The correct answer is A: x=2 and y=-3. Either method would work, but for example, let's use elimination. If you multiply the second equation by 5, you get: 10x +5y = 5. When you add both equations, you can then cross out both y terms. You are left with one equation that reads: 13x=26. Solving for x gives you 2. You can substitute 2 in for x in either equation and you will receive -3 for your y value.
Given equation :−1/2 (x+2) + 112x = 3
We have -1/2 in front of parenthesis on left side .
It's better to remove fraction in an equation, in order make it easier to solve.
In order to remove 2 from denominator of 2, we need to multiply each and every term by 2.
Multiplying each term in the equation by 2, we get
2* −1/2(x+2) +2* 112x = 2*3.
On simplifying this step, we get
-1(x+2) +224x = 6.
Distributing -1 over (x+2), we get
-x -2 +224x = 6
Combining like terms on left side, -x+224x=223x
223x -2 = 6
Adding 2 on both sides, we get
223x -2+2 = 6+2
223x = 8
Dividing both sides by 223, we get
223x/223 = 8/223.
x= 8/223.
The speed of the current is 13 mph
<h3>What is speed?</h3>
speed refers to distance travelled per unit time. This is a vector quantity this implies that it has magnitude and direction.
The unit for speed as used here is miles per hour and can be written in short form as mph
<u>Given data</u>
speed of boat = 15 miles per hour = 15 mph
distance = 44 miles upstream
total time for the trip = 7.5 hours
<h3>solving for the speed of the current</h3>
let the water current be x
speed = distance / time
the total travel time upstream and downstream is known
for upstream
15 - x = 44 / time
time = 44 / 15 - x
for downstream
15 + x = 44 / time
time = 44 / 15 + x
total time = time for upstream + time for downstream = 7.5
7.5 = (44 / 15 - x ) + ( 44 / 15 + x )
7.5 = ( 44 ( 15 + x ) + 44 ( 15 - x ) ) / ( 15 + x )( 15 - x )
7.5 ( 15 + x )( 15 - x ) = 210 +44x + 210 - 44x
7.5 ( 225 - x ^ 2 ) = 420
( 225 - x ^ 2 ) = 56
169 = x ^ 2
x = sqrt ( 169 )
x = 13 miles per hour
hence speed of current is 13 miles per hour
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The answer is (0,3)
Hope this helps you
The interval of the convergence is x < -3 or x > 3 if the series n 3^n/x^n goes infinitely.
<h3>What is convergent of a series?</h3>
A series is convergent if the series of its partial sums approaches a limit; that really is, when the values are added one after the other in the order defined by the numbers, the partial sums getting closer and closer to a certain number.
We can find the interval for the convergent by root test.
Like the Ratio Test, the root Test is used to determine absolute convergence (or not) with factorials, the ratio test is useful.
For the given series:
As the series goes infinitely, we can use root test.
By the root test, the convergence interval will be;
The interval of convergence is:
x < -3 or x > 3 we can write this as:
|x| < 3
Thus, the interval of the convergence is x < -3 or x > 3 if the series n 3^n/x^n goes infinitely.
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