A good math problem in the second year of junior high school will also add 10 points

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1) Because the parabola passes through two points, e and f, and e and f are two points that are symmetrical to each other, the equation of the axis of symmetry of the parabola can be obtained from (k+3-k-1) 2=-b 2*( b=1 so the analytic formula of the parabola is y=

2) From the analytic formula, we can deduce the coordinates of a and b at two points, a(4,0) and b(0,4).

Since m is the midpoint of points A and B, the coordinates of point m are m(2,2).

From the question, it can be seen that the coordinates of point C are c(0,4-n) and the coordinates of point D are (4-m,0).

The intersection angle of the straight line mc and the straight line md is 45°, so tan45° = (kmc-kmd) 1+kmc*kmd (plus absolute value).

kmc=(n-2) 2 kmd=2 (m-2) is reduced to mn=8(m>0).

3) Since f is a point on a parabola, the coordinates of point f are brought into the analytic equation to solve k=1 or k=3

Therefore, the coordinates of point f are (-2,0) or (-4,-8) and then discussed on a case-by-case basis.

1) When the coordinates of point F are (-2,0), if the line MP passes the point F, then the analytical formula of the line MP is Y=

The y-axis intersects at the point (0,1) then n=3,m=8 3

If the straight line mq passes the f point, then the analytic formula of the straight line mq is y=then m=6, and n=4 3

In the same way, when the f coordinate is (-4, -8), m2=16 5 n2=5 2 or m4=3 2 n4=16 3 is discussed

The maximum distance between the chopsticks and the outside of the cup is: 15 cm - 12 cm = 3 cm.

The minimum distance is (chopsticks are placed obliquely) solution: set the diagonal distance between the mouth of the cup and the bottom of the cup to x, and find x as centimeters, so it is 2 to 3 centimeters.

If you analyze it, it should be like this.

The range of h is greater than or equal to 2 cm and less than or equal to 3 cm.

When upright, the longest is 15-12 = 3 cm, when placed obliquely, by the Pythagorean theorem, the hypotenuse = root number (5 2 + 12 2) = 13, and the shortest oblique is 15-13 = 2 cm, then the value range of h is 2 cm h 3 cm.

2-3 When inserting the chopsticks vertically into the cup, h is the maximum, h=15-12=13;When the chopsticks are placed diagonally into the cup, and the lower end is against the wall of the cup at the bottom of the cup, the h value is the smallest, h=15- 12 12+5 5=2 (the square can't be typed, so it is expressed).

h is greater than or equal to 2 less than or equal to 3

h is between 2 and 3, 2 is the use of the Pythagorean theorem, calculated to the diagonal is the longest is 13, then 15-13 to get 2. The other one is very simple!

The Pythagorean theorem is a minimum of 2 and a straight maximum of 3

Take the point: connect EO and extend the circle o at the point g, pass o as fh eg and cross the circle o at the points f and h.

Proof: Connecting ao, bo can have squares diagonal perpendicular to each other, and the triangle aoe and triangle doh can be proved to be congruent, so the angle eao = angle hdo, and the same can be proved otherwise.

The axis of symmetry is: x=1

That is, to seek |1+（y＋2）^2-（4-1）^2-(y+2/3)^2|The y-value when there is a maximum value.

Divide and return to the item|-40/9+32y/9|, at this time, when y tends to be positive and negative infinity, the distance difference is the largest.

Wrong question, right?!

The distance difference is the smallest, then 1+(y 2) 2-(4-1) 2-(y+2 3) 2 is the smallest, then 1+(y 2) 2 (4-1) 2-(y+2 3) 2

distance sum minimum, then 1+(y 2) 2 (4-1) 2 (y+2 3) 2 minimum, into the form of (y-a) 2+b, when y=a, and minimum, the minimum value is b

You can set the coordinates of m as (1,y), and the coordinates of the two points of a and b can be obtained from the title, and then find md ma to find the maximum plant.

Proof: Connect OC, pass the O point to do OD BN, OE AC, OF BM, and pass bn, ac, and BM to the points D, E, and F. respectively

ao,bo is the angular bisector of mac, mbn oe=of,od=of

OE=ODOC divides ACN

That is, point o is on the angular bisector of the ACN.

Let y=ax+b

164=15a+b

144=45a+b

a=-2 3 b=174 y=-2 3x+17410s's heartbeat22, then 132 beats per minute, the 69-year-old's extreme heartbeat is substituted y=-46+174=128, which is life-threatening.

1) Let y=kx+b.

164=15k+b

144=45k+b

k=-2 3,b=174

y=-2/3x+174

2) Substituting x=69 into the function to get y=128

128 jumps a minute, 10 is about 21-22 jumps, and there is no danger to life.

(1) y=-2 3x+174 (let y=ax+b, a=(164-144) (15-45))=-2 3, b=164-(-2 3*15)=174

2) The number of times it can withstand is y=-2 3*69+174=128 times Minutes = so there is danger.

Sum of principal and interest = principal + interest. If Uncle Li should buy this kind of treasury bill now for x yuan, the interest after 3 years will be 3x·, and the sum of principal and interest will be x+3x·yuan.