Answer: With 11 pipes, you need 31.82 minutes to fill the tank.
Step-by-step explanation:
Let's define R as the rate at which one single pipe can fill a tank.
We know that 7 of them can fill a tank in 50 minutes, then we have the equation:
7*R*50min = 1 tank
Whit this equation, we can find the value of R:
R = 1 tank/(7*50min) = (1/350) tank/min.
Now that we know the value of R, we can do the same calculation but now with 11 pipes.
Then the time needed to fill the tank, T, is such that:
11*(1/350 tank/min)*T = 1 tank
We need to isolate T.
T = 1 tank/(11*(1/350 tank/min)) = 31.82 min
With 11 pipes, you need 31.82 minutes to fill the tank.
B) Detergent B is less expensive than Detergent A
2/15 sorry if it’s wrong all I did was just divide both of them
<h3>
Answer:</h3>
System
Solution
- p = m = 5 — 5 lb peanuts and 5 lb mixture
<h3>
Step-by-step explanation:</h3>
(a) Generally, the equations of interest are one that models the total amount of mixture, and one that models the amount of one of the constituents (or the ratio of constituents). Here, there are two constituents and we are given the desired ratio, so three different equations are possible describing the constituents of the mix.
For the total amount of mix:
... p + m = 10
For the quantity of peanuts in the mix:
... p + 0.2m = 0.6·10
For the quantity of almonds in the mix:
... 0.8m = 0.4·10
For the ratio of peanuts to almonds:
... (p +0.2m)/(0.8m) = 0.60/0.40
Any two (2) of these four (4) equations will serve as a system of equations that can be used to solve for the desired quantities. I like the third one because it is a "one-step" equation.
So, your system of equations could be ...
___
(b) Dividing the second equation by 0.8 gives
... m = 5
Using the first equation to find p, we have ...
... p + 5 = 10
... p = 5
5 lb of peanuts and 5 lb of mixture are required.
The identity Sin(α)/Tan(α) = Cos(α) is valid
Trigonometry is study of triangles. All trigonometric ratios are defined using the sides of the right triangle, such as an adjacent side, opposite side, and hypotenuse side. Three major of them are as follows :-
Sine Function:
sin(θ) = Opposite / Hypotenuse
Cosine Function:
cos(θ) = Adjacent / Hypotenuse
Tangent Function:
tan(θ) = Opposite / Adjacent
Lets prove this identity by proceeding with the LHS
= Sin(α)/Tan(α)
= Sin(α)/ (Sin(α)/Cos(α)) (Tan(α) = Sin(α)/Cos(α))
= Sin(α)xCos(α) / Sin(α)
= Cos(α)
Hence verified
Learn more about Trigonometric Ratios here :
brainly.com/question/13776214
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