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3 years ago

What is the area of the shaded region?

Mathematics

1 answer:

bazaltina [42]3 years ago

3 0

A = 1/2(12)(5) - 1/2(4)(3)
A = 30 - 6
A = 24

answer
24 mm^2

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Can anyone help me solve this? Please and thank you!

AveGali [126]

It's the sum of a geometric sequence.

Let's rewrite it a bit:

$\displaystyle\\\sum_{n=1}^{10}8\left(\dfrac{1}{4}\right)^{n-1}=8\sum_{n=1}^{10}\left(\dfrac{1}{4}\right)^n\cdot \left(\dfrac{1}{4}\right)^{-1}=8\sum_{n=1}^{10}\left(\dfrac{1}{4}\right)^n\cdot 4=32\sum_{n=1}^{10}\left(\dfrac{1}{4}\right)^n$

And now let's calculate this sum $\displaystyle \sum_{n=1}^{10}\left(\dfrac{1}{4}\right)^n$ :

$S_n=\dfrac{a(1-r^n)}{1-r}\\\\a=\dfrac{1}{4}\\n=10\\r=\dfrac{1}{4}\\\\S_{10}=\dfrac{\dfrac{1}{4}\cdot\left(1-\left(\dfrac{1}{4}\right)^{10}\right)}{1-\dfrac{1}{4}}=\dfrac{\dfrac{1}{4}\cdot\left(1-\dfrac{1}{1048576}\right)}{\dfrac{3}{4}}=\dfrac{\dfrac{1048575}{1048576}}{3}=\dfrac{1048575}{3145728}=\\=\dfrac{349525}{1048576}$

Now let's calculate the initial sum:

$\displaystyle 32\cdot \sum_{n=1}^{10}\left(\dfrac{1}{4}\right)^n=32\cdot \dfrac{349525}{1048576}=\dfrac{349525}{32768}\approx10.67$

8 0

2 years ago

Solve for v. 144v2 + 76 = 85 Write your answers as integers or as proper or improper fractions in the simplest form.

coldgirl [10]

Answer:

$144 {v}^{2} + 76 = 85 \\ 144 {v}^{2} = 85 - 76 \\ 144 {v}^{2} = 9 \\ {v}^{2} = 9 \div 144 \\ \\ {v}^{2} = \frac{9}{144} \\ \\ {v}^{2} = \frac{1}{16} \\ \\ v = \sqrt{ \frac{1}{16} } \\ \\ v = \frac{1}{4} \: , - \frac{1}{4} \\ \\ v = 0.25 \: , - 0.25$

I hope I helped you^_^

7 0

3 years ago

4 cm on a map are equal to 5 km in real life. If two points are 16 cm apart on the map, how far apart are they in real life? *

Alex

Answer:

20km if 4cm=5km then 16cm=20km

5 0

3 years ago

Evaluate 7w -14 for w=9

densk [106]

It is 49. 7(9) -14 is 49.

5 0

4 years ago

Solve the equation. Then check your solution.

Arte-miy333 [17]

8x+5= 69

Move +5 to the other. Sign changes from +5 to -5.

8x+5-5= 69-5

8x= 64

Divide by 8

8x/8= 64/8

x= 8

Answer : x= 8

4 0

3 years ago