There are 16 cups in a gallon. So they made 62 cups of jam in all.
Assuming that arcs are given in degrees, call S the following sum:
S = sin 1° + sin 2° + sin 3° + ... + sin 359° + sin 360°
Rearranging the terms, you can rewrite S 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)
But for any real k,
sin(360° – k) = – sin k
then,
S = [sin 1° – sin 1°] + [sin 2° – sin 2°] + ... + [sin 179° – sin 179°] + sin 180° + sin 360°
S = 0 + 0 + ... + 0 + 0 + 0 (... as sin 180° = sin 360° = 0)
S = 0
Each pair of terms in brackets cancel out themselves, so the sum equals zero.
∴ sin 1° + sin 2° + sin 3° + ... + sin 359° + sin 360° = 0 ✔
I hope this helps. =)
Tags: <em>sum summatory trigonometric trig function sine sin trigonometry</em>
Answer:
Supplementary angles
Step-by-step explanation:
Supplementary angles are two angles whose sum is 180 degrees while complementary angles are two angles whose sum is 90 degrees.
Answer:
84 Percentage increase
Step-by-step explanation:
Detailed calculations & verification
Introduction. Percent, p%
'Percent (%)' means 'out of one hundred':
p% = p 'out of one hundred',
p% is read p 'percent',
p% = p/100 = p ÷ 100.
40% = 40/100 = 40 ÷ 100 = 0.4.
100% = 100/100 = 100 ÷ 100 = 1.
Increase the number by 40% of its value.
Percentage increase = 40% × 210
New value = 210 + Percentage increase
Calculate the New Value
New value =
210 + Percentage increase =
210 + (40% × 210) =
210 + 40% × 210 =
(1 + 40%) × 210 =
(100% + 40%) × 210 =
140% × 210 =
140 ÷ 100 × 210 =
140 × 210 ÷ 100 =
29,400 ÷ 100 =
294
Calculate absolute change (actual difference)
Absolute change (actual difference) =
New value - 210 =
294 - 210 =
84
Answer:
Step-by-step explanation:
area of Δ=1/2×8×6=24
also area ofΔ=1/2×10×x
1/2×10×x=24
5x=24
x=24/5=4.8