Answer:
There is no point of the form (-1, y) on the curve where the tangent is horizontal
Step-by-step explanation:
Notice that when x = - 1. then dy/dx becomes:
dy/dx= (y+2) / (2y+1)
therefore, to request that the tangent is horizontal we ask for the y values that make dy/dx equal to ZERO:
0 = ( y + 2) / (2 y + 1)
And we obtain y = -2 as the answer.
But if we try the point (-1, -2) in the original equation, we find that it DOESN'T belong to the curve because it doesn't satisfy the equation as shown below:
(-1)^2 + (-2)^2 - (-1)*(-2) - 5 = 1 + 4 + 2 - 5 = 2 (instead of zero)
Then, we conclude that there is no horizontal tangent to the curve for x = -1.
6 times because you find the common denominator which is 8 so 3/4 is 6/8. He needs to fill his cup 6 times.
The width would be 9 inches. Here's how I got the answer:
Double 12
Subtract from total
Take your difference and divide by two.
That will give you the width.
(You go from left to right)
(Dividend is 931, divisor is 7)
Step 1: Look for a number smaller than 9 that is divisible by 7. 7 is the only one which is smaller than 9 and is divisible by 7. Now that you know 7*1=7, you put 1 above 931 (Dividend)
Step 2: You subtract that number from the number in tens place. And bring the leftover down.
Step 3: You repeat Step 1 and 2 until either you get a remainder of 0 or the remainder in smaller than the divisor (in this case 7)
(Therefore 931/7=133, quotient=133, remainder=0)
^Hope this helps.