So even postive integers are by defention in form 2k where k is a natural number so
let the sum of even integers to n=S
S=2(1+2+3+4+5+6+7+8+......+k-1+k
divide bith sides of equation 1 by 2
0.5S=1+2+3+4+5+...........+k-1+k
S=2(k+(k-1)+..............................+2+1)
divide both sides of equation 2 by 2
0.5S=k+k-1+..............................+2+1)
by adding both we will get
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S=(k+1)(k)
so the sum will be equal to
S=
so let us test the equation
for the first 3 even number there sums will be
2+4+6=12
by our equation 3^2+3=12
gave us the same answer so our equation is correct
Answer:
B. No
Step-by-step explanation:
-A right angle triangle has two complimentary acute angles and one right angle.
-
is usually one of the acute angles and is equivalent to 90º minus it's complimentary acute angle.
-Complimentary angles add up to 90º.
#For complimentary angles:
The two acute angles cannot have the same Cosine value.
Hence, she's not correct.
Answer:
255
Step-by-step explanation:
total cost paid = fixed cost + total variable cost
total variable cost = distance travelled x variable cost per unit
two equations can be derived from the question
a + 10b = 105 equation 1
a + 15b = 155 equation 2
a = fixed cost
b = variable cost per unit
Subtract equation 1 from 2
5b = 50
b = 10
Substitute for b in equation 1
a + 10(10) = 105
a = 105 - 100 = 5
a = 5
cost of travelling a distance of 25km
5 + 10(25) = 255
<h3>
Answer: Choice A) 212 square meters</h3>
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Explanation:
14.10 has four sig figs. The 0 at the end is significant. This measurement is accurate to the hundredths place. If the author wrote 14.1, then it would be accurate to the tenths place with three sig figs.
15.0 has three sig figs. The 0 is significant. If they wrote 15 or 15. then we'd be dealing with 2 sig figs instead; however they placed the 0 there to tell the reader "this measurement is accurate to the tenths place"
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Multiply the values given
14.10*15.0 = 211.5
Round that to three sig figs. We pick the smaller sig fig count to round to since we cannot be certain it is accurate to four sig figs. In a sense, we pick the weakest link and use that to determine rounding when it comes to multiplication and division.
This means 211.5 rounds to 212
Answer:
The directrix is y=6 and focus is (0,4)
The equation of the parabola is,
20-4y=x²
