The bottom 2 i’m pretty sure, sorrry if it’s wrong
The line y = x + 3 has slope 1, so we look for points on the curve where the tangent line, whose slope is dy/dx, is equal to 1.
y² = x
Take the derivative of both sides with respect to x, assuming y = y(x) :
2y dy/dx = 1
dy/dx = 1/(2y)
Solve for y when dy/dx = 1 :
1 = 1/(2y)
2y = 1
y = 1/2
When y = 1/2, we have x = y² = (1/2)² = 1/4. However, for the given line, when y = 1/2, we have x = y - 3 = 1/2 - 3 = -5/2.
This means the line y = x + 3 is not a tangent to the curve y² = x. In fact, the line never even touches y² = x :
x = y² ⇒ y = y² + 3 ⇒ y² - y + 3 = 0
has no real solution for y.
I think it would be 8 miles: it would have been 2 hours, so 4 * 2 is 8 miles.
:) Hope this helps!
The arc length of the semicircle is 5π units
<h3>Calculating length of an arc</h3>
From the question, we are to calculate the arc length of the semicircle
Arc length of a semicircle = 1/2 the circumference of the circle
∴ Arc length of a semicircle = 1/2 × 2πr
Arc length of a semicircle = πr
Where r is the radius
From the given information,
r = 5
∴ Arc length of the semicircle = 5 × π
Arc length of the semicircle = 5π units
Hence, the arc length of the semicircle is 5π units
Learn more on Calculating length of an arc here: brainly.com/question/16552139
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You'd use the equation y2-y1/x2-x1
0-(-3)/-7-5 = 3/-12 = -1/4
So -1/4 would be the slope
m= -1/4
