A cuboid has a volume of 120 cubic centimeters, a bottom area of 12 square centimeters and a bottom perimeter of 14 centimeters. What is the surface area of the cuboid?

A cuboid has a volume of 120 cubic centimeters, a bottom area of 12 square centimeters and a bottom perimeter of 14 centimeters. What is the surface area of the cuboid?

Height = volume / bottom area = 120 / 12 = 10cm
So side area = perimeter of bottom * height = 14 * 10 = 140
So surface area = side area + 2 bottom area = 140 + 12 * 2 = 164 square centimeters

Simplification of COS (27 degree + a) cos (33 degree - a) - sin (27 degree + a) sin (33 degree - a)

By using the formula of trigonometric function angle difference cos (a + b) = cosacosb sinasinb, we can assume that (27 ° + a) = a (33 ° - a) = B, and the above formula can be transformed into cos (27 degree + a) cos (33 degree - a) - Sin (27 degree + a) sin (33 degree - a) = cosacosb sinasinb = cos (a + b) = cos (27 ° + A + 33 ° - a) = cos60 ° = 1 / 2

A circle passes through two points a (4,2), B (- 1,3), and the sum of four intercepts on two coordinate axes is 2

Let the equation of circle be x2 + DX + Y2 + ey + F = 0, and substitute two points a (4, 2) and B (- 1, 3) into the equation to get: e = 5D + 10, f = - 14d-40, because the four intercepts are 2, so - D-E = 2, so the solution is: D = - 2, f = - 12, e = 0, so the equation of circle is x2-2x + y2-12 = 0, that is, (x-1) 2 + y2 = 13

It is known that the quadratic function is y = 1 / 2x & # 178; + 2x + 2, and the range of independent variables is 1 ≤ x ≤ 4

Y = 1 / 2 (x + 2) &# 178;, when x = - 2, the minimum value is 0, when 1 ≤ x ≤ 4, it is an increasing function, so the maximum value is 18 when x = 4, and the minimum value is 9 / 2 when x = 1

The quotient of x minus 5 divided by 2.5, the difference is 3.8, find X2, 6 times of a number minus the product of 4 and 0.8, the difference is 8.8, find this number
3. Four times the number of a is one less than three times the number of B. the number of B is 0.5. What's the number of a?
4. If a number is expanded by 5 times, it is equal to 6 and reduced by 10 times

1. X-5 / 2.5 = 3.8x-2 = 3.8x = 2 + 3.8x = 5.82.6x-4 * 0.8 = 8.86x-3.2 = 8.86x = 3.2 + 8.86x = 12x = 12 / 6x = 23. Let a number be x4x = 3 * 0.5-14x = 1.5-14x = 0.5x = 0.5 / 4x = 1 / 84. Let a number be x5x = 6 / 105x = 0.6x = 0.6 / 5x = 0.12

F (x) = 2x ^ 3-mx + 3, when x (- 2, + ∞) is an increasing function, when x (- ∞, - 2) is a decreasing function, then f (1) is equal to

Derivation f '(x) = 6x ^ 2-m
Because when x (- 2, + ∞) is an increasing function, when x (- ∞, - 2) is a decreasing function, so when x = - 2, the derivative value is 0
That is, f '(- 2) = 24-m = 0
So m = 24
So f (x) = 2x ^ 3-24x + 3
So f (1) = 2-24 + 3 = - 19

How much is 7 out of 12 times 8 out of 33 times 11 out of 13

14/119

Is cosa + cosa equal to cos2a?

Of course not
It should be 2cosa
cos2a=2(cosa)^2-1=1-2(sina)^2=(cosa)^2-(sina)^2

When m takes what value, the solution of equation 3 (x + m) = 5x-2 is negative?
Speed, reward is not a problem

3(x+m)=5x-2
3x+3m=5x-2
3x-5x=-2-3m
-2x=-2-3m
x=(2+3m)/2
∴0＞x=(2+3m)/2
2+3m＜0
3m＜-2
∴m＜-2/3

All denominators are four digits. Please fill in one digit in each square so that the equation holds 1 / () + 1 / 1990 = 1 / ()

The denominator of the right fraction should be smaller than 1990
1990=398×5
① 398 × 3 = 1194 is a four digit number
1/1194=（2＋3）/1194×5=2/1194×5＋3/1194×5=1/2985＋1/1990
②398×4=1592
1/1592＝（1＋4）/1592×5=1/1592×5＋4/1592×5=1/7960＋1/1990
There are two answers to this question. Do you understand?