Find the tangent equation of curve f (x) = LNX at point (1, f (1))

Find the tangent equation of curve f (x) = LNX at point (1, f (1))

F (1) = 0 point is (1,0)
f'(x)=1/x
k=f'(1)=1/1=1
Line equation: Y - 0 = k * (x - 1)
y = x - 1

A bucket has a volume of 24 cubic decimeters and a bottom area of 7.5 square decimeters. There is a hole 0.8 meters away from the bucket mouth. How many kg of water can this bucket hold at most
How many kilos of water is it?

24 divided by 7.5 and bucket height = 3.2dm
[0.8 meter should be changed to 0.8 decimeter] (3.2 minus 0.8) × 7.5 = 18 cubic decimeter = 18000 cubic centimeter
And can hold up to 18000 grams

As shown in the figure, the front view, left view and top view of a space geometry are congruent isosceles right triangles. If the right side of the right triangle becomes 1, then the surface area of the geometry is 1______ ．

It can be seen from the title that the geometry of three view restoration is a triangular pyramid with an angle of a cube, so the surface area of the geometry is the sum of the areas of three isosceles right triangles and one equilateral triangle, that is, 3 × 12 × 1 × 1 + 34 × (2) 2 = 3 + 32

Quadratic function y = (x + 1) square, the parabola right translation 2 units
By the way, how to think about this kind of problem

Y = (x + 1) &#, and the parabola is shifted to the right by 2 units,
We get y = (x + 1-2) &;
=(x-1)²

How many cubic meters is a ton of soil equal to?

The density of soil is large, and the ratio of soil density to water density is the number of tons. 1.768/1 = 1.768 (tons)

Solving equation 7200 (1 + x) = 8712

（1+x）=8712/7200
(1+x)=1.21
1+x=√1.21
x=√1.21-1

It is known that a vertex of △ ABC is the vertex o of parabola y ^ 2 = 2x, both points a and B are on the parabola, and ∠ AOB = 90 °
(1) Proof: the line AB must pass a certain point
(2) Finding the minimum value of △ AOB area

(1) It is proved that for any point a (XA, ya) on the parabola which does not coincide with point O, let B (XB, Yb) satisfy the meaning of the problem, then ya ^ 2 = 2xa; (1) Yb ^ 2 = 2xb; (2) Ya / XA * Yb / XB = - 1 (AO ⊥ Bo)

How to convert area density into line density in College Physics

Divide area density by area and multiply by line length

Use the square difference formula to calculate: as follows
(3/2x-y)(3/2x+y)
(xy+1)(xy-1)
(2a-3b)(3b+2a)
(-2b-5) .（2b-5)
2 001x1 999
988x1 002.

Let the parabola C: y2 = 4x, f be the focal point of C, and the line L passing through f intersects with C at two points a and B. (1) let the slope of l be 1, and find the size of | ab |; (2) prove that OA · ob is a fixed value

(1) Let a (x1, Y1), B (X2, Y2), simultaneous y = x-1y2 = 4x, eliminate y to get x2-6x + 1 = 0, △ & gt; 0, ｜ X1 + x2 = 6, x1x2 = 1. Let a (x1, Y1), B (X2, Y2), simultaneous y = x-1y2 = 4x, eliminate y to get x2-6x + 1 = 8. (2) it is proved that let x = KY + 1, simultaneous x = KY + 1Y2 = 4x, eliminate x to get y2-4ky-4 = 0; Let a = (x1, Y1), B = (X2, Y2), then OA = (x1, Y1), OB = (X2, Y2).. OA · ob = x1x2 + y1y2 = (KY1 + 1) (ky2 + 1) + y1y2 = k2y1y2 + K (Y1 + Y2) + 1 + y1y2 = - 4k2 + 4k2 + 1-4 = - 3. OA · ob = - 3 is a fixed value