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3 years ago

Best explained and correct answer gets brainliest!

Mathematics

1 answer:

Hunter-Best [27]3 years ago

5 0

Given two points: A(x₁,y₁) and B(x₂,y₂), the slope of the line that passes through these points will be:
m=(y₂-y₁)/(x₂-x₁)

If we take two points of this line (3,0) and (3,1) and calculate the slope, we have:
m=(1-0)(0/0)=1/0 (any number divided by zero gives an indetermined value).

Therfore the slope is undefined.

Answer: D The slope is undefined.

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At the Tesla factory, a machine tests 1 out of every 75 windshields produced for quality. The machine requires a safety inspecti

Sloan [31]

Answer:

pretty sure it's 675

Step-by-step explanation:

could be wrong but if there are 303,750 windsheilds per year and the machine needs an inspection after every 450 you just divide them.

6 0

3 years ago

Sam collects baseball cards. He gave 6 cards to his brother. He then got 4 new cards from his father. Sam now has 12 cards. How

JulijaS [17]

Answer:

Step-by-step explanation:

If he had 14 then he gave away 6, he'd have 8. 8 plus 4 is 12. He had 14 before giving any away.

8 0

3 years ago

Read 2 more answers

happy paws $17.00 plus $3.50 per hour to keep a dog during the day. Woof charges $11.00 plus $4.75 per hour. complete equeation

yKpoI14uk [10]

Answer:

3.50h + 17

4.75h + 11

Step-by-step explanation:

3.50 per hour times the hours, h, plus the fee, 17

4.75 per hour times the hours, h, plus the fee, 11

4 0

3 years ago

A bacteria culture starts with 400 bacteria and grows at a rate proportional to its size. After 4 hours, there are 9000 bacteria

Kaylis [27]

Answer:

A) The expression for the number of bacteria is $P(t) = 400e^{0.7783t}$ .

B) After 5 hours there will be 19593 bacteria.

C) After 5.55 hours the population of bacteria will reach 30000.

Step-by-step explanation:

A) Here we have a problem with differential equations. Recall that we can interpret the rate of change of a magnitude as its derivative. So, as the rate change proportionally to the size of the population, we have

$P' = kP$

where $P$ stands for the population of bacteria.

Writing $P'$ as $\frac{dP}{dt}$ , we get

$\frac{dP}{dt} = kP$ .

Notice that this is a separable equation, so

$\frac{dP}{P} = kdt$ .

Then, integrating in both sides of the equality:

$\int\frac{dP}{P} = \int kdt$ .

We have,

$\ln P = kt+C$ .

Now, taking exponential

$P(t) = Ce^{kt}$ .

The next step is to find the value for the constant $C$ . We do this using the initial condition $P(0)=400$ . Recall that this is the initial population of bacteria. So,

$400 = P(0) = Ce^{k0}=C$ .

Hence, the expression becomes

$P(t) = 400e^{kt}$ .

Now, we find the value for $k$ . We are going to use that $P(4)=9000$ . Notice that

$9000 = 400e^{k4}$ .

Then,

$\frac{90}{4} = e^{4k}$ .

Taking logarithm

$\ln\frac{90}{4} = 4k$ , so $\frac{1}{4}\ln\frac{90}{4} = k$ .

So, $k=0.7783788273$ , and approximating to the fourth decimal place we can take $k=0.7783$ . Hence,

$P(t) = 400e^{0.7783t}$ .

B) To find the number of bacteria after 5 hours, we only need to evaluate the expression we have obtained in the previous exercise:

$P(5) =400e^{0.7783*5} = 19593.723 \approx 19593$ .

C) In this case we want to do the reverse operation: we want to find the value of t such that

$30000 = 400e^{0.7783t}$ .

This expression is equivalent to

$75 = e^{0.7783t}$ .

Now, taking logarithm we have

$\ln 75 = 0.7783t$ .

Finally,

$t = \frac{\ln 75}{0.7783} \approx 5.55$ .

So, after 5.55 hours the population of bacteria will reach 30000.

6 0

3 years ago

lim x rightarrow 0 1 - cos ( x2 ) / 1 - cosx The limit has to be evaluated without using l'Hospital'sRule.

zaharov [31]

Answer with Step-by-step explanation:

Given

$f(x)=\frac{1-cos(2x)}{1-cos(x)}\\\\\lim_{x \rightarrow 0}f(x)=\lim_{x\rightarrow 0}(\frac{1-(cos^2{x}-sin^2{x})}{1-cos(x)})\\\\(\because cos(2x)=cos^2x-sin^2x)\\\\\lim_{x \rightarrow 0}f(x)=\lim_{x\rightarrow 0}(\frac{1-cos^2x}{1-cos(x)}+\frac{sin^2x}{1-cosx})\\\\=\lim_{x\rightarrow 0}(\frac{(1-cosx)(1+cosx)}{1-cosx}+\frac{sin^2x}{1-cosx})\\\\=\lim_{x\rightarrow 0}((1+cosx)+\frac{sin^2x}{1-cosx})\\\\\therefore \lim_{x \rightarrow 0}f(x)=1$

6 0

3 years ago