).Find all numbers for which the rational expression is undefined.
(4)/(v-2)
2).Find the lcm of (6+7u), (36-49^(u^2)),and(6-7u) ?
3). The speed of train a is 14 mph slower than the speed of train b. Train a travels 190 miles in the same time it takes train b to travel 260 miles. Speed of each train?
Train A?
Train B?
4). To determine the number of deer in a game preserve, a conservationist catches 685 deer, tags them and lets them loose. Later 428 deer are caught, 214 of them are tagged. How many deer are on the preserve?
5). Find the lcm of 2(x-11) and 22(x-11)?
For this one I come out with 2 was wondering if it was correct?
6). (7r)/(r2-1)+(r)/(r-1) = (r(r+8))/((r-1)(r+1)) Can someone please tell me if this is correct?
2
4) It can be assumed from the count that that half of the deer in the preserve had been tagged. If the total number of deer present did not change, there are equal numbers of tagged and untagged deer. That makes 1370 total.
5). Find the lcm of 2(x-11) and 22(x-11)?
For this one I come out with 2 was wondering if it was correct?
LCM means Least Common Multiple. 2 is a factor, not a multiple.
The LCM is 22(x-11)in this case, becasue the larger number is a multiple of the smaller number.
Find the lcm of (6+7w), (36-49w^2),and (6-7w)?
(6+7v)(6-7v)^2
1) To find the numbers for which the rational expression (4)/(v-2) is undefined, we need to determine the values of "v" that make the denominator (v-2) equal to zero. So, we solve the equation (v-2) = 0 for "v":
v - 2 = 0
v = 2
Therefore, the rational expression is undefined when v = 2.
2) To find the least common multiple (LCM) of (6+7u), (36-49^(u^2)), and (6-7u), we can factor each expression and then multiply the highest powers of each factor.
(6+7u) can be factored as (6+7u) = (3+u)(2+3u)
(36-49^(u^2)) is already factored as it is.
(6-7u) can be factored as (6-7u) = -(3+u)(2-3u)
Now, we can find the LCM by multiplying the highest powers of each factor:
LCM = (3+u)(2+3u)(36-49^(u^2))
3) Let's denote the speed of train a as "a" and the speed of train b as "b".
From the given information:
The speed of train a is 14 mph slower than the speed of train b ⇒ a = b - 14
Train a travels 190 miles in the same time it takes train b to travel 260 miles. This implies the time taken by both trains is equal ⇒ 190/a = 260/b
We can use these two equations to solve for the speeds of each train.
From the first equation, substitute a = b - 14 into the second equation:
190/(b-14) = 260/b
Now, we can solve for "b" by cross-multiplying:
190b = 260(b - 14)
190b = 260b - 3640
70b = 3640
b = 52
Substitute the value of "b" back into the first equation:
a = b - 14
a = 52 - 14
a = 38
Therefore, the speed of Train A is 38 mph and the speed of Train B is 52 mph.
4) To determine the number of deer on the preserve, we can use a proportion since the ratio of tagged deer to total caught deer would be equal to the ratio of tagged deer initially caught to the total number of deer on the preserve.
Let's denote the total number of deer on the preserve as "x".
The proportion can be set up as follows:
(tagged deer caught later) / (total deer caught later) = (tagged deer initially) / (total deer on the preserve)
214 / 428 = 685 / x
To solve for "x", cross-multiply and then divide:
214x = 428 * 685
x = (428 * 685) / 214
Evaluate the expression on the right side of the equation to find the number of deer on the preserve.
5) To find the LCM of 2(x-11) and 22(x-11), we need to factor both expressions.
2(x-11) can be simplified as 2x - 22.
22(x-11) can be simplified as 22x - 242.
Now, we can find the LCM by multiplying the highest powers of each factor:
LCM = 2x - 22 * 22x - 242
Simplify the expression and combine like terms, if possible.
6) To check if the equation (7r)/(r^2-1) + (r)/(r-1) = (r(r+8))/((r-1)(r+1)) is correct, we can simplify the left side and right side of the equation separately and see if they are equal.
Using the factoring identities, we can simplify the equation:
(7r)/(r^2-1) + (r)/(r-1)
= (7r)/((r-1)(r+1)) + (r)/(r-1)
= [7r + r(r+1)] / ((r-1)(r+1))
= [7r + r^2 + r] / ((r-1)(r+1))
= (r^2 + 8r) / ((r-1)(r+1))
Comparing this to the right side of the equation:
(r(r+8))/((r-1)(r+1))
We can see that the left side and right side of the equation are equivalent. Therefore, the equation is correct.