30 pts.!!!!

Each side of a square is increasing at a rate of 6 cm/s. At what rate is the area of the square increasing when the area of the

siniylev [52]

<u>Solution:</u> 48cm/s^2

<u>Working:</u>

A = s^2

Derivate s^2 (as it is area formula) which gives

dA/dt = 2s dL/dt

dL/dt = 6cm/s

Hence,

2(6) = 12

Side: 4cm

Hence,

dA/dt = (4)(12) = 48cm/s^2

<em>Feel free to mark this as brainliest :D</em>

7 0

2 years ago

Determine the location of a point (x, y, z) that satisfies the given condition. xyz > 0

ollegr [7]

Xyz>0, a-location of a point
if
a∈{{x<0∧y<0∧z>0}∨{x>0∧y<0∧z<0}∨{x<0∧y>0∧z<0}∨{x>0∧y>0∧z>0}}

8 0

3 years ago

Darren wants to estimate the mean age in a population of trees. He'll sample nnn trees and build a 90\%90%90, percent confidence

Alchen [17]

Using the z-distribution, as we have the standard deviation for the population, it is found that the smallest sample size required to obtain the desired margin of error is of 77.

<h3>What is a z-distribution confidence interval?</h3>

The confidence interval is:

$\overline{x} \pm z\frac{\sigma}{\sqrt{n}}$

In which:

$\overline{x}$ is the sample mean.

z is the critical value.

n is the sample size.

$\sigma$ is the standard deviation for the population.

The margin of error is given by:

$M = z\frac{\sigma}{\sqrt{n}}$

In this problem, we have that the parameters are given as follows:

$M = 3, z = 1.645, \sigma = 16$ .

Hence, solving for n, we find the sample size.

$M = z\frac{\sigma}{\sqrt{n}}$

$3 = 1.645\frac{16}{\sqrt{n}}$

$3\sqrt{n} = 1.645 \times 16$

$\sqrt{n} = \frac{1.645 \times 16}{3}$

$(\sqrt{n})^2 = \left(\frac{1.645 \times 16}{3}\right)^2$

$n = 76.97$

Rounding up, the smallest sample size required to obtain the desired margin of error is of 77.

More can be learned about the z-distribution at brainly.com/question/25890103

4 0

1 year ago

Item 12 What is the shape of the cross section of the cylinder in each situation? Drag and drop the answer into the box to match

Goryan [66]

You can build a cylinder in two ways: either you draw a circle on a plane, and "raise" it perpendicularly to the plane itself, or you start with a rectangle, and rotate it around one of its sides.

For these reasons, if you cut the cylinder with a plane parallel to the base you have a circular cross section, while if you cut the cylinder with a plane perpendicular to the base you have a rectangular cross section.

5 0

3 years ago

Read 2 more answers

What is the number of positive integers not larger than 210 and not divisible by 2, 3 or 7?

vladimir1956 [14]

Number of +ve integers divisible by 2 less than or equal to 210=a=210/2=105

number of +ve integers divisible by 3 less than or equal to 210=b=210/3=70

number of +ve integers divisible by 7 less than or equal to 210=c=210/7=30

number of +ve integers divisible by 2&3 less than or equal to 210=d=210/6=35

number of +ve integer divisible by 2&7 less than or equal to 210=e=210/14=15

number of +ve integer divisible by 3&7 less than or equal to 210=e=210/21=10

number of +ve integer divisible by 2&7&3 less than or equal to 210=e=210/42=5

<span>number of positive integers not larger than 210 and divisible by 2, 3 or 7=105+70+30-(35+15+10)+5

=150

so numbers not divisible=total-150
=210-150
=</span>60

7 0

3 years ago