Answer:
5
Step-by-step explanation:
To solve with calculus, distance is the integral of speed:
d = ∫ |v| dt
d = ∫₀⁴ |t − 3| dt
d = -∫₀³ (t − 3) dt + ∫₃⁴ (t − 3) dt
d = ∫₀³ (3 − t) dt + ∫₃⁴ (t − 3) dt
d = (3t − ½ t²) |₀³ + (½ t² − 3t) |₃⁴
d = [ (9 − 9/2 ) − (0 − 0) ] + [ (8 − 12) − (9/2 − 9) ]
d = 9/2 + 1/2
d = 5
You can also find this geometrically. Graph y = |x − 3|, then find the area under the curve. You will find it's the area of two triangles.
d = ½ (3)(3) + ½ (1)(1)
d = 5
It's important to note that distance is not the same thing as displacement. Displacement is the difference between where you start and where you stop. Distance is length of the path you take.
Answer:
Divide both the numerator and denominator by the largest number that divides evenly into both to simplify the fraction
In the example, divide 2 by 2, which equals 1, and divide 20 by 2, which equals 10. This leaves 1/10, which is the simplified form of the fraction with a decimal.
Step-by-step explanation:
Answer:
y=1/2x-5
Step-by-step explanation:
We have slope so we just need to find the y intercept.
slope intercept formula is
y=mx+b
(m) is slope
(b) is y int
y=1/2x+b
now apply our given x and y values (4 & -3)
-3=1/2(4)+b
simplify
-3=2+b
subtract 2 from each side
-5=b
put that into our equation
y=1/2x-5
Answer:
a. 1,000 trees
b. 3,250 trees
Step-by-step explanation:
a. How many trees will they plant during the fifth year?
b. How many trees will they have planted by the end of the tenth year?
Using the sum of an arithmetic progression formula
Sn = n/2 {2a+(n-1)d}
Where,
Sn = Sum of an n terms
n = number of terms
a = first term
d = common difference
a.
n = 5
a = 100
d = 50
S5 = n/2 {2a+(n-1)d}
= 5/2 {2*100 + (5-1)50}
= 5/2 {200+(4)50}
= 5/2{200 + 200}
= 5/2(400)
= 2,000 / 2
= 1,000
S5 = 1,000 trees
b. Sn = n/2 {2a+(n-1)d}
n = 10
a = 100
d =50
S10 = 10/2{2*100 + (10-1)50}
= 5{200 + (9)50}
= 5{200 + 450}
= 5(650)
= 3,250
S10 = 3,250 trees