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CaHeK987 [17]
2 years ago
13

Jasmine unfolded a cardboard box. The figure of the unfolded box is shown below:

Mathematics
1 answer:
kodGreya [7K]2 years ago
5 0

Answer:

6×2×2

Step-by-step explanation:

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Find the measure of the arc
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Hmmm I think it’s...
4 0
2 years ago
Determine determine whether the following geometric series converges or diverges. if the series converges find its sum.
Lilit [14]

For starters,

\dfrac{3^k}{4^{k+2}}=\dfrac{3^k}{4^24^k}=\dfrac1{16}\left(\dfrac34\right)^k

Consider the nth partial sum, denoted by S_n:

S_n=\dfrac1{16}\left(\dfrac34\right)+\dfrac1{16}\left(\dfrac34\right)^2+\dfrac1{16}\left(\dfrac34\right)^3+\cdots+\dfrac1{16}\left(\dfrac34\right)^n

Multiply both sides by \frac34:

\dfrac34S_n=\dfrac1{16}\left(\dfrac34\right)^2+\dfrac1{16}\left(\dfrac34\right)^3+\dfrac1{16}\left(\dfrac34\right)^4+\cdots+\dfrac1{16}\left(\dfrac34\right)^{n+1}

Subtract S_n from this:

\dfrac34S_n-S_n=\dfrac1{16}\left(\dfrac34\right)^{n+1}-\dfrac1{16}\left(\dfrac34\right)

Solve for S_n:

-\dfrac14S_n=\dfrac3{64}\left(\left(\dfrac34\right)^n-1\right)

S_n=\dfrac3{16}\left(1-\left(\dfrac34\right)^n\right)

Now as n\to\infty, the exponential term will converge to 0, since r^n\to0 if 0. This leaves us with

\displaystyle\lim_{n\to\infty}S_n=\lim_{n\to\infty}\sum_{k=1}^n\frac{3^k}{4^{k+2}}=\sum_{k=1}^\infty\frac{3^k}{4^{k+2}}=\frac3{16}

8 0
3 years ago
Read 2 more answers
Let f(x) = 5x – 8 and g(x) = x + 3. Find f(g(x)) and g(f(x)).
wlad13 [49]

Answer and work down below. Let me know if you have any questions

3 0
3 years ago
If G = 70° and J = 40°, then GH ___ HJ. Choose the correct symbol to put in the blank.
Novosadov [1.4K]

Answer:

GH > HJ

The correct symbol is " >" (greater)

Step-by-step explanation:

we know that

In the triangle GHJ applying the law of sines

\frac{GH}{sin(J)}=\frac{HJ}{sin(G)}

substitute the given values

\frac{GH}{sin(40\°)}=\frac{HJ}{sin(70\°)}

Isolate GH

GH=\frac{HJ}{sin(70\°)}(sin(40\°))

GH=1.46(HJ)

therefore

GH > HJ

The correct symbol is " >" (greater)

7 0
3 years ago
Read 2 more answers
Determine the area of the blue triangle below. Round your answer to<br> the nearest tenth.
Sholpan [36]

Answer:

68.9 in^2

Step-by-step explanation:

first lets find the height of the blue triangle

hypotenuse = 15 in

one side is 12 in whereas other has to be find.

take 50 degree as reference angle

using sin rule

sin 50 = opposite/hypotenuse

0.76 = opposite/15

0.766*15 = opposite

11.49 = opposite

area of triangle = base*height/2

=12*11.49/2

=136.88/2

=68.94

=68.9 in^2

5 0
2 years ago
Read 2 more answers
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