Answer:
log₅(3125) = 5
Step-by-step explanation:
Given:
log₅(3125)
Now,
using the property of log function that
logₐ(b) = 
thus,
Therefore, applying the above property, we get
⇒ 
(here log = log base 10)
now,
3125 = 5⁵
thus,
⇒ 
Now,
we know from the properties of log function that
log(aᵇ) = b × log(a)
therefore applying the above property we get
⇒ 
or
⇒ 5
Hence,
log₅(3125) = 5
Answer:
Step-by-step explanation:
The segment joining an original point with its rotated image forms a chord of the circle of rotation containing those two points. The center of the circle is the center of rotation.
This means you can find the center of rotation by considering the perpendicular bisectors of the segments joining points with their images. Here, the only proposed center that is anywhere near the perpendicular bisector of DE is point M.
__
Segment AD is perpendicular to corresponding segment FE, so the angle of rotation is 90°. (We don't know which way (CW or CCW) unless we make an assumption about which is the original figure.)
1. 40 units___16 workers
20 units___x= 8 workers
(20*16)/40=8
2. 40 units___16 workers
25 units___x= 10 workers
(25*16)/40=10
3. 40 units___16 workers
100 units___x= 40 workers
(100*16)/40=40
To make it easier, you calculate the volume of the first aquarium.
1st aquarium:
V = L x W x H
V = 8 x 9 x 13
V = 72 x 13
V = 936 in.
Rate: 936 in./2 min.
Now that you've got the volume and rate of the first aquarium, you can find how many inches of the aquarium is filled within a minute, which is also known as the unit rate. To do that, you have to divide both the numerator and denominator by their least common multiple, which is 2. 936 divided by 2 is 468 and 2 divided by 2 is 1.
So the unit rate is 468 in./1 min. Now that you've got the unit rate, you can find out how long it'll take to fill the second aquarium up by finding its volume first.
2nd aquarium:
V = L x W x H
V = 21 x 29 x 30
V = 609 x 30
V 18,270 inches
Calculations:
Now, you divide 18,270 by 468 to find how many minutes it will take to fill up the second aquarium. 18,270 divided by 468 is about 39 (the answer wasn't exact, so I said "about").
2nd aquarium's rate:
18,270 in./39 min.
As a result, it'll take about 39 minutes to fill up an aquarium measuring 21 inches by 29 inches by 30 inches using the same hose. I really hope I helped and that you understood my explanation! :) If I didn't, I'm sorry. I tried. :(
Answer:
1, 2
2, 5
3, 8
4, 11
5, 14
Step-by-step explanation:
you just plug each n value into the <em>n</em>
