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3 years ago

Write in standard form y=2(x-1)^2+6

Mathematics

1 answer:

vlabodo [156]3 years ago

4 0

Answer:

Y=2x+2

Step-by-step explanation:

Im not 100% sure this is correct but what I did was

Y=2(x-1)^2+6

2(x-1) = 2x -2

Y=2x -2^2 +6

Y=2x -4 + 6

-4 + 6 = 2

So y=2x+2 (y=mx+b)

I hope this helps you

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Nora is flying a kite, holding her hands a distance of 3 feet above the ground and

jek_recluse [69]

Answer:

$55.7 feet$

Step-by-step explanation:

$h=\sin{\left(23\right)\times135}$

$\sin{23}\approx0.39$

$h=0.39\times135=52.65\left(feet\right)\$

$H=h+3$

$=52.65+3$

$=55.65\left(feet\right)$

$55.65\ feet\approx55.7\ feet$

I hope this helps you

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5 0

2 years ago

Y=9x+30 what’s the answer i need help

zmey [24]

Answer: look at the picture

Step-by-step explanation: hope this help:)

8 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

4 years ago

Given the formula PV = nRT , solve for the variable T

aleksley [76]

T=PV/Rn you just divide both sides by Rn

8 0

3 years ago

Your friend is looking at laptops for college, and is comparing the different screen sizes. Use the diagram and formula below to

elena-14-01-66 [18.8K]

For this case what we should do is write correctly the given equation:
D ^ 2 = W ^ 2 + H ^ 2
We substitute the values:
D = 17inch
H = 9inch
Substituting:
17 ^ 2 = W ^ 2 + 9 ^ 2
We clear the value of W:
W = root (17 ^ 2 - 9 ^ 2)
W = 14.4 inch
Answer:
The width of the laptop screen is:
D. W = 14.4 inch

5 0

3 years ago

Read 2 more answers