Short answers to high school math questions, high school one math short answer questions

Question 16: a1 + a1 + 2d = 6, a1 + 3d + a1 + 5d = 18, so a1 = 1, d = 2, the first five terms are: , which add up to 25

Question 17: Bring f(1) and f(-1) in: 1<=a+b<=3,-10<=2a<=4, so 0<=a<=2, subtract the two equations to get: 2<=2b<=2, so b=1, and then substitute f(2) into: f(2)=4a+2b=4a+2

The value ranges from 2 to 10.

Question 18: 1): s=1 2absinc, substituting data, can obtain ab=4, and then according to the cosine theorem:

cosc=[a square + b squared - c squared] 2ab, substituting the data can obtain: a square + b square = 8, and then according to ab = 4, combine an equation: (a + b) square = a square + b square + 2ab = 16, and a and b are both positive numbers, so a + b = 4, ab = 4, solve this unary quadratic equation to get a = b = 2

2): According to the sinusoidal theorem: sina a = sinb b, i.e., sina sinb = a b = 1 2, i.e., 2a = b.

According to the cosine theorem: substituting the data can obtain: 1 2=[a square + 4a squared-4] 4a square, and the equation is solved: a = 2 (root number 3).

b = 4 (root number 3), then s = 1 2absinc = two-thirds of the root number three...

Increase the interval [2, positive infinity).

Let 2 be less than or equal to x10 1-4 x1x2>0, so f(x2)-f(x1)>0

i.e. f(x) at [2, positive infinity) is an increasing function.

The increasing interval of f(x)=x+4 x is [2,+infinity)Prove: Let x1>x2>=2

f(x1)-f(x2)=(x1+4/x1)-(x2+4/x2)=(x1-x2)+4(x2-x1)/(x1x2)=(x1-x2)[1-4/(x1x2)]

Since x1-x2>0,x1x2>4,0<1 x1x2<1 4, 1-4 (x1x2)>0

i.e. f(x1)-f(x2)>0

f(x1)>f(x2)

So, f(x) is an increasing function on [2,+infinity).

1.。m+d=mq

m+2d=mq2 So mq-m=1 hand hail 2 (mq2-m) q2-2q+1=0 q=1 and q is 1 is b has the element of repetition of filial piety, so it is abandoned.

2. m+d=mq2

m+2d=mq so 2q2-q-1=0 and q is not 1 socks and potatoes are written with q=-1 2

m+d=mq is known to be obtained

m+2d=mq2 imitation.

The draft is vertically multiplied by 2 minus

Removing the key size m gives q 2-2q+1=0q=1

Do it with vectors.

It can be seen from the title.

Vector ab=(-1,1), vector ac=(1,5) so |Vector ab|=√2,|Vector ac|= 26 because the vector ab*vector ac=-1*1+1*5=4 and the vector ab*vector ac=|Vector ab|*|Vector ac|*cos∠bac=2*√13*cos∠bac

So cos bac=2 13

The simplest thing is to create a Cartesian coordinate system, and then represent the three into a solution triangle.

a=(cosa,sina),b=( 3,-1)So 2a-b=(2cosa- 3,2sina+1)Therefore|2a-b|=√[(2cosa-√3)^2+(2sina+1)^2]

[4(cosa)^2-4√3cosa+3+4(sina)^2+4sina+1]

(8-4√3cosa+4sina)

[8+8sin(a-π/3)]

Because -1 sin(a-3) 1

So 0 8 + 8 sin(a- 3) 16

Therefore 0 |2a-b|≤4

If you don't understand, please hi me and have fun studying!

I won't give you detailed steps, it's better to learn math by yourself, look at the structure of the left and right, find the method by yourself, multiply both sides by 2 (n-1) times, and then keep simplifying.