Answer:
-2/√3 atan ((2t + 1)/√3) + C
Explanation:
∫ (t − 1) / (1 − t³) dt
Factor the difference of cubes:
∫ (t − 1) / ((1 − t)(1 + t + t²)) dt
Divide:
∫ -1 / (1 + t + t²) dt
-∫ 1 / (t² + t + 1) dt
Complete the square:
-∫ 1 / (t² + t + ¼ + ¾) dt
-∫ 4 / (4t² + 4t + 1 + 3) dt
-∫ 4 / ((2t + 1)² + 3) dt
If u = 2t + 1, du = 2 dt:
-∫ 2 / (u² + 3) du
Use an integral table, or use trigonometric substitution:
-2 (1/√3) atan (u/√3) + C
-2/√3 atan (u/√3) + C
Substitute back:
-2/√3 atan ((2t + 1)/√3) + C
Answer:
• it charges banks more interest
• it sells more securities
• it decreases the money supply
In response to high inflation, the Fed charges banks more interests and pays the banks less interests. It also sells not securities.
Answer:
The hydrostatic force of 313920 N is acted on each wall of the swimming pool and this force is acted at 1 m from the ground. The hydrostatic force is quadruple if the height of the walls is doubled.
<u>Explanation:</u>
To calculate force on the walls of swimming pool whose dimensions are given as <em>8-m-long, 8-m-wide, and 2-m-high</em>. We know that formula for hydrostatic force is
, we know ρ=density of fluid=1000
,
g=acceleration due to gravity=9.81
, h=height of the pool=2 m and l=length of the pool=8 m.
hydrostatic force on each wall=
= 313920 N.
<em>The distance at which hydrostatic force is acted is half of the height of the swimming pool.
</em>
At 1 m from the ground this hydrostatic force is acted on each wall.
The force is <em>quadruple if the height of the walls of the pool is doubled</em> this is because, the<em> height is doubled and taken as h=4 m</em> and substitute in the equation =
=
= 1255680 N. This is 4 times 313920 N.
To solve this problem we will proceed to calculate the specific volume from the area of the cylinder and the sensitivity. Later we will calculate the volumetric coefficient of thermal expansion and finally we will be able to calculate the volume through the relation of the two terms mentioned above. Our values are



Let's start by calculating the specific volume which is given by

Here,
d = Diameter
= Sensitivity
Replacing our values we have


Now we will obtain the value of the volumetric coefficient of thermal expansion of mercury through the differential expansion coefficient of Hg whic is three times, then



Finally the relation to calculate the volume the bulb must is





Therefore the volume that the bulb must have is 