Answer:
The particle changes its direction 2 times within the time -3<t<3
Step-by-step explanation:
The particle is moving only in a single dimension (x-axis), and whenever the particle changes its direction it also means that it's velocity while changing the direction will be zero.
Hence,
v(t) = 0
but since we're not concerned with the actual values of t when v(t)=0, we'll only consider how many times does the particle changes its direction.
for that we'll simply plot the curve using half-steps from -3 to 3.
t, v(t)
-3, 115
-2.5, 23.9375
-2, -16
-1.5, -25.0625
-1, -19
-0.5, -9.0625
0, -2
0.5, -0.0625
1, -1
1.5, 1.9375
2, 20
2.5, 68.9375
3, 169
What we need to check is at what points does the sign of v(t) values change (because only between those points will v(t) cross the x-axis, hence it's value would've crossed 0)
so there are two points!
between the intervals t = [-2.5,2] and [1,1.5]
so there are two points where the particle changes its directions and those points lie somewhere between these two aforementioned intervals.
Answer:
£9000
Step-by-step explanation:
= £10 000×<u> </u><u> </u><u>5</u><u> </u><u> </u>×2
100
= 1000
= £10 000-1000
= £9000
Based on the terms of the invoice, the gross amount on the invoice and the date of payment, the cash discount is $19 and the net amount paid is $931.
<h3 /><h3>What is the cash discount?</h3>
The terms of the invoice are such that if the person pays within 10 days they get a 3% discount. If they pay in 15 days, they get a 2% discount.
The person paid on the 22nd after buying on the 8th so they qualify for the 2% for paying within 15 days.
The cash discount is:
= 2% x 950
= $19
The net amount paid is:
= 950 - 19
= $931
Find out more on cash discounts at brainly.com/question/14883253
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Its 43 because between each number it has a pattern that is 9,13,6 then it repeats
Answer:
160 m²
Step-by-step explanation:
The surface area of the prism is the sum of the area of its surfaces. This prism has 5 surfaces, namely the front, back, right, left and bottom surface.
<u>Area of front surface</u>
Area of triangle= ½ ×base ×height
Base= 6 m
Height= 4 m
Area= 6(4)= 24 m²
<u>Area of back </u><u>surface</u>
Area of back surface
= area of front surface
= 24 m²
<u>Area of right </u><u>surface</u>
Area of rectangle= length ×breadth
Length= 7 m
Breadth= 5 m
Area= 7(5)= 35 m²
<u>Area of left </u><u>surface</u>
Area of left surface
= area of right surface
= 35 m²
<u>Area of bottom </u><u>surface</u> (base of prism)
Area of rectangle= length ×breadth
Length= 7 m
Breadth= 6 m
Area= 6(7)= 42 m²
The total surface area can be found by adding all of the surface areas we have found earlier.
Total surface area
= 24 +24 +35 +35 +42
= 160 m²
