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Junior high school mathematics moving point problem (super urgent In the rectangular trapezoid ABCD, ad ‖ BC, ∠ B = 90 °, ad = 25cm, BC = 30cm, the moving point P starts from point a and moves along the ad side to D at a speed of 2cm / s, and the moving point Q starts from point C and moves along the CB side at a speed of 3cm / s to point B. P and Q start at the same time. When one point reaches the end point, the other point also stops moving. Let the moving time be t s, What is the value of T when (1) quadrilateral PQCD is parallelogram; (2) quadrilateral PQCD is isosceles trapezoid? Please, the process must be written clearly
PD=25-2t
QC=3t
Pd / / QC, when PD = QC, it is a parallelogram, that is, 25-2t = 3T
When qc-pd = 10, it is equal trapezoid, that is 3T - (25-2t) = 10
Given that x ^ 2 + X-6 is the factor of polynomial 2x ^ 4 + x ^ 3-ax ^ 2 + BX + A + B-1, find the value of a and B
(2x ^ 4 + x ^ 3-ax ^ 2 + BX + A + B-1) / (x ^ 2 + X-6) = 2x ^ 2-x + 13-A remainder (a + B-19) x + (- 5A + B + 77) (polynomial division)
Let the remainder be equal to Oh, that is, a + B-19 = 0, - 5A + B + 77 = 0,
The solution is a = 16, B = 3
Find the maximum and minimum values of the function f (x, y) = (x-1) ^ 2 + (Y-2) ^ 2 + 1 in the whole region D: x ^ 2 + y ^ 2 ≤ 20
Change the second word "big" in the penultimate line to "small"
Let │ 4xx-12x-27 be the sum of all integers x of a prime number
4xx-12x-27=(2x+3)(2x-9)
Let │ 4xx-12x-27 be prime, that is, 2x + 3 = plus or minus 1, or 2x-9 = plus or minus 1
X = - 1 or - 2 or 5 or 4
The substitution meets the requirements
So the sum is 6
What is the minimum value of the absolute value of X-1 plus the absolute value of X-2 plus the absolute value of X + 3
The simplest way
When x ＜ - 3, y = 1-x + 2-x-3-x = - 3x; when - 3 ≤ x ＜ 1, y = 1-x + 2-x + 3 + x = 6-x; when 1 ≤ x ＜ 2, y = X-1 + 2-x + X + 3 = 4 + X; when 2 ≤ x, y = X-1 + X-2 + X + 3 = 3x
When m (x, y) moves on the image of y = f (x), n (X-2, y) moves on the image of function y = g (x)
See figure for details. What you can't see in the figure is "in function"
Given the function f (x) = log2x, when point m (x, y) moves on the image of y = f (x), point n (X-2, y) moves on the image of function y = g (x). 1) Find the analytic formula of y = g (x). 2) Find the equation g (x) = 2g (X-2 + a) of set a = {a | with respect to X has real roots, a belongs to R... Tnnd, I can't go to the picture
1. Point m (x, y) on the image of F (x) = log2x, that is, y = log2xn (X-2, y) on the image of function y = g (x), let X-2 = t, x = t + 2, point n (T, y), point m (T + 2, y) substitute m (T + 2, y) into f (x) = log2x to get y = log2 (T + 2), replace T with X to get g (x) = log2 (x + 2) 2. G (x) = 2g (X-2 + a) log2 (x + 2) = 2log2 (
The product of two primes is 39, and the two primes are______ And______ ．
Decompose 39 into prime factors: 39 = 3 × 13, so the two prime numbers are 3 and 13
Given the probability density function of random variable x, find the distribution function f (x) of X. the details are shown in the figure below
1.P{1/2
Y = sin (x + π / 4) x ∈ [0, π] for range
x+π/4∈【π/4,5π/4】
When x + π / 4 = π / 2, the maximum value is 1
When x + π / 4 = 5 π / 4, the minimum value - (√ 2) / 2 is obtained
So the value range is [- (√ 2) / 2,1]
Let a = x quadratic XY, B = XY + y quadratic, find (1) a + B (2) 3a-b
(1) A + B = (x quadratic - XY) + (XY + y quadratic)
=x²-xy+xy+y²
=x²+y²
(2) 3a-b = 3 (x quadratic - XY) - (XY + y quadratic)
=3x²-3xy-xy-y²
=3x²-4xy-y²
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