Evaluate functions <br> g(0)=-x-2

Suppose you are climbing a hill whose shape is given by the equation z = 1400 − 0.005x2 − 0.01y2, where x, y, and z are measured

Anarel [89]

Answer: You start to ascend

Explanation:

Since you are walking due south and the positive y-axis points north, the y-coordinate decreases.

Let

$y'$ = y-coordinate after walking due south
$z'$ = z-coordinate (or the height) after walking due south

So, the point where you stand after walking due south has a coordinate of $(100, y', z')$ . Moreover,

$z' = 1,400 - 0.05(100)^2 - 0.01(y')^2
\\ \boxed{z' = 1350 - 0.01(y')^2}$

Since the y-coordinate decreases after walking due south and $z' = 1350 - 0.01(y')^2$ ,

$y' \leq 120\\ \Rightarrow (y')^2 \leq 120^2 = 14,400\\ \Rightarrow -0.01(y')^2 \geq -0.01(14,400) = -144\\ \Rightarrow z' = 1,350 - 0.01(y')^2 \geq 1,350 - 0.01(14,400) = 1,206\\ \Rightarrow \boxed{z' \geq 1,206}$

So, the height after walking due south exceeds 1,206 meters, which is the previous height before walking due south. Therefore, if you walk due south from point with coordinates (100, 120, 1206), you are ascending.

5 0

3 years ago

WILL MAKE BRAINLIEST!!! A Ferris wheel has a diameter of 220 feet and the center of the wheel is 125 feet above the ground. The

daser333 [38]

Since the radius of a circle is half its diameter, the radius of our Ferris wheel is $r= \frac{220}{2} =110$ ft

Next, we are going to convert from revolutions per minute to degrees per second.
We know that t<span>he wheel makes a complete turn every 2 minutes, so it makes a complete turn in 120 seconds. Since there are 360° in a complete turn, we can set up our conversion factor:
</span> $\frac{1*360}{120}=3$ degrees per second
<span>
Now, lets find the height:
</span>We know that <span>the passenger is at the lowest point on the wheel when t=0; since the wheel is 125 feet above the ground, at t=0 h=125. To find t at the top, we are going to take advantage of the fact that the wheel will turn 180° from the lowest point to the top and that it turns 3° every second:
</span> $t= \frac{180}{3}$
$t=60$
Notice that the height at the top is the diameter of the wheel plus the height above the ground, so $h=220+125=345$ .

To model the situation we are going to use the cosine function, but notice that $cos (\alpha)$ is 1 when $\alpha =0$ and -1 wen $\alpha =180$ . Since we want the opposite, we are going to use negative cosine.
Notice that we want $\alpha =180$ when $t=60$ , so we are going to use $-cos(3t)$ . Next, we are going to multiply our cosine by the radius of our wheel: $-110cos(3t)$ , and last but not least we are going to add the sum of the radius of the wheel plus the height above the ground:
$h=110+125-110cos(3t)$
$h=225-110cos(3t)$

Now that we have our height function lets check if everything is working:
<span>the passenger is at the lowest point at t=0; we also know that the lowest point is 125 feet above the ground, so lets evaluate our function at t=0:
</span> $h=225-110cos(3t)$
$h=225-110cos(3*0)$
$h=125$ feet
So far so good.
We also know that at t=60, our passenger is 345 feet above the ground, so lets evaluate our function at t=60 and check if coincides:
$h=225-110cos(3t)$
$h=225-110cos(3*60)$
$h=225-110cos(180)$
$h=345$ feet

We can conclude that cosine function that express the height h (in feet) of a passenger on the wheel as a function of time t (in minutes) ) is: $h=225-110cos(3t)$

8 0

3 years ago

What is 6 1/4 x 3 3/5

aliya0001 [1]

Answer:

Step-by-step explanation:

Change mixed fraction to improper fraction. Then reduce to lowest term if possible.

6 1/4 x 3 3/5 = 25/4 * 18/5 = 25* 18 /4*5

= 5 * 18 / 4 {giving by 5th table}

= 5* 9 /2 { giving by 2nd tables}

= 45/2

8 0

3 years ago

Can y’all pls help with number 6

barxatty [35]

1500x1.04^6=£1898 to the nearest whole number

8 0

3 years ago

If you calculate sle to be $25,000 and that there will be one occurrence every four years (aro), then what is the ale?

Cloud [144]

If you calculate SLE to be $25,000 and that there will be one occurrence every four years (ARO), then the ALE is $40,000.

<h3>What is Single-loss expectancy (SLE)?</h3>

A expected monetary decline each moment an asset is at risk is referred to as single-loss expectancy (SLE). It is a term that is most frequently used during risk analysis and attempts to assign a monetary value to each individual threat.

Quantitative risk analysis predicts the likelihood of certain risk outcomes as well as their approximate monetary cost using relevant, verifiable data.

IT professionals must consider a wide range of risks, including the following:

Errors caused by humans
Cyber attacks, unauthorised data disclosure, or data misuse are examples of hostile action.
Errors in application
System or network failures
Physical harm caused by fire, natural disasters, or vandalism.

To know more about the Single-loss expectancy (SLE), here

brainly.com/question/14587600

#SPJ4

5 0

1 year ago

Evaluate functions g(0)=-x-2