Pls help ! MAPPING SHAPES A) only sequence a b) only sequence b c)both d) neither

How do you factor: step by step <img src="https://tex.z-dn.net/?f=%20%7Bx%7D%5E%7B3%7D%20-%20%7Bx%7D%5E%7B2%7D%20%20%2B%20x%2

Trava [24]

Answer:

It is 1

Step-by-step explanation:

6 0

3 years ago

Please help me out when u can ty

Ket [755]

Answer:

Ian's pattern: 15, 31, 63, and 127.

Nicole's pattern: 485, 1457, and 4373.

Have a nice rest of your day :)

6 0

3 years ago

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on a winter’s morning, the temperature was 0°F. The temperature increased during the daytime. At night, the temperature decrease

TEA [102]

Answer:

6 degrees F

Step-by-step explanation:

It's asking for the temperature change which it went down to 0 degrees F then went back up to 6 which only means it changed by 6 degrees F.

5 0

3 years ago

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4. Using the geometric sum formulas, evaluate each of the following sums and express your answer in Cartesian form.

nikitadnepr [17]

Answer:

$\sum_{n=0}^9cos(\frac{\pi n}{2})=1$

$\sum_{k=0}^{N-1}e^{\frac{i2\pi kk}{2}}=0$

$\sum_{n=0}^\infty (\frac{1}{2})^n cos(\frac{\pi n}{2})=\frac{1}{2}$

Step-by-step explanation:

$\sum_{n=0}^9cos(\frac{\pi n}{2})=\frac{1}{2}(\sum_{n=0}^9 (e^{\frac{i\pi n}{2}}+ e^{\frac{i\pi n}{2}}))$

$=\frac{1}{2}(\frac{1-e^{\frac{10i\pi}{2}}}{1-e^{\frac{i\pi}{2}}}+\frac{1-e^{-\frac{10i\pi}{2}}}{1-e^{-\frac{i\pi}{2}}})$

$=\frac{1}{2}(\frac{1+1}{1-i}+\frac{1+1}{1+i})=1$

2nd

$\sum_{k=0}^{N-1}e^{\frac{i2\pi kk}{2}}=\frac{1-e^{\frac{i2\pi N}{N}}}{1-e^{\frac{i2\pi}{N}}}$

$=\frac{1-1}{1-e^{\frac{i2\pi}{N}}}=0$

3th

$\sum_{n=0}^\infty (\frac{1}{2})^n cos(\frac{\pi n}{2})==\frac{1}{2}(\sum_{n=0}^\infty ((\frac{e^{\frac{i\pi n}{2}}}{2})^n+ (\frac{e^{-\frac{i\pi n}{2}}}{2})^n))$

$=\frac{1}{2}(\frac{1-0}{1-i}+\frac{1-0}{1+i})=\frac{1}{2}$

What we use?

We use that

$e^{i\pi n}=cos(\pi n)+i sin(\pi n)$

and

$\sum_{n=0}^k r^k=\frac{1-r^{k+1}}{1-r}$

6 0

3 years ago

A fire station is to be located along a road of length A, A < q. If fires occur at points uniformly chosen on (0, A), where s

Shtirlitz [24]

Answer:

Step-by-step explanation:

Given that X is uniform in the interval (0,A)

X is continuous since it represents the distance

A fire station is to be located along a road of length A, A < q. If fires occur at points uniformly chosen on (0, A), we should find where the station be located so as to minimize the expected distance from the fire

Distance can be taken as absolute values here as either side is the same.

E(|x-a|] is to be minimum

E(|x-a|)=E(x-a) for 0<x<a

=E(a-x), for a<x<A

Using integral we find this value

$E(|x-a|)=\int\limits^a_0 {x-a} \, dx +=\int\limits^A_a -{x-a} \, dx\\f(a)=\frac{a^2}{2} -\frac{(A-a)^2}{2}$

$f(a)=\frac{a^2}{2} +\frac{(A-a)^2}{2} \\f'(a) = a-(A-a)\\f"(a) =2$

Using calculus we find that f" is positive so when f' =0 we get solution

f'(a) =0 gives

$a=\frac{A}{2}$

Hence fire station to be located at the mid point of 0 and A

8 0

4 years ago