The consequences of losing the mandate of heaven include that if the leader becomes unvirtous and people in the monarchs realm are suffering or starving from certain events seenot as a sign of ruler not being virtous, then being replaced and losing position of the emporer or being in charge is a threat. The mandate of heaven giveso you the authority to rule under the supposed word of God. Without this holy order, the people wouldn't want to follow the Supreme leader because they'd believe that they're not obligatedo tof anymore. Religion was very important at the time that the mandate of heaven was a key document in ruling political states, so it was very effective.

7 0

3 years ago

The regions bounded by the graphs of y=x2 and y=sin2x are shaded in the figure above. What is the sum of the areas of the shaded

Alex Ar [27]

Answer:

The sum of the area of the shaded regions = 0.248685

Explanation:

The sum of the area of the shaded region is given as follows;

The point of intersection of the graphs are;

y = x/2

y = sin²x

∴ At the intersection, x/2 = sin²x

sinx = √(x/2)

Using Microsoft Excel, or Wolfram Alpha, we have that the possible solutions to the above equation are;

x = 0, x ≈ 0.55 or x ≈ 1.85

The area under the line y = x/2, between the points x = 0 and x ≈ 0.55, A₁, is given as follows

1/2 × (0.55)×0.55/2 ≈ 0.075625

The area under the line y = sin²x, between the points x = 0 and x ≈ 0.55, A₂, is given using as follows;

$\int\limits {sin^n(x)} \, dx = -\dfrac{1}{n} sin^{n-1}(x) \cdot cos(x) + \dfrac{n-1}{n} \int\limits {sin^{n-2}(x)} \, dx$

Therefore;

$A_2 = \int\limits^{0.55}_0 {sin^2x} \, dx = \dfrac{1}{2} \left [x -sin(x) \cdot cos(x) \right]_0 ^{0.55}$

∴ A₂ =1/2 × ((0.55 - sin(0.55)×cos(0.55)) - (0 - sin(0)×cos(0)) ≈ 0.0522

The shaded area, $A_{1 shaded}$ = A₁ - A₂ = 0.075625 - 0.0522 ≈ 0.023425

Similarly, we have, between points 0.55 and 1.85

A₃ = 1/2 × (1.85 - 0.55) × 1/2 × (1.85 - 0.55) + (1.85 - 0.55) × 0.55/2 = 0.78

For y = sin²x, we have;

$A_4 = \int\limits^{1.85}_{0.55} {sin^2x} \, dx = \dfrac{1}{2} \left [x -sin(x) \cdot cos(x) \right]_{0.55} ^{1.85} \approx 1.00526$

The shaded area, $A_{2 shaded}$ = A₄ - A₃ = 1.00526 - 0.78 ≈ 0.22526

The sum of the area of the shaded regions, ∑A = $A_{1 shaded}$ + $A_{2 shaded}$

∴ A = 0.023425 + 0.22526 = 0.248685

The sum of the area of the shaded regions, ∑A = 0.248685

8 0

3 years ago

Please help me will give BRAILIEST!!!!!

mars1129 [50]

They add different things to the car so that they can make the cars faster so they can go onto the market they also make the car more expensive so they can make more money. Don't know if that helps but there.

3 0

3 years ago

Có một "tàu lạ" của nước ngoài hoạt động khảo sát dầu khí trên biển, cách bờ biển Vũng Tàu của nước ta 160 hải lý. Vận dụng nhữn

Vladimir79 [104]

Answer:

Explanation:

Có nhé

4 0

3 years ago