Answer and Step-by-step explanation:
Given the function y = 5x where x is the total number of cars parked in her lot and y is the total money earned. Since x is the independent variable as the money earned, y, depends on the amount of cars parked, we can say that the domain (the actual values the independent variable can assume) of this function is:
x = {0, 1, 2, 3, . . .}
This is because x, the number of cars, can never be a negative number..
Also, the range, the set of all the values of the dependent variable y, is: {all the numbers divisible by 5, including 0}
There are some online calculators
∠BDC and ∠AED are right angles, is a piece of additional information is appropriate to prove △ CEA ~ △ CDB
Triangle AEC is shown. Line segment B, D is drawn near point C to form triangle BDC.
<h3> What are Similar triangles?</h3>
Similar triangles, are those triangles which have similar properties,i.e. angles and proportionality of sides.
Image is attached below,
as shown in figure
∡ACE = ∡BCD ( common angle )
∡AED = ∡BDC ( since AE and BD are perpendicular to same line EC and make right angles as E and C)
∡EAC =- ∡DBC ( corresponding angles because AE and BD are parallel lines)
Thus, △CEA ~ △CDB , because of the two perpendiculars AE and BD.
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When the pile is 10 feet high, the rate at which sand is released from the chute is 125 ft^3/min
Let x denote the cone's height.
We've been told that when sand is poured down a chute, it always creates a conical pile whose height is equal to its diameter.
Since radius is known to be equal to half of diameter, the radius of a cone would be x/2.
To resolve the issue at hand, we shall use the volume of cone formula.
v=1/3
v= 1/3(x/2)^2(x/2)
v= 1/3(x^2/4)(x/2)
v= x^3/12
When we translate the height and radius values into terms of x, we obtain:
dv/dt =1/3 (3x^2)dx/dt
By solving the equation,
dv/dt =125
Consequently, 125ft^3/min of sand per minute are being released from the chute.
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