= (1/2) (17.2) (7.1) sin (21.67)
= 22.5470 square meters
water evaporates from a pond at a rate of 0.05 inches per hour hour what is the change in the water level of the pond after 24 h
2 answers:
Answer:
The change in the water level of the pond after 24 hours is 1.2 inches or what is the same inches
Step-by-step explanation:
The rule of three or is a way of solving problems of proportionality between three known values and an unknown value, establishing a relationship of proportionality between all of them. That is, what is intended with it is to find the fourth term of a proportion knowing the other three. Remember that proportionality is a constant relationship or ratio between different magnitudes.
If the relationship between the magnitudes is direct, that is, when one magnitude increases, so does the other, the direct rule of three must be applied. To solve a direct rule of three, the following formula must be followed:
a ⇒ b
c ⇒ x
So,
The direct rule of three is the rule applied in this case as follows: If the change in water level is 0.05 inches per hour, what is the change in water level after 24 hours?
<u><em>change in water level=1.2 inches</em></u>
To pass a decimal number to a fraction, you must:
- Put the decimal number in a fraction above a 1. That is, the decimal number is the numerator, 1 the denominator.
- Find an equivalent fraction. That fraction will carry in the denominator a 1, and as many zeros as decimals the number has.
- Multiply the number above by that number.
- Simplify the fraction.
Applied to this case would be:
Since the denominator was multiplied by 10, the decimal numerator is also multiplied by 10:
Simplifying the rational number (for this the numerator and denominator is divided by the same number, in this case by number 2), you get:
Finally, <u><em>the change in the water level of the pond after 24 hours is 1.2 inches or what is the same inches</em></u>
You might be interested in
The first thing we are going to assume for this case is that the tree and the post are located in the same place.
From that place, both cast a shadow in the same direction.
We then have two similar triangles.
Therefore, we have the following relationship:
From here, we clear the value of x.
We have then:
Rewriting:
Answer:
the tree is 30 feet tall
From that place, both cast a shadow in the same direction.
We then have two similar triangles.
Therefore, we have the following relationship:
From here, we clear the value of x.
We have then:
Rewriting:
Answer:
the tree is 30 feet tall
The given complex number is
z = 1 + cos(2θ) + i sin(2θ), for -1/2π < θ < 1/2π
Part (i)
Let V = the modulus of z.
Then
V² = [1 + cos(2θ)]² + sin²(2θ)
= 1 + 2 cos(2θ) + cos²2θ + sin²2θ
Because sin²x + cos²x = 1, therefore
V² = 2(1 + cos2θ)
Because cos(2x) = 2 cos²x - 1, therefore
V² = 2(1 + 2cos²θ - 1) = 4 cos²θ
Because -1/2π < θ < 1/2π,
V = 2 cosθ PROVEN
Part ii.
1/z = 1/[1 + cos2θ + i sin 2θ]
The denominator is
Therefore
The real part of 1/ = 1/ (constant).
z = 1 + cos(2θ) + i sin(2θ), for -1/2π < θ < 1/2π
Part (i)
Let V = the modulus of z.
Then
V² = [1 + cos(2θ)]² + sin²(2θ)
= 1 + 2 cos(2θ) + cos²2θ + sin²2θ
Because sin²x + cos²x = 1, therefore
V² = 2(1 + cos2θ)
Because cos(2x) = 2 cos²x - 1, therefore
V² = 2(1 + 2cos²θ - 1) = 4 cos²θ
Because -1/2π < θ < 1/2π,
V = 2 cosθ PROVEN
Part ii.
1/z = 1/[1 + cos2θ + i sin 2θ]
The denominator is
Therefore
The real part of 1/ = 1/ (constant).