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2 years ago

Consider in the figure below.

Mathematics

2 answers:

ELEN [110]2 years ago

6 0

⚘ Refer to the attachments!!~

marusya05 [52]2 years ago

5 0

Let's solve

in ∆GNK

GN=130
GJ=94
GK=GJ/2=47

Apply pythagorean theorem

$\\ \sf\longmapsto NK^2=GN^2-GK^2=130^2-47^2=16900-2209=14691$

$\\ \sf\longmapsto NK=\sqrt{14691}$

$\\ \sf\longmapsto NK=121(Approx)$

If you observe the traingle

GN=NJ=130

$\\ \sf\longmapsto LJ^2=JN^2-LN^2$

$\\ \sf\longmapsto LJ^2=130^2-78^2$

$\\ \sf\longmapsto LJ^2=16900-6084$

$\\ \sf\longmapsto LJ^2=10816$

$\\ \sf\longmapsto LJ=\sqrt{10816}$

$\\ \sf\longmapsto LJ=104$

LH=LJ =104

in ∆HNL

$\\ \sf\longmapsto HN^2=104^2+78^2$

$\\ \sf\longmapsto HN^2=10816+6084$

$\\ \sf\longmapsto HN^2=16900$

$\\ \sf\longmapsto HN=\sqrt{16900}$

$\\ \sf\longmapsto HN=130$

Done .

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Solve 9(8 - x) = 3x.

bulgar [2K]

Hello - let's do this step by step. Show your work.

You're asking: 9(8−x)=3x.

Now, simplify both sides of the equation.

9(8−x)=3x

(9)(8)+(9)(−x)=3x (To do that, distribute)

72+−9x=3x

−9x+72=3x

Now, subtract 3x from both sides.

−9x+72−3x=3x−3x

Simplify,

−12x+72=0

After, subtract 72 from both sides.

−12x+72−72=0−72

−12x=−72

Last thing, divide both sides by -12.

-12x/12 = -72/-12

Divide.

Therefore, you have x = 6 as your final answer.

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3 years ago

There are 8 action, 3 comedy, and 5 drama DVDs on a shelf. Suppose three DVDs are selected at random from the shelf. Find each p

nordsb [41]

8 action, 3 comedy, 5 drama....total = 16 dvd's

P(2 action, then a comedy)...without replacement

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3 years ago

C=1/21.22.23+1/22.23.24+................+1/200.201.202 . = là dấu nhân

Aneli [31]

It looks like you have to find the value of the sum,

$C = \displaystyle \frac1{21\times22\times23} + \frac1{22\times23\times24} + \cdots + \frac1{200\times201\times202}$

so that the n-th term in the sum is

$\dfrac1{(21+(n-1))\times(21+n)\times(21+(n+1))} = \dfrac1{(n+20)(n+21)(n+22)}$

for 1 ≤ n ≤ 180.

We can then write the sum as

$\displaystyle C = \sum_{n=1}^{180} \frac1{(n+20)(n+21)(n+22)}$

Break up the summand into partial fractions:

$\dfrac1{(n+20)(n+21)(n+22)} = \dfrac a{n+20} + \dfrac b{n+21} + \dfrac c{n+22}$

Combine the fractions into one with a common denominator and set the numerators equal to one another:

$1 = a(n+21)(n+22) + b(n+20)(n+22) + c(n+20)(n+21)$

Expand the right side and collect terms with the same power of n :

$1 = a(n^2+43n+462)+b(n^2+42n+440) + c(n^2+41n + 420) \\\\ 1 = (a+b+c)n^2 + (43a+42b+41c)n + 462a+440b+420c$

Then

a + b + c = 0

43a + 42b + 41c = 0

462a + 440b + 420c = 1

==> a = 1/2, b = -1, c = 1/2

Now our sum is

$\displaystyle C = \sum_{n=1}^{180} \left(\frac1{2(n+20)}-\frac1{n+21}+\frac1{2(n+22)}\right)$

which is a telescoping sum. If we write out the first and last few terms, we have

C = 1/(2×21) - 1/22 + 1/(2×23)

… … + 1/(2×22) - 1/23 + 1/(2×24)

… … + 1/(2×23) - 1/24 + 1/(2×25)

… … + 1/(2×24) - 1/25 + 1/(2×26)

… … + … - … + …

… … + 1/(2×198) - 1/199 + 1/(2×200)

… … + 1/(2×199) - 1/200 + 1/(2×201)

… … + 1/(2×200) - 1/201 + 1/(2×202)

Notice the diagonal pattern of underlined and bolded terms that add up to zero (e.g. 1/(2×23) - 1/23 + 1/(2×23) = 1/23 - 1/23 = 0). So, like a telescope, the sum collapses down to a simple sum of just six terms,

C = 1/(2×21) - 1/22 + 1/(2×22) + 1/(2×201) - 1/201 + 1/(2×202)

which we simplify further to

C = 1/42 - 1/44 - 1/402 + 1/404

C = 1,115/1,042,118 ≈ 0.00106994

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3 years ago

If the domain of the coordinate transformation f(x,y)=(y+2,-x-4) is (1,-4),(3,-2), (0,-1)

Mama L [17]

Answer:

The Fundamental Graphing Principle for Functions says that for a point (a, b) to be on the graph,

f(a) = b. In particular, we know f(0) = 1, f(2) = 3, f(4) = 3 and f(5) = 5. Suppose we wanted to

graph the function defined by the formula g(x) = f(x) + 2. Let’s take a minute to remind ourselves

of what g is doing. We start with an input x to the function f and we obtain the output f(x).

The function g takes the output f(x) and adds 2 to it. In order to graph g, we need to graph the

points (x, g(x)). How are we to find the values for g(x) without a formula for f(x)? The answer is

that we don’t need a formula for f(x), we just need the values of f(x). The values of f(x) are the

y values on the graph of y = f(x). For example, using the points indicated on the graph of f, we

can make the following table.

x (x, f(x)) f(x) g(x) = f(x)

In general, if (a, b) is on the graph of y = f(x), then f(a) = b, so g(a) = f(a) + 2 = b + 2. Hence,

(a, b+ 2) is on the graph o

main role x (x, f(x)) f(x) g(x) = f(x) + 2 (x, g(x))

0 (0, 1) 1 3 (0, 3)

2 (2, 3) 3 5 (2, 5)

4 (4, 3) 3 5 (4, 5)

5 (5, 5) 5 7 (5, 7)

Step-by-step explanation:

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3 years ago

Irrotional number I need a example

tekilochka [14]

Irrational numbers are numbers that can not be written as a simple fraction. An example of one would be $\pi$ . Pi is about 3.14, but it goes on forever. You can not write pi as a simple fraction.

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4 years ago