Answer:
distance:5.099
Step-by-step explanation:
The minimum distance from the point to the line would be found by drawing a segment perpendicular to the line directly to the point. Our first step is to find the equation of the new line that connects the point to the line given in the problem. Because we know this new line is perpendicular to the line we're finding the distance to, we know its slope will be the negative inverse of the line its perpendicular to. So if the line we're finding the distance to is:
f(x)=−13x+2
Then its slope is -1/3, so the slope of a line perpendicular to it would be 3. Now that we know the slope of the line that will give the shortest distance from the point to the given line, we can plug the coordinates of our point into the formula for a line to get the full equation of the new line:
f(x)=mx+b
f(x)=3x+b
−4=3(−2)+b→b=2
f(x)=3x+2
Now that we know the equation of our perpendicular line, our next step is to find the point where it intersects the line given in the problem:
3x+2=−13x+2
103x=0→x=0
So if the lines intersect at x=0, we plug that value into either equation to find the y coordinate of the point where the lines intersect, which is the point on the line closest to the point given in the problem and therefore tells us the location of the minimum distance from the point to the line:
f(0)=3(0)+2=2
So we now know we want to find the distance between the following two points:
(−2,−4) and (0,2)
Using the following formula for the distance between two points, which we can see is just an application of the Pythagorean Theorem, we can plug in the values of our two points and calculate the shortest distance between the point and line given in the problem:
d=(x2−x1)2+(y2−y1)2−−−−−−−−−−−−−−−−−−√
d=(0−(−2))2+(2−(−4))2−−−−−−−−−−−−−−−−−−−−√=(2)2+(6)2−−−−−−−−−√=40−−√
Which we can then simplify by factoring the radical:
40−−√=4⋅10−−−−√=210−−√
Answer:
=-43
Step-by-step explanation:
=(5)(−4)−23
=−20−23
=−43
Answer:
(a-1) *(a^2 +a-1) (a+2)
Step-by-step explanation:
a^4+2a^3-a-2
Lets factor by grouping
a^4-a + 2a^3-2
Factor out an a from the first group and a 2 from the second group
a(a^3 -1) +2(a^3-1)
Factor out (a^3-1)
(a^3-1)(a+2)
We need to recognize that a^3-1 is the difference of cubes
(x^3-y^3) = (x-y) (x^2+xy+y^2)
Let x=a and y=1
(a-1) *(a^2 +a-1) (a+2)
The book value at the end of year 2 of the equipment depreciated using the sum-of-the-years’-digits method is $65,560.
<h3>What is the book value at the end of year 2? </h3>
Depreciation is a method used to expense the cost of an asset. Book value is the cost of the asset less the accumulated depreciation.
Sum-of-the-year digits = (remaining useful life / sum of the years ) x (Cost of asset - Salvage value)
Depreciation expense in year 1:
Sum of the years = 1 +2 +3 +4 + 5 + 6 + 7 + 8 + 9 + 10+ 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 + 20 = 210
Undepreciated life of the asset = 20
(20 / 210) x ($79,600 - 4,000) = 7200
Depreciation expense in year 2:
19 / 210 x ($79,600 - 4,000) = 6840
Book value = 79600 - 7200 - 6840 = $65,560
To learn more about depreciation, please check: brainly.com/question/25552427
Percent change = (new - old)/old * 100
(6/7 - 3/7)/(3/7) * 100
3/7 * 7/3 * 100
1 * 100
100%