The intercept of the line y = KX + B on the y-axis is 4, passing through the point C (3,2), the line intersects with the x-axis and y-axis at a, B, D is (3 / 2,0) to find the value of K

The intercept of the line y = KX + B on the y-axis is 4, passing through the point C (3,2), the line intersects with the x-axis and y-axis at a, B, D is (3 / 2,0) to find the value of K

Your question is not clear, because the intercept of the straight line on the y-axis is 4, so B = 4. At this time, the equation is y = KX + 4, and it passes through the point C (3,2), which is 2 = 3K + 4. The solution is k = - 2 / 3, which is y = - 2 / 3x + 4

In the sequence {an}, if an = 1 / N (n + 1) and the sum of the first n terms is 9 / 10, then the number of terms n is A12 B11 C10 D9
emergency

an=1/n-1/(n+1)
Sn=1/(1*2)+1/(2*3)+...+1/[n(n+1)]
=(1-1/2)+(1/2-1/3)+...+(1/n-1/(n+1))
=1-1/(n+1)
=9/10
=1-1/10
So: n + 1 = 10
Solution
n=9

If the intercept of the line passing through the fixed point P (1,2) on the positive half axis of X axis and Y axis is a and B respectively, the minimum value of 4a2 + B2 is ()
A. 8B. 32C. 45D. 72

∵ a ＞ 0, B ＞ 0, 1A + 2B = 1 ℅ (2a + b) · 1 = (2a + b) (1a + 2b) = 2 + 2 + Ba + 4AB ≥ 8 if and only if Ba = 4AB, i.e. 2A = b = 4, it is true 〈 2 (4a2 + B2) ≥ (2a + b) 2 ≥ 64, 〈 4a2 + B2 ≥ 32 If and only if 2A1 = B1 = 4, it is true 〈 (4a2 + B2) min = 32, so B is selected

The general term formula of sequence {an} is an = 1n (n + 1) (n ∈ n *). If the sum of the first n terms is 1011, then the number of terms is ()
A. 12B. 11C. 10D. 9

An = 1n (n + 1) = 1n − 1n + 1, (n ∈ n *), the sum of the first n terms Sn = (1 − 12) + (12 − 13) + (1n − 1n + 1) = 1-1n + 1 = NN + 1, when Sn = 1011, the solution is n = 10, so C

If the intercept of the straight line passing through the fixed point P (1,2) on the positive half axis of X axis and Y axis is a and B respectively, then the minimum value of a + B is______ ．

Let the straight line be XA + Yb = 1, and substitute the point P (1,2) to get: 1A + 2B = 1, a + B = (a + b) (1a + 2b) = 3 + (2Ab + BA) ≥ 3 + 22ab · Ba = 3 + 22. So the answer is: 3 + 22

The general term formula of the sequence {an} is: an = 1 (n + 1), the first n terms and Sn = 9 / 10, then in the rectangular coordinate system, the intercept of the line (n + 1) x + y + n = 0 on the Y axis is

Calculate n
Sn=1/(1*2)+1/(2*3)+...+1/[n(n+1)]=(1-1/2)+(1/2-1/3)+...+(1/n-1/(n+1))=1-1/(n+1)=9/10
So n = 9
So the linear equation 10x + y + 9 = 0
y=-10x-9
The intercept on the y-axis is - 9

Given that the general term of sequence {an} is an = (n + 1) [(9 / 10) n power], find the maximum term of an

A(n+1)-An=(0.9^n)*(0.8-0.1n)
Obviously, when n > 8, the sequence begins to decrease, so A8 max = 9 * 0.9 ^ 8

In the plane rectangular coordinate system, O (0,0), point m (a, b) is on the image with inverse scale function y = 48 / X (x > 0), and Ma ⊥ X axis is on a,
MB is perpendicular to the Y-axis of B. calculate the minimum perimeter of rectangular oamb and the M coordinate at this time

∵ m (a, b) on the image with inverse scale function y = 48 / X (x > 0), ∵ B = 48 / A, that is ab = 48
Rectangle oamb small perimeter = 2 (a + b) ≥ 4 √ AB = 4 √ 48 = 16 √ 3
Therefore, the minimum perimeter of rectangular oamb is 16 √ 3
When a = B, the perimeter of oamb is the smallest, and a & sup2; = B & sup2; = 48
∴a＝b＝4√3
So the M coordinate is (4 √ 3,4 √ 3)

In the rectangular coordinate system, if the coordinates of a and B are known as a (0,1) and B (2,3) respectively, M is a point on the x-axis, and Ma + MB is the smallest, then the coordinates of M are______ ．

As shown in the figure, take the symmetric point a '(0, - 1) of point a (0,1) about X axis, and connect a' B. let the analytic formula of the line a 'B be y = KX + B, ∵ a' (0, - 1), B (2,3), B = − 12K + B = 3, and the solution is k = 2B = − 1. The analytic formula of the line a 'B is y = 2x-1. When y = 0, the coordinates of x = 12, ∵ m are (12,0). So the answer is (12,0)

In the plane rectangular coordinate system, point a (6,0) point B (3,4), point m is a point on the y-axis, when Ma + MB takes the minimum value, find the minimum value

Let m point coordinate (0. Y) MA square = (6) ~ 2 + (y) ~ 2, the square of MB = 3 ~ 2 + (4-y) ~ 2. From the problem, we know that Ma + MB is the minimum, since it is the minimum = (6) ~ 2 + (y) ~ 2 + 3 ~ 2 + (4-y) ~ 2, so when y = 0, the minimum = 5 + 6 = 11