# To find: the distance between the lakes to the nearest mile. Given: (26,15) and (9,20)

Question
Alternate coordinate systems
To find: the distance between the lakes to the nearest mile.
Given:
(26,15) and (9,20)

2021-01-24

Formula used:
The distance between the points are calculated as
$$\displaystyle{d}^{2}={\left({y}_{{2}}-{y}_{{1}}\right)}^{2}+{\left({x}_{{2}}-{x}_{{1}}\right)}^{2}$$
Calculation:
Let the two lakes be at the points F and E respectively.
The coordinates are
$$\displaystyle{F}{\left({26},{15}\right)}{E}{\left({9},{20}\right)}$$
Apply distance formula by keeping the values of two coordinates
$$\displaystyle{d}=\sqrt{{{\left({26}-{9}\right)}^{2}+{\left({15}-{20}\right)}^{2}}}$$
Or, $$\displaystyle{d}=\sqrt{{{\left({17}\right)}^{2}+{\left(-{5}\right)}^{2}}}$$
Or, $$\displaystyle{d}=\sqrt{{{289}+{25}}}$$
Or, $$\displaystyle{d}=\pm\sqrt{{314}}$$
Or, $$\displaystyle{d}=\sqrt{{314}}$$ (distance can't be negative so omit the negative root found)
Reduse the solution to decimals
$$\displaystyle{d}={17.7}$$ units
2 units on coordinate scale is equivalent to 1 mile in actual measurements.
Thus, for 17.7 units in coordinates systems
The actual distance will be equal to
$$\displaystyle{\left(\frac{1}{{2}}\right)}{17.7}={8.86}$$ miles
Conclusion:
Thus, the distance between the lakes to the nearest mile is 8.86 miles

### Relevant Questions

Common salt, NaCl, has a density of 2.165 $$\displaystyle\frac{{g}}{{c}}{m}^{{3}}$$. The molecular weight of NaCl is 58.44. Estimate the distance between nearest neighbor Na and Cl ions. (Hint: each ion can be considered to have one cube or cell of side s (our unknown) extending out from it)
A 10 kg objectexperiences a horizontal force which causes it to accelerate at 5 $$\displaystyle\frac{{m}}{{s}^{{2}}}$$, moving it a distance of 20 m, horizontally.How much work is done by the force?
A ball is connected to a rope and swung around in uniform circular motion.The tension in the rope is measured at 10 N and the radius of thecircle is 1 m. How much work is done in one revolution around the circle?
A 10 kg weight issuspended in the air by a strong cable. How much work is done, perunit time, in suspending the weight?
A 5 kg block is moved up a 30 degree incline by a force of 50 N, parallel to the incline. The coefficient of kinetic friction between the block and the incline is .25. How much work is done by the 50 N force in moving the block a distance of 10 meters? What is the total workdone on the block over the same distance?
What is the kinetic energy of a 2 kg ball that travels a distance of 50 metersin 5 seconds?
A ball is thrown vertically with a velocity of 25 m/s. How high does it go? What is its velocity when it reaches a height of 25 m?
A ball with enough speed can complete a vertical loop. With what speed must the ballenter the loop to complete a 2 m loop? (Keep in mind that the velocity of the ball is not constant throughout the loop).
A 15.0 kg block is dragged over a rough, horizontal surface by a70.0 N force acting at 20.0 degree angle above the horizontal. The block is displaced 5.0 m, and the coefficient of kinetic friction is 0.3. Find the work done on the block by ; a) the 70.0 N force,b) the normal force, and c) the gravitational force. d) what is the increase in the internal energy of the block-surface system due to friction? e) find the total change in the kinetic energy of the block.
A ship leaves port and travels due east 15 nautical miles,then changes course to N 20 W and travels 40 more nauticalmiles. How would you find the bearing to the port of departure, andhow would you draw the diagram for this problem.
Plotting points and finding distance in three dimensions. Two points P and $$\underline{O}$$ are given.
(a) Plot P and $$\underline{O}$$.
(b) Find the distance between P and $$\underline{O}.$$
$$P(3, 1, 0), \underline{O}(-1, 2, -5)$$
Aidan knows that the observation deck on the Vancouver Lookout is 130 m above the ground. He measures the angle between the ground and his line of sight to the observation deck as $$\displaystyle{77}^{\circ}$$. How far is Aidan from the base of the Lookout to the nearest metre?
To determine:
Find the sets of points in space whose coordinates satisfy the given combinations of equation and inequalities:
a) $$\displaystyle{y}\ge{x}^{2},{z}\ge{0},$$
b) $$\displaystyle{x}\le{y}^{2},{0}\le{z}\le{2}.$$
An equation that expresses a relationship between two or more variables, such as $$H = \frac{9}{10} (20 - a)$$ is called a/an ? The process of finding such equations to describe real-world phenomena is called mathematical ? Such equations, together with the meaning assigned to the variables, are called mathematical ?
A medical technician is trying to determine what percentage of apatient's artery is blocked by plaque. To do this, she measures theblood pressure just before the region of blockage and finds that itis $$\displaystyle{1.20}\times{10}^{{{4}}}{P}{a}$$, while in the region of blockage it is $$\displaystyle{1.15}\times{10}^{{{4}}}{P}{a}$$. Furthermore, she knows that blood flowingthrough the normal artery just before the point of blockage istraveling at 30.0 cm/s, and the specific gravity of this patient'sblood is 1.06. What percentage of the cross-sectional area of thepatient's artery is blocked by the plaque?