Answer:
74°
Step-by-step explanation:
A rhombus is a quadrilateral that has its opposite sides to be parallel to be each other. This means that the two interior opposite angles are equal to each other. Since the sum of the angles of a quadrilateral is 360°.
According to the triangle, since one of the acute angle is 32°, then the acute angle opposite to this angle will also be 32°.
The remaining angle of the rhombus will be calculated as thus;
= 360° - (32°+32°)
= 360° - 64°
= 296°
This means the other two opposite angles will have a sum total of 296°. Individual obtuse angle will be 296°/2 i.e 148°
This means that each obtuse angles of the rhombus will be 148°.
To get the unknown angle m°, we can see that the diagonal cuts the two obtuse angles equally, hence one of the obtuse angles will also be divided equally to get the unknown angle m°.
m° = 148°/2
m° = 74°
Hence the angle measure if m(1) is 74°
Answer:
It will take about 35.49 hours for the water to leak out of the barrel.
Step-by-step explanation:
Let 
be the depth of water in the barrel at time 
, where 
is measured in inches and in hours.
We know that water is leaking out of a large barrel at a rate proportional to the square root of the depth of the water at that time. We then have that
where 
is a constant of proportionality.
Separation of variables is a common method for solving differential equations. To solve the above differential equation you must:
Multiply by 
Multiply by 
Take integral
Integrate
Isolate
We know that the water level starts at 36, this means 
. We use this information to find the value of 
.
At t = 1, y = 34
So our formula for the depth of water in the barrel is
To find the time, , at which all the water leaks out of the barrel, we solve the equation
Thus, it will take about 35.49 hours for the water to leak out of the barrel.
