The average speed for his entire journey from York to Blackpool is about 61.41 km/h.
Here’s a breakdown of how we arrive at this:
The distance he travelled from York to Leeds is 45 km,
and the speed during that section was 54 km/h.
Therefore, the time taken to travel from York to Leeds is 45/54 hours (since Time = Distance/Speed).
Next, the distance from Leeds to Blackpool is 42 km,
and the time for that leg of the journey is 35 minutes, which is 35/60 hours.
This leads to the total duration for his trip as
hours.
The cumulative distance covered equals 45 + 42 = 87 km.
Thus, his average speed is calculated as:
Assuming arcs are measured in degrees, let S represent the following sum:
S = sin 1° + sin 2° + sin 3° +... + sin 359° + sin 360°
By rearranging, S can be reformulated as
S = [sin 1° + sin 359°] + [sin 2° + sin 358°] +... + [sin 179° + sin 181°] + sin 180° +
+ sin 360°
S = [sin 1° + sin(360° – 1°)] + [sin 2° + sin(360° – 2°)] +... + [sin 179° + sin(360° – 179)°]
+ sin 180° + sin 360° (i)
However, for any real k,
sin(360° – k) = – sin k
Thus,
S = [sin 1° – sin 1°] + [sin 2° – sin 2°] +... + [sin 179° – sin 179°] + sin 180° + sin 360°
S results in 0 + 0 +... + 0 + 0 + 0 (... since sine of 180° and 360° are both equal to 0)
Therefore, S equals 0.
Each pair within the brackets negates itself, leading the sum to total zero.
∴ sin 1° + sin 2° + sin 3° +... + sin 359° + sin 360° equals 0. ✔
I hope this clarifies things. =)
Tags: sum summatory trigonometric trig function sine sin trigonometry
Answer:
The constant pay of $25 signifies the intercept
Step-by-step explanation:
To address this query, we first need to comprehend and relate it to the formula for a straight line.
i.e 
this represents the line's equation
where m= slope
y= dependent variable
x= independent variable
c= intercept
Given
by comparing the two expressions, we can observe that
25 is equivalent to c, which denotes the intercept
Answer: You would need 40 bushels of seed to plant 30 acres of wheat.
Step-by-step explanation:
<pTypically, 1 1/3 bushels of seed are necessary to cultivate 1 acre of wheat. In improper fraction form, 1 1/3 bushels becomes 4/3 bushels.
Let x denote the bushels of seed required for 30 acres. Thus, we have
4/3 bushels = 1 acre
x = 30 acres
Cross multiplying gives us
x × 1 = 4/3 × 30
x = 40 bushels of seed
Step-by-step explanation:
Begin with expressing 492,623 in standard form.
4 hundred thousands + 9 ten thousands + 2 thousands + 6 hundreds + 2 tens + 3 ones.
We can rephrase this in varied forms by shifting a digit to the next lower place value. For instance, shifting the 4 one place right results in 49 ten thousands:
49 ten thousands + 2 thousands + 6 hundreds + 2 tens + 3 ones.
Next, we can move 49 ten thousands one place right to express it as 492 thousands, and shift 6 hundreds right to yield 62 tens.
492 thousands + 62 tens + 3 ones.
Alternatively, we can phrase it as:
4926 hundreds + 23 ones.
