For an experiment, a scientist designs a can, 20 cm in height, that can hold water. A
1 answer:
Step-by-step explanation:
The height of the water in the can is a function of time, because it depends on the time the water flows out each minute.
The height h in cm is a function f of time t in minutes since poking the hole, h= f(t)h=f(t). The expression for f(t) = 20. \frac{2}{3}^{t}f(t)=20.
3
2
t
The values of f -> f(0) = 20f(0)=20; f(1) = \frac{40}{3}f(1)=
3
40
; f(2) = \frac{80}{9}f(2)=
9
80
; f(3) = \frac{160}{27}f(3)=
27
160
The value of f(5) = \frac{640}{243}f(5)=
243
640
The level of water approaches close to the x-axis as time moves on. It does not completely approach zero.
Sorry if wrong answer
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Answer:
<h2>on the positive y-axis</h2>Step-by-step explanation:
Look at the picture.
(1) If x = 0, then the point is on the y-axis.
(2) If y > 0, then the point is above the x-axis.
From (1) and (2) we have: The point is on the positive y-axis.
Answer:
Shorter leg: 8 units
Longer leg: 15 units
Hypotenuse: 17 units
Step-by-step explanation:
We are given where
is the hypotenuse and
is the length of the shorter leg.
We got this equation from reading that the "hypotenuse of a triangle is 1 foot more than twice the length of the shorter leg". I replaced the "hypotenuse of a triangle" with , "is" with
, "1 foot more than" with
and finally "twice the length of the shorter leg" with
.
We also have "longer leg is 7 feet longer than the shorter leg".
I'm going to replace "longer leg" with .
I'm going to replace "is" with .
I'm going to replace "7 feet longer than the shorter leg" with .
So we have the equation .
So we have a right triangle since something there is a side being referred to as the hypotenuse. We can use Pythagorean Theorem to find a relation between all these sides.
So by Pythagorean Theorem, we have: .
Let's make some substitutions from above:
Let's expand the powers using:
Applying this now:
Combine like terms on right hand side:
Subtract everything on left hand side to get 0 on that side:
Simplify:
Reorder into standard form for a quadratic:
Every term is even and therefore divisible by 2. I will divide both sides by 2:
I'm going to see if this is factoroable.
We need to see if we can come up with two numbers that multiply -24 and add up to be -5.
Those numbers are -8 and 3.
So the factored form is:
This implies that either os
.
The first equation can be solved by adding 8 on both sides: .
The second equation can be solved by subtracting 3 on both sides: .
The only solution that makes sense for is 8 since it can't the shorter length cannot be a negative number.
So the dimensions of the right triangle are:
Shorter leg: 8 units
Longer leg: 15 units
Hypotenuse: 17 units
ANSWER= 30 rides
STEP-BY-STEP EXPLANATION
y=mx+b
m= $0.5 (per ride)
b= $5 (the cost)
x(rides) and y(parents money)
y= 0.5 x + 5
20= 0.5 x +5
20 - 5 = 0.5 x
15=0.5x
x=
x=30 rides