.8536 + t*0.0487\\t*0.0487 - t*0.039 = 9.952 - 8.8536\\t*0.0097 = 1.0984\\t = \frac{1.0984}{0.0097}\\t = 113.24$

They'll reach the same population in approximately 113.24 years.

4 0

3 years ago

Which of these functions has an inverse function? Select all that apply.

ElenaW [278]

ANSWER

y=x

y=x³

EXPLANATION

A function, f(x) has an inverse if and only if

$f(a) = f(b) \Rightarrow \: a = b$

Thus, the function is one to one.

For y=x or

$f(x) = x$

$f(a) = f(b) \Rightarrow \: a = b$

Hence this function has an inverse.

For the function y=x² or f(x)=x².

$f(a) = f(b) \Rightarrow \: {a}^{2} = {b}^{2} \Rightarrow \: a = \pm \: b$

This function has no inverse on the entire real numbers.

For the function y=x³ or f(x)=x³

$f(a) = f(b) \Rightarrow \: {a}^{3} = {b}^{3} \Rightarrow \: a = b$

This function also has an inverse.

For y=x⁴ or f(x) =x⁴

$f(a) = f(b) \Rightarrow \: {a}^{4} = {b}^{4} \Rightarrow \: a = \pm \: b$

This function has no inverse over the entire real numbers.

5 0

3 years ago

Read 2 more answers

Can anyone help me out on this question?

svp [43]

Firstly , we will check continuity at x=1

we can use method

Suppose, f(x) is continuous at x=c

then it must satisfy

$\lim_{x \to c} f(x)=f(c)$

$\lim_{x \to 1} f(x)=f(1)$

firstly , we can find limit

$\lim_{x \to 1-} f(x)= \lim_{x \to 1-}(x+3)=1+3=4$

$\lim_{x \to 1+} f(x)= \lim_{x \to 1-}(3x+1)=3*1+1=4$

so, we get

$\lim_{x \to 1} f(x)= 4$

now, we can find f(1)

$f(1)=3*1+1=4$

so, we got

$\lim_{x \to 1} f(x)=f(1) =4$

so, this is continuous at x=1

Hence , option-D...........................Answer

5 0

3 years ago

Could anyone help me out with my math questions? I'd really really appreciate it thanks

Roman55 [17]

Answer:

yes

Step-by-step explanation:

this is an answering website

6 0

3 years ago

Read 2 more answers

Daniel drew a toy from a treasure chest containing 30 different toys. He selected a bouncy ball without replacement and then sel

borishaifa [10]

Answer:

$Pr = \frac{1}{870}$

Step-by-step explanation:

Given

$n =30$

Required

Probability of selecting 2 toys of different types

From the question, we understand that all toys are different i.e. 1 of each type.

And the selection is without replacement;

So, after the first toy is selected; there are n - 1 toys left.

So, the probability is:

$Pr = \frac{1}{n} * \frac{1}{n - 1}$

Substitute $n =30$

$Pr = \frac{1}{30} * \frac{1}{30- 1}$

$Pr = \frac{1}{30} * \frac{1}{29}$

$Pr = \frac{1}{30*29}$

$Pr = \frac{1}{870}$

5 0

3 years ago