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4 years ago

Just need help with #6

Mathematics

1 answer:

Anarel [89]4 years ago

3 0

Answer:

Step-by-step explanation:

a) The rate of change is referred to as slope

Slope = change in value of y on the vertical axis / change in value of x on the horizontal axis

change in the value of y = y2 - y1

Change in value of x = x2 -x1

From the graph,

y2 = 160 = final value of y

y 1 = 260 = initial value of y

x2 = 10 = final value of x

x1 = 5 = initial value of x.

Slope = (160 - 260)/10 - 5)=-100/5

Slope = -20

b) initial height of the biker above the Canyon was 360 feets. It is reducing as the time is increasing.

c) it took the hiker 18 minutes to reach the Canyon floor.

d) After 9 minutes, the hiker was 180 feets above the Canyon floor

e) it took 7 minutes for the hiker to reach 220 feets above the Canyon floor.

f) The domain is the set of all possible values of the independent variable and the independent variable is time.

The time between which the hiker was at the maximum height and the minimum height lies between 18 minutes and 0 minutes.

The domain is 0 lesser than or equal to t lesser than or equal to 18.

The range is the set of all possible values of the dependent variable and the dependent variable is height of the hiker above the Canyon. The maximum height of the hiker was 360 feet and the minimum height of the hiker was 0 feet. Let the height be h.

The range is 0 lesser than or equal to h lesser than or equal to 360

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sineoko [7]

Recall that over an appropriate domain,

$\arcsin(x) \pm \arcsin(y) = \arcsin\left(x \sqrt{1-y^2} \pm y \sqrt{1-y^2}\right)$

Let $x=\frac1{n+1}$ and $y=\frac1{n+2}$ (these belong to the "appropriate domain", so the identity holds). We have

$\dfrac{\sqrt{n+3}}{(n+2)\sqrt{n+1}} = \dfrac1{n+1} \sqrt{\dfrac{(n+3)(n+1)}{(n+2)^2}} = \dfrac1{n+1} \sqrt{1 - \dfrac1{(n+2)^2}} = x \sqrt{1-y^2}$

and

$\dfrac{\sqrt n}{(n+1)\sqrt{n+2}} = \dfrac1{n+2} \sqrt{\dfrac{n(n+2)}{(n+1)^2}} = \dfrac1{n+2} \sqrt{1 - \dfrac1{(n+1)^2}} = y \sqrt{1-x^2}$

Then the sum telescopes, as

$\displaystyle \sum_{n=0}^\infty \arcsin\left(x \sqrt{1-y^2} - y \sqrt{1-x^2}\right) = \sum_{n=0}^\infty \left( \arcsin(x) - \arcsin(y) \right) \\\\ = \left(\arcsin(1) - \arcsin\left(\frac12\right)\right) + \left(\arcsin\left(\frac12\right) - \arcsin\left(\frac13\right)\right) + \cdots \\\\ = \arcsin(1) = \boxed{\frac\pi2}$

3 0

2 years ago

Suppose the heights of 18-year-old men are approximately normally distributed, with mean 67 inches and standard deviation 5 inch

Karolina [17]

(a) The probability that an individual is within 1 standard deviation of the mean is 0.1585

(b) The probablity that the mean of a sample of 12 is within 1 standard deviation of the population mean is 0.5116

6 0

4 years ago

How many complex roots does the equation below have? x^6+x^3+1=0

gogolik [260]

Here, x⁶ + x³ + 1 = 0
Now, Let, x³ = u
Then, x⁶ = u²

So, u² + u + 1 = 0
We know, b² - 4ac = 1² - 4(1)(1) = 1 - 4 = -3

which is negative u has two complex roots.
So there are two complex values x³.
Again, There are 3 complex cube roots of each of those two complex roots for u.

In short, Your Answer would be 3*2 = 6 Complex roots

Hope this helps!

4 0

3 years ago

Solve with algebra: <img src="https://tex.z-dn.net/?f=2%5Ex%20-%202%5E%7B-x%7D%20%3D%2012" id="TexFormula1" title="2^x - 2^{-

ValentinkaMS [17]

Answer: No solution.

Step-by-step explanation: There are no values of x that make the equation true.

Hope this helps you out.

6 0

4 years ago

6.) What is the sum of 3x² + x+8 and x? - 9 ?

Dennis_Churaev [7]

Step-by-step explanation:

= (3x² + x + 8) + (x² - 9)

= (3 + 1)x² + x + (8 - 9)

= 4x² + x - 1

5 0

3 years ago