Recall that a sequence
is convergent if and only if
is also a Cauchy sequence, which means to say that for any
, we can find a sufficiently large
for which
whenever both
and
exceed
.
But this never happens if we choose
and
; under these conditions, we have
Therefore
is not a Cauchy sequence and hence does not converge.
Answer:
4 mph
Step-by-step explanation:
Travel time is proportional to distance and inversely proportional to speed. If c represents the speed of the current in miles per hour, an equation for the total trip time is ...
825/(29 -c) +825/(29 +c) = 58 . . . . . . hours travel time
825(29 +c) +825(29 -c) = 58(29 -c)(29 +c)
58c² -928 = 0 . . . . . . . rearrange to standard form
58(c -4)(c +4) = 0 . . . . factor
Values of c that satisfy this equation are 4 and -4. For the purpose here, we'll choose the positive solution.
The speed of the current is 4 miles per hour.
The number of pretzels and hot dog sales will be 33 and 48.
<h3>What is the solution to the equation?</h3>
The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.
Let x be the number of pretzels and y be the number of hot dogs.
Joanie runs the concession stand for the school's baseball games.
At each game, the best-selling items are pretzels and hot dogs.
Pretzels are $3 each, and hot dogs are $2 each.
Today she sold 15 more hot dogs than pretzels and made $195 in total sales. Then the equations will be
y = x + 15 ....1
3x +2y = 195 ...2
From equations 1 and 2, then we have
3x + 2(x + 15) = 195
3x + 2x + 30 = 195
5x = 165
x = 33
Then the value of y will be
y = 33 + 15
y = 48
Then the number of pretzels and hot dog sales will be 33 and 48.
More about the solution of the equation link is given below.
brainly.com/question/545403
#SPJ1
Since the triangle has a 30° angle and a right angle which is 90°, this triangle must be a 30 - 60 - 90 triangle, which is a triangle with special properties. The length of the leg adjacent to the 30° angle is equal to the √3 times x where x is the length of the angle adjacent to the 60<span>° angle. Here is a visual representation:
</span>
Percent decrease : (original number - new number) / original number..*100
= (225,000 - 191,250) / 225,000.....* 100
= 33,750 / 225,000....* 100
= 0.15 * 100
= 15% decrease <==
