If tangent to the curve y = √x is parallel to the line y = 8x, then this implies that the tangent to y = <span>√x has the same slope as the line y = 8x. In other words, the derivative (slope) function of y = √x is equal to the slope of the line y = 8x, which is m = 8. Hence y' = 8 once we find y'
y = </span><span>√x = x^(1/2)
Applying the power rule and simplifying, we find that the derivative is
y' = 1/(2</span>√x)
Now remember that y' must equal 8
1/(2<span>√x) = 8
Multiplying both sides by 2</span><span>√x, we obtain
1 = 16</span><span>√x
Dividing both sides by 16, yields
</span><span>√x = 1/16
But wait a minute, √x = y. Thus 1/16 must be the y-coordinate of the point at which the tangent to y = √x is drawn.
Squaring both sides, yields
x = 1/256
This is the x-coordinate of the point on the curve where the tangent is drawn.
</span><span>∴ the required point must be (1/256, 1/16)
GOOD LUCK!!!</span>
Answer:
Y=x+6
Step-by-step explanation:
Answer:
The coordinates are (-7sqrt(3)/2, 7/2).
Step-by-step explanation:
The rectangular coordinates from polar coordinates is found by:
x = r*cos(theta)
y = r*sin(theta)
Substituting the given values, we get:
x = 7*cos(150 deg) = 7*(-sqrt(3)/2) = -7sqrt(3)/2
y = 7*sin(150 deg) = 7*(1/2) = 7/2
The coordinates are (-7sqrt(3)/2, 7/2).
I hope this helps! :)
How to do the vertex is using the formula -b/2a
your a=-9 and b is -18 but it going to become +18 because you are multiplying the -(-18) which there a 1 in front the neg. you going to multiply the -9 by 2 and do 18/18 so your x= -1. You got your x, you going to put in the equation as y=-9(-1)^2-18(-1)-1 then you got your y... hope this is helpful :)
Answer:
There are infinite solutions that solve the system 
Step-by-step explanation:
- The solution can be expressed as (there are infinite solutions that solve the system). This results from rearranging terms in the first or second equation.
- This is because the first equation is a linear combination of the second one (this is, the first equation equals (-1) times the second equation). This means that the second equation does not add any information about x and y: it says exactly the same as the first equation about the relationship between x and y.
- Then, in terms of solving the system, you have one unique expression (not repeated) that shows the relationship between y and x. This means that, any pair of (x,y) that meet the requirements expressed by , will solve the system. Then we have infinite solutions.
