What is an equation of the line that passes through the points (-7,7) and (3,7)

E temperature t of a metal sphere is inversely proportional to the distance from the centre of the sphere (the origin (0, 0, 0))

olasank [31]

(-x, -y, -z) the vector form (x, y, z) to the origin, in the direction of the greatest increase.

<h3>How to calculate temperature?</h3>

The quantity or amount of radiation contained in material or item, as measured by a temperature or sensed by touch and stated on a numerical scale.

The temperature T of a ball bearing is inverse to the length first from the origin, which we consider to be the center of the ball. The temperature at the exact location

(x, y, z) is a point on the sphere, the temperature at this point is given by

$T(x,y,z)= \dfrac{k}{(x^2 +y^2+z^2)^{1/2}}$

Where k is constant, then we have

T(1, 2, 2) = k/3 = 170

k = 510

So

$T(x,y,z)= \dfrac{510}{(x^2 +y^2+z^2)^{1/2}}$

Then we have

$\rm \triangledown T = \left ( -\dfrac{510x}{(x^2 +y^2+z^2)^{1/2}}, -\dfrac{510y}{(x^2 +y^2+z^2)^{1/2}}, \dfrac{510z}{(x^2 +y^2+z^2)^{1/2}} \right )\\\\\\\triangledown T (1, 2, 2) = -\dfrac{510}{27} (1, 2, 2) =-\dfrac{170}{9} (1, 2, 2)$

Then the direction will be from (1, 2, 2) to (4, 3, 5) will be (3, 1, 3)

So u = (3/√19, 1/√19, 3/√19)

Then we get

$\rm \triangledown T \cdot u = \dfrac{-170}{9}(1, 2, 2) \cdot \left (\dfrac{3}{\sqrt{19}}, \dfrac{1}{\sqrt{19}}, \dfrac{3}{\sqrt{19}} \right )\\\\\\\triangledown T \cdot u = - \dfrac{170}{9\sqrt{19}} (3 + 2 + 6)\\\\\\\triangledown T \cdot u = -\dfrac{1870}{9\sqrt{19}}$

The direction of the greatest inverse in the temperature is given by any vector parallel to and having the same direction $\triangledown$ T. (-x, -y, -z) the vector form (x, y, z) to the origin, in the direction of the greatest increase.

More about the temperature link is given below.

brainly.com/question/11464844

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6 0

2 years ago

Thaddeus and lan start at the same location and drive in opposite directions, but leave at different times. When they are 365 mi

LUCKY_DIMON [66]

Answer:

Thaddeus: 7 h
Ian: 9 h

Step-by-step explanation:

If Thaddeus drives the whole 16 hours, the distance between them is ...

distance = speed · time

distance = 20 mi/h · 16 h

distance = 320 miles.

It is 45 miles more than that. For each hour that Ian drives, their separation distance increases by (25 mph -20 mph)·(1 h) = 5 mi. Then Ian must have driven ...

(45 mi)/(5 mi/h) = 9 h

The rest of the 16 hours is the time that Thaddeus drove: 7 hours.

___

Let x represent the time Ian drives. Then 16-x is the time Thaddeus drives. Their total distance driven is ...

distance = speed · time

365 mi = (25 mi/h)(x) + (20 mi/h)(16 h -x)

45 mi = (5 mi/h)(x) . . . . . . . . subtract 320 miles, collect terms

(45 mi)/(5 mi/h) = x = 9 h . . . . . . divide by the coefficient of x

_____

Comment on the solution

You may notice a similarity between the solution of this equation and the verbal discussion above. (That is intentional.) It works well to let a variable represent the amount of the highest contributor. Here, that is Ian's time, since he is driving at the fastest speed.

4 0

3 years ago

Correct Answers only!

aleksley [76]

Answer:

$128000

Step-by-step explanation:

Using the given formula :

I = P × R × T

I = 80000 × 15/100 × 4

I = $48000

He saves = 48000 +80000 = $128000

3 0

3 years ago

Trevor rode his bicycle 25 miles in 2 hours. Assuming Trevor rode at a constant speed, how many miles did Trevor ride in one hou

11Alexandr11 [23.1K]

So for this one all you have to do is find the average. Simply do 25 divided by 2 to get 12.5 miles per hour.

3 0

4 years ago

The personnel department of a large corporation wants to estimate the family dental expenses of its employees to determine the f

Verizon [17]

Answer:

CI(95%): [205,5;400.8]dolars

Step-by-step explanation:

Hello!

So you need to construct a confidence interval for the average family dental expenses (μ) using the sample given in the problem. To estimate it you need to first choose a statistic. For this small sample, considering that the variable has a normal distribution (I made a quick Shapiro Wilks test, with p-value 0.3234, you can assume normality) the best statistic to use is the Student's t-test.

t= [x(bar)-μ]/S/√n ≈ t₍ₙ₋₁₎

The formula for the confidence interval to estimate the mean is

x(bar)± $t_{n-1; 1-\alpha/2}$ * (S/√n)

The critical value is from a t-distribution with 11 degrees of freedom

± $t_{n-1; 1-\alpha/2} = t_{11; 0.975} = 2.201$

>remember since it's two-tailed, to get the right critical value you have to divide α by 2. So in the text, you received a confidence level of 1-α=0.95 so α=0.05 then α/2=0.025 and 1-α/2=0.975

To construct the interval, you need to first calculate the sample mean and the standard derivation.

Sample

115; 370; 250; 593; 540; 225; 117; 425; 318; 182; 275; 228

n= 12

∑xi = 3638 ∑xi² = 1362670

Sample mean

x(bar): (∑xi)/n = 3638/12 = 303.17 dolars

Standard derivation

S²= 1/n-1*[∑xi²- (∑xi)²/n] = 1/11 * [1362670-((3638)²/12)] = 23614.47 dolars²

S= 153.67 dolars

Confidence interval (95%)

303.17± 2.201* (153.67/√12)

[205,5;400.8]dolars

I hope you have a SUPER day!

3 0

4 years ago