Answer:
(a) 498501
(b) 251001
Step-by-step explanation:
According Gauss's approach, the sum of a series is
.... (1)
where, n is number of terms.
(a)
The given series is
1+2+3+4+...+998
here,
Substitute , and in equation (1).
Therefore the sum of series is 498501.
(b)
The given series is
1+3+5+7+...+ 1001
The given series is the sum of dd natural numbers.
In 1001 natural numbers 500 are even numbers and 501 are odd number because alternative numbers are even.
Substitute , and in equation (1).
Therefore the sum of series is 251001.
Answer:
<h3>x=9 answer...</h3>
Step-by-step explanation:
- 6/x=18/27
- 162=18x
- x=162/18
- x=9
<h2>hope it helps.</h2><h2>stay safe healthy and happy..</h2>
7 and 5
105/3= 35
Factors of 35: 1,5,7,35
The only two factors that have a sum of 12 are 5 and 7
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y
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x
2
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3
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y
=
(
x
2
-
3
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Find the Derivative - d/dx
Differentiate using the Power Rule,
d
d
x
[
x
n
]
=
n
x
n
−
1
d
d
x
[
x
n
]
=
n
x
n
-
1
.
2
x
2
x
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You are currently in the Algebra section, but it looks like you might be trying to do calculus. You might find more of the topics and symbols you need if you switch your subject over to Calculus.
y
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x
2
−
3
)
y
=
(
x
2
-
3
)
Solve for y
Remove parentheses.
y
=
x
2
−
3
y
=
x
2
-
3
y
=
(
x
2
−
3
)
y
=
(
x
2
-
3
)
Graph
Graph the parabola using the direction, vertex, focus, and axis of symmetry.
Direction: Opens Up
Vertex:
(
0
,
−
3
)
(
0
,
-
3
)
Focus:
(
0
,
−
11
4
)
(
0
,
-
11
4
)
Axis of Symmetry:
x
=
0
x
=
0
Directrix:
y
=
−
13
4
y
=
-
13
4
x
y
−
2
1
−
1
−
2
0
−
3
1
−
2
2
1
x y -2 1 -1 -2 0 -3 1 -2 2 1
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image of graph
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y
=
(
x
2
−
3
)
y
=
(
x
2
-
3
)
Find dy/dx
Differentiate each term with respect to
x
x
, then solve for
y
'
y
.
d
y
d
x
=
2
x
