How much greater is 300 than3?

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

Multi-Step Max's school bought boxes of

Dovator [93]

Answer:

564 pencils

Step-by-step explanation:

1 box = 12 pencils

25 boxes = 25 × 12 pencils = 300 pencils

22 boxes = 22 × 12 pencils = 264 pencils

300 + 264 = 564 pencils

8 0

3 years ago

Fabio and Gwen are saving money to buy a new gaming station. They need at least $510 to purchase the new gaming station. Gwen we

Phoenix [80]

Answer-

Set of constraints to model the problem are,

$12x+9y\geq 510$

$y \leq 2x$

$y \geq 25$

Solution-

x = the number of lawns weeded by Gwen,

y = the number of dogs walked by Fabio.

1.

As, Gwen charges $12 each time she weeds a yard and Fabio charges $9 each time he walks a dog,

$\text{Earnings of Gwen} = 12x$

$\text{Earnings of Fabio} = 9y$

$\text{Total earning} = 12x+9y$

They need at least $510 to purchase the new gaming station, means they need $510 or more than $510.

The equation for this is,

$12x+9y\geq 510$

2.

The number of dog walks that Fabio has scheduled is no more than twice the number of yards Gwen has scheduled to weed, means

y must be less than or equal to 2x.

The equation for this is,

$y \leq 2x$

3.

Fabio will walk at least 25 dogs, means y must be greater than of equal to 25.

The equation for this is,

$y \geq 25$

8 0

3 years ago

Read 2 more answers

PLEASE ANSWER ASAP REALLY EASY QUESTION WILL GET BRAINLEST!!!!!!!!!!!

-Dominant- [34]

Answer:

random since it doesn't have a specific opinion, it is required by bank service

Step-by-step explanation:

3 0

3 years ago

A machine that produces a major part for an airplane engine is monitored closely. In the past, 10% of the parts produced would b

nata0808 [166]

Answer:

With a .95 probability, the sample size that needs to be taken if the desired margin of error is .04 or less is of at least 216.

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.