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Oliga [24]
3 years ago
12

Please help problem is in the image.

Mathematics
1 answer:
nika2105 [10]3 years ago
5 0

Answer:

16.5

Step-by-step explanation:

this is beacuse 16.5 times 2 is 33

You might be interested in
The additional cost per month of a sunroof, spoiler and stereo is represented by three consecutive even integers, respectfully.
lesya [120]

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

3 0
3 years ago
The length of the minute hand is 150% of the length of the hour hand. In 2 hours, how much farther does the tip of the minute ha
nekit [7.7K]

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

7 0
3 years ago
Determine whether the sequences converge.
Alik [6]
a_n=\sqrt{\dfrac{(2n-1)!}{(2n+1)!}}

Notice that

\dfrac{(2n-1)!}{(2n+1)!}=\dfrac{(2n-1)!}{(2n+1)(2n)(2n-1)!}=\dfrac1{2n(2n+1)}

So as n\to\infty you have a_n\to0. Clearly a_n must converge.

The second sequence requires a bit more work.

\begin{cases}a_1=\sqrt2\\a_n=\sqrt{2a_{n-1}}&\text{for }n\ge2\end{cases}

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

Monotonicity is often easier to establish IMO. You can do so by induction. When n=2, you have

a_2=\sqrt{2a_1}=\sqrt{2\sqrt2}=2^{3/4}>2^{1/2}=a_1

Assume a_k\ge a_{k-1}, i.e. that a_k=\sqrt{2a_{k-1}}\ge a_{k-1}. Then for n=k+1, you have

a_{k+1}=\sqrt{2a_k}=\sqrt{2\sqrt{2a_{k-1}}\ge\sqrt{2a_{k-1}}=a_k

which suggests that for all n, you have a_n\ge a_{n-1}, so the sequence is increasing monotonically.

Next, based on the fact that both a_1=\sqrt2=2^{1/2} and a_2=2^{3/4}, 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

a_3=\sqrt{2\times2^{3/4}}=\sqrt{2^{7/4}}=2^{7/8}
a_4=\sqrt{2\times2^{7/8}}=\sqrt{2^{15/8}}=2^{15/16}

and so on. We're getting an inkling that the explicit closed form for the sequence may be a_n=2^{(2^n-1)/2^n}, 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, a_1=2^{1/2}. Let's assume this is the case for n=k, i.e. that a_k. Now for n=k+1, we have

a_{k+1}=\sqrt{2a_k}

and so by induction, it follows that a_n for all n\ge1.

Therefore the second sequence must also converge (to 2).
4 0
3 years ago
An angle measures 10° less than the measure of its complementary angle. What is the measure of each angle?
Wewaii [24]

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.

5 0
3 years ago
. Simplify: (2 x 2 + 6-10 ÷<br><br> 2)​
Maurinko [17]

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

7 0
2 years ago
Read 2 more answers
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