Answer:
16
Step-by-step explanation:
First of all, I think it was "respectively", not "respecfully", =))). A noticeable point.
From the problem, three item's costs are represented by three consecutive even integer.
Thus, we can call cost of spoiler is x, sunroof is x-2, stereo is x + 2. It is conditioned that x is an even number.
Since the sum of the three is 48, we have
(x-2) + x + (x+2) = 48
x+x+x -2 +2 = 48
3x =48
x=16
So the spoiler is 16; thus, the sunroof is 14 and the stereo is 18
The question seems incomplete, as the length of the hour hand isn't given ;
If the tip of the hour hand is taken as 30mm
Answer:
534.1 mm
Step-by-step explanation:
In 2 hours ; cycle performed :
2/ 12
Circumference of a circle = 2 * pi *r
Circumference = 2 * pi * 30 = 60pi
Distance traveled : 60pi * 2/12 = 120pi/ 12 =10pi
The minute hand travels 2 comply cycle in 2 hours
150% taller than short hand :
1.5 * 30 = 45 mm
Distance traveled : 2 (2 * pi * 45) = 180pi
(180pi - 10pi) = 170pi
170π = 534.07075
= 534.1 mm

Notice that

So as

you have

. Clearly

must converge.
The second sequence requires a bit more work.

The monotone convergence theorem will help here; if we can show that the sequence is monotonic and bounded, then

will converge.
Monotonicity is often easier to establish IMO. You can do so by induction. When

, you have

Assume

, i.e. that

. Then for

, you have

which suggests that for all

, you have

, so the sequence is increasing monotonically.
Next, based on the fact that both

and

, a reasonable guess for an upper bound may be 2. Let's convince ourselves that this is the case first by example, then by proof.
We have


and so on. We're getting an inkling that the explicit closed form for the sequence may be

, but that's not what's asked for here. At any rate, it appears reasonable that the exponent will steadily approach 1. Let's prove this.
Clearly,

. Let's assume this is the case for

, i.e. that

. Now for

, we have

and so by induction, it follows that

for all

.
Therefore the second sequence must also converge (to 2).
Answer:
50º & 40º
Step-by-step explanation:
complementary anlges add up to 90º. so, we can make an equation:
x+x-10=90
2x=100
x=50
so the angles are 50º and 40º.
Answer: 5
Step-by-step explanation:
You see 2x2 = 4 right and since this is operation 2 / 10 = 5 and 6-5 = 1 so add 1 and that gives you 5
2x2 = 4 / 10/2 = 5 / 6-5 = 1 +4 = 5