Find the minimum distance between the point with the square of parabola y = 64x and the line 4x + 3Y + 46 = 0, and find the coordinates of the point on the parabola when the minimum value is obtained

The distance L from the point m (a ^ 2,8a) on the parabola y ^ 2 = 64x to the straight line 4x + 3Y + 46 = 0:
L=|4a^2+3*8a+46|/√(4^2+3^2)=|4(a+3)^2+10|/5
A = - 3, m (9, - 24), lmin = 2
The minimum distance between the point (9, - 24) on the parabola y ^ 2 = 64x and the line 4x + 3Y + 46 = 0 = 2

Find the minimum value from the point on the parabola y square = 64x to the line 4x + 3Y + 46 = 0

Let the line 4x + 3Y + M = 0 and the parabola y & sup2; = 64x be tangent
（4x/3 +m/3）²=64x
16x²+(8m-576)x +m²=0
Discriminant = 0
Then M = 36 x = (576-8m) / 32 = 9
Y = 24, y = - 24 (rounding off)
The coordinates of this point are (9,24)
The minimum value is 6

When x is less than or equal to O and greater than or equal to - 5, what are the maximum and minimum values of the function y = x square + 4x + 3?

Y=X^2+4X+3=X^2+4X+4-1=(X+2)^2-1
So when x = - 5, there is a maximum, and the maximum = (- 5 + 2) ^ 2-1 = 9-1 = 8
When x = - 2, there is a minimum value, and the minimum value = (- 2 + 2) ^ 2-1 = 0-1 = - 1

Please add + or - between the numbers 3 / 2, 5 / 6, 7 / 12, 9 / 20, 11 / 30, 13 / 42, 15 / 56 so that the result of the equation is one and one eighth

3/2=1+1/2
5/6=1/2+1/3
7/12=1/3+1/4
9/20=1/4+1/5
11/30=1/5+1/6
13/42=1/6+1/7
15/5=1/7+1/8
So the answer is 3 / 2-5 / 6 + 7 / 12-9 / 20 + 11 / 30-13 / 42 + 15 / 56

Ax & # 178; + BX + C = 0, a + B + C = 0, B & # 178; - 4ac = 0, a = C

If a + B + C = 0 leads to B = - a-c, then B & # 178; = 4ac, then (- A-C) &# 178; = 4ac, and (A-C) &# 178; = 0, then a = C

The computer answer to this question is 1,
1+1+1+1+11+1+1+1+11+1 x 0+1=1
According to the law of multiplication and division is not equal to 30?

It can't add up all the numbers in front and multiply them by 0. In that case, it will be 1. Well, it's just a spoof game

There are two equal real roots on both sides of the equation x-ax + 1 = 0

From the discriminant Δ = (- a) &# 178; - 4 = 0, ｜ a = ± 2

Can the transformation of indefinite integral trigonometric function be in the form of x = π / 2-T
A = ∫ cosx / (SiNx + cosx) DX = (let x = π / 2-T) ∫ Sint / (cost + Sint) d (π / 2-T) = b
So 2A = a + B = ∫ (cosx SiNx) / (SiNx + cosx) DX = ∫ 1 / (SiNx + cosx) d (SiNx + cosx),
Why is this wrong,

A and B are not equal!

Calculation of partial ellipse area
The calculation of the area formula of a part of the ellipse after being divided by a straight line parallel to the y-axis or X-axis at any position

I also need this answer, but it's really higher mathematics`
I found one, but what I need is that I don't know the function of ellipse. I hope some friends can help me`
Find the two intersection x coordinates x1, X2 of Secant and ellipse
Subtract the elliptic function Y1 and secant function Y2 to get the function y
Product (y * DX) from X1 to x2
Simpson integral should be enough
Area=(dx/3)*[Y(x1)+4*Y(x1+dx)+2*Y(x1+2*dx))+4*Y(x1+3*dx)+...+Y(x2)]
dx=(x2-x1)/n
It depends on how thin you want to cut

There are 36 students in the art group of the experimental primary school, and the number of girls is 80% of that of boys. How many boys and girls are there in the art group?

Boys: 36 △ 1.8, = 20; girls: 36-20 = 16 or 20 × 80% = 16; a: there are 20 boys and 16 girls

Find the minimum distance between the point with the square of parabola y = 64x and the line 4x + 3Y + 46 = 0, and find the coordinates of the point on the parabola when the minimum value is obtained