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denpristay [2]
2 years ago
5

A mouse climbs up a well of 86 meters. It advances 14 meters during the night, but during the day it retreats 2. The mouse will

reach the surface on the day:
Mathematics
1 answer:
Deffense [45]2 years ago
7 0

Step-by-step explanation:

we assume day and night are equally long.

and the mouse will start at night of day 1.

then, on day 2, it will first retreat 2 meters (during daylight) and then advance 14 meters (at night).

so, on every full day, the mouse will effectively advance 12 meters (-2 + 14 = 12).

with a starting value of 14 (the first night).

so, we are getting an arithmetic sequence

an = an-1 + c

c = 12 in our case.

a1 = 14

a2 = a1 + 12 = 14+12 = 26

a3 = a2 + 12 = a1 + 12 + 12 = 14 + 2×12 = 38

an = a1 + (n-1)×12 = 14 + 12(n-1)

at what n will it reach 86 ?

86 = 14 + 12(n-1) = 14 + 12n - 12 = 2 + 12n

84 = 12n

n = 7

so, on the 7th day the mouse will reach the surface (if we truly count the first starting night day 1 - this is up to your teacher, but I would).

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  HL

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The triangles are right triangles, opening the possibility of using the special right-triangle congruence theorems.

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The volume of the rectangular prism is 648 feet. The rectangular base is 6 feet by 9 feet. What is the height of the prism?
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Answer:

h=12ft

Step-by-step explanation:

The formula one would use for finding the volume of a rectangular prism is as follows:

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With this in mind, let's plug in the given variables in the question for this formula.

V=648ft^3

l=6ft

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h= ?

  • We don't know the height, but that's just fine. We will plug in all our values and isolate h.

V=lwh\\648ft^3=(6ft)(9ft)h

  • I'm leaving in units just because I want to show that units aren't just for show. They can be used when in doubt of how to go about your math.

648ft^3=(6ft)(9ft)h\\648ft^3=(54ft^2)h\\\frac{648ft^3}{54ft^2}=\frac{(54ft^2)h}{54ft^2}

  • Notice, that the units on the left side cancel out, leaving only the unit ft left next to the solution. In the same way, the units on the right side cancel out too, leaving only h, height.

\frac{648ft^3}{54ft^2}=\frac{(54ft^2)h}{54ft^2}\\12ft=h

If involving units only confuses you, like it does for me, you can remove them like so, you just need to know what units your solution uses instead of being able to come to the proper units by using math.

V=lwh\\648=(6)(9)h\\648=54h\\\frac{648}{54}=\frac{54h}{54}\\12ft=h

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