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4 years ago

Compute the distance between (a,b,c) and (-2,5,6).

Mathematics

2 answers:

yan [13]4 years ago

8 0

Answer:

b. sqrt(a+2)^2+(b-5)^2+(c-6)^2

Step-by-step explanation:

Use distance formula

sqrt (a-(-2)^2 + (b-5)^2 + (c-6) ^2

sqrt (a+2)^2 +(b+5)^2 + (c-6)^2

Elza [17]4 years ago

7 0

Answer:

Step-by-step explanation:

took it on edge, it's the right answer :)

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What is the length of BC ?<br>

galben [10]

The answer is c.

Since a^2+b^2=c^2, b^2=c^2-a^2 thus,
16=4-b^2= srt. of 12

7 0

3 years ago

Read 2 more answers

Marine scientists categorize signature whistles of bottlenose dolphins by typelong dash—type a, type b, type c, etc. In one s

r-ruslan [8.4K]

Answer:

The 95% confidence interval for the true proportion of bottlenose dolphin signature whistles that are type a whistles is (0.4687, 0.6123).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

For this problem, we have that:

$n = 185, \pi = \frac{100}{185} = 0.5405$

95% confidence level

So $\alpha = 0.05$ , z is the value of Z that has a pvalue of $1 - \frac{0.05}{2} = 0.975$ , so $Z = 1.96$ .

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.5405 - 1.96\sqrt{\frac{0.5405*0.4595}{185}} = 0.4687$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.5405 + 1.96\sqrt{\frac{0.5405*0.4595}{185}} = 0.6123$

The 95% confidence interval for the true proportion of bottlenose dolphin signature whistles that are type a whistles is (0.4687, 0.6123).

3 0

4 years ago

Hamburger sells 3 pounds for six dollars if Samantha 510 pounds of hamburger how much will she pay

Lina20 [59]

I believe you meant to say that if Samantha bought 510 pounds of hamburger, how much will she pay?

Now from the information we already have, we know that 3 pounds of hamburger will cost 6 dollars.

The next thing we need to know is how much one pound of hamburger will cost. This will help us calculate how much the rest will cost.

we now form an equation to assist us.
3 = 6
1= x

(where x represents the unknown price of one pound of hamburger)

Now we must cross-multiply:

3 * x = 6 x 1

3x = 6

x = 6/3

x = 2

therefore one pound of hamburger costs 2 dollars.

Now, If one pound costs 2 dollars, how about 510 pounds?

We simply multiply: 510 x 2 = 1,020

Therefore Samantha will pay 1, 020 dollars for 510 pounds of hamburger.

5 0

3 years ago

Solve y'' + 10y' + 25y = 0, y(0) = -2, y'(0) = 11 y(t) = Preview

svetlana [45]

Answer: The required solution is

$y=(-2+t)e^{-5t}.$

Step-by-step explanation: We are given to solve the following differential equation :

$y^{\prime\prime}+10y^\prime+25y=0,~~~~~~~y(0)=-2,~~y^\prime(0)=11~~~~~~~~~~~~~~~~~~~~~~~~(i)$

Let us consider that

$y=e^{mt}$ be an auxiliary solution of equation (i).

Then, we have

$y^prime=me^{mt},~~~~~y^{\prime\prime}=m^2e^{mt}.$

Substituting these values in equation (i), we get

$m^2e^{mt}+10me^{mt}+25e^{mt}=0\\\\\Rightarrow (m^2+10y+25)e^{mt}=0\\\\\Rightarrow m^2+10m+25=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~[\textup{since }e^{mt}\neq0]\\\\\Rightarrow m^2+2\times m\times5+5^2=0\\\\\Rightarrow (m+5)^2=0\\\\\Rightarrow m=-5,-5.$

So, the general solution of the given equation is

$y(t)=(A+Bt)e^{-5t}.$

Differentiating with respect to t, we get

$y^\prime(t)=-5e^{-5t}(A+Bt)+Be^{-5t}.$

According to the given conditions, we have

$y(0)=-2\\\\\Rightarrow A=-2$

and

$y^\prime(0)=11\\\\\Rightarrow -5(A+B\times0)+B=11\\\\\Rightarrow -5A+B=11\\\\\Rightarrow (-5)\times(-2)+B=11\\\\\Rightarrow 10+B=11\\\\\Rightarrow B=11-10\\\\\Rightarrow B=1.$