In the RT triangle ABC, the angle c = 90, BC = a, AC = B, a + B = 16, then the function analysis of the area s of the RT triangle with respect to the variable length a When s = 32, a=______

In the RT triangle ABC, the angle c = 90, BC = a, AC = B, a + B = 16, then the function analysis of the area s of the RT triangle with respect to the variable length a When s = 32, a=______

b=16-a
S=ab/2=a(16-a)/2
S=32
a(16-a)/2=32
A=8
Finding the discontinuous point and type of F (x) = x / SiNx in (- 2 π, 2 π)
For the function f (x) = x / SiNx, in the interval (- 2 π, 2 π), it is obvious that only when x = - π, 0 and π, the denominator SiNx = 0 may be the breakpoint, when x = - π and π, SiNx = 0, and the molecule x is not equal to 0, so x / SiNx tends to infinity, that is, x = - π and x = π are the infinite breakpoints of F (x) = x / SiNx, while when x = 0, f (x)
It is known that the sum of the first four terms of the arithmetic sequence {an} with non-zero tolerance is 10, and A2, A3 and A7 are equal proportion sequence. (I) find the general term formula an (II) let BN = 2An, find the first n terms and Sn of the sequence {BN}
(1) From the meaning of the title, we can get that 4A1 + 6D = 10 (a1 + 2D) 2 = (a1 + D) (a1 + 6D) ∵ D ≠ 0 ∵ A1 = − 2D = 3 ∵ an = 3n-5 (II) ∵ BN = 2An = 23n-5 = 14 · 8N − 1 ∵ sequence {an} is an equal ratio sequence with 14 as the first term and 8 as the common ratio ∵ Sn = 14 (1 − 8N) 1 − 8 = 8N − 128
Let the system of homogeneous linear equations with 3 variables {ax1 + x2 + X3 = 0, X1 + AX2 + X3 = 0, X1 + x2 + AX3 = 0} (1) determine that the system of equations has non-zero solution when a is a; (2)
(2) When a system of equations has nonzero solutions, the basic solution system and all solutions are obtained
The coefficient determinant | a | = a 111a 111a = (a + 2) (A-1) ^ 2, so when a = - 2 or a = 1, the equations have non-zero solutions. When a = 1, a = 11111111 -- > 111000, the basic solution system of the equations is A1 = (- 1,1,0) ', A2 = (- 1,0,1)', all the solutions are k1a1 + k2a2a = - 2, a = - 2
It is known that in RT △ ABC, ∠ C = 90 °, AC = 6, BC = 8, fold an acute angle so that the vertex of the acute angle falls at the midpoint D of the opposite side, the crease intersects the other right angle side at e, and the cross bevel side at F, then the perimeter of △ CDE is______ .
When angle B is folded, point B coincides with point D, and the sum of De and EC is BC, that is to say, equal to 8, CD is half of AC, so the perimeter of △ CDE is 8 + 3 = 11; when angle a is folded, point a coincides with point D. similarly, the sum of De and EC is AC = 6, CD is half of BC, so the perimeter of CDE is 6 + 4 = 10
Point x = 0 is the (). A. continuous point of function f (x) = {SiNx, x = 0; B. removable breakpoint; C. jump breakpoint; D. second type breakpoint?
Choose C
It is known that a1 + a3 = 10 and the sum of the first four terms is 40 in the equal ratio sequence {an}. (I) find the general formula of the sequence {an); (II) if the items of the equal difference sequence {BN} are positive
The sum of the first n terms is TN, and T3 = 15, and a1 + B1, A2 + B2, A3 + B3 form an equal ratio sequence to find TN
1.A1+A2+A3+A4=40A2+A4=40-10=30A2+A4=A1×q+A3×q=10×q=30q=3A1+A3=A1×(1+q^2)=10A1=10A1=1An=3^(n-1)2.A1=1 A2=3 A3=9T3=3B2=15 B2=5A2+B2=3+5=8A1+B1=A1+B2-d=6-dA3+B3=A3+B2+d=14+d(A1+B1)×(A3+B3)=(A2+B2...
If the system of homogeneous linear equations λ X1 + x2 + X3 = 0 x 1 + λ x2 + X3 = 0 x 1 + x2 + X3 = 0 has only zero solution, then the condition that λ should satisfy is______ .
The sufficient and necessary condition for the homogeneous system AX = 0 of n equations and n unknowns to have only zero solution is | a ≠ 0, because the number of unknowns is equal to the number of equations, that is, when a is a square matrix, it is more convenient to use | a | to determine, and | a | to =. λ 111, λ 1111. =. λ − 1000, λ − 10111. = (λ − 1) 2, so | a | to ≠ 0, that is, λ ≠ 1
It is known that the middle angle c of RT triangle ABC is equal to 90 ° AC = 8cm BC = 6cm. Now we fold the triangle ABC so that the vertices a and B coincide and find the length of crease De
We need a specific process
Solution 1: from ab & sup2; = AC & sup2; + BC & sup2;, ab = 10cm ∵ e is the midpoint of ab ∵ AE = 5cm
Let ad be x, then BD = ad = x, CD = 8-x
From BD & sup2; = CD & sup2; + BC & sup2;, we get X & sup2; = (8-x) & sup2; + 6 & sup2;; X = 5 / 4
∴AD=5/4cm
From AD & sup2; = de & sup2; + AE & sup2;, de = 15 / 4
Solution 2: from △ ade ∽ ABC, de: BC = AE: AC
∴DE：6=5：8∴DE=15/4
What is the discontinuous point of the function f (x) = SiNx / x + e ^ X / (2 + x) + ln (1 + x)
F (x) = SiNx / x + e ^ X / (2 + x) + ln (1 + x) the domain is x > - 1 and X ≠ 0,
The discontinuity is x = 0, which is a removable discontinuity