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4 days ago

Given the points below find XY. Round to the nearest hundred. X(-9,2) Y(5,-4)

2 answers:

8 0

$\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ X(\stackrel{x_1}{-9}~,~\stackrel{y_1}{2})\qquad Y(\stackrel{x_2}{5}~,~\stackrel{y_2}{-4})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ XY=\sqrt{[5-(-9)]^2+[-4-2]^2}\implies XY=\sqrt{(5+9)^2+(-4-2)^2} \\\\\\ XY=\sqrt{14^2+(-6)^2}\implies XY=\sqrt{232}\implies XY\approx 15.23$

Leona [4.1K]4 days ago

3 0

Answer: $XY=15.23$

Step-by-step explanation:

The distance between two points A(a,b) and B(c,d) can be calculated using the following formula:

$AB=\sqrt{(c-a)^2+(d-b)^2}$

For the points provided: X(-9,2) Y(5,-4)

Thus, the distance between the points X(-9,2) and Y(5,-4) is calculated as follows:

$XY=\sqrt{(5-(-9))^2+(-4-2)^2}\\\\\Rightarrow\ XY\sqrt{(5+9)^2+(-6)^2}\\\\\Rightarrow\ XY=\sqrt{(14)^2+(-6)^2}\\\\\Rightarrow\ XY=\sqrt{196+36}\\\\\Rightarrow\ XY=\sqrt{232}=15.2315462117\approx15.23$

Therefore, $XY=15.23$

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10 days ago

What is the nearest ten thousand, the population of Vermont was estimated to be about 620,000 in 2008 . What might have been the

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The exact population of Vermont in 2008 could have been around 618,000

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* Here's how rounding to the nearest ten thousand works:

- Numbers ending with the last four digits between 0001 and 4999 are rounded down to the nearest lower multiple of ten thousand

- Example: 83,525 rounds down to 80,000.

- If the last four digits are 5000 or above, round up to the next higher ten thousand

- Example: 58,988 rounds up to 60,000

* Applying this rule to the problem given:

Since the rounded population is 620,000 to the nearest ten thousand, the actual population could be any value with the last four digits from 0001 to 4999 (like 618,000) or from 5000 upwards (like 624,000).

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15 days ago

The temperature, H, in degrees Celsius, of a cup of coffee placed on the kitchen counter is given by H = f(t), where t is in min

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f'(t) is negative

The unit is degC/min

At 35 minutes since the coffee was placed on the counter, the temperature is 68, and it will drop by approximately 0.75 in the next 30 seconds.

Detailed explanation:

According to the question, we are informed that

The temperature of a cup of coffee on a counter is represented by the equation

$H= f(t)$

where t indicates the time in minutes since the coffee was set on the counter.

In general, f(t)' denotes the derivative of f(t), indicating the change in temperature over time for the coffee

As the coffee rests on the counter, its temperature tends to decrease after a few minutes; thus, f(t)' is negative.

The temperature is measured in degrees Celsius while time is expressed in minutes.

Therefore, the change in temperature with respect to time, f(35)', will be given in degrees Celsius per minute (i.e., degC/min).

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which means the rate of temperature change after 35 minutes is 1.5.

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$R = |f(35)'| * t$

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At 35 minutes since the coffee was placed on the counter, its temperature is 68 and will drop by roughly 0.75 in the next 30 seconds.

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