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1 year ago

Show that the three points whose position vectors are 7j+ 10k,-i + 6j+6k and - 4i + +9j + 6k form an isosceles right

Mathematics

1 answer:

Novay_Z [31]1 year ago

3 0

Answer:

AB = √18 , BC=√18 and CA =4

AB²+BC² = CA² and AB=BC

ΔABC isosceles right angled triangle.

Step-by-step explanation:

Given vectors are 7j+ 10k,-i + 6j+6k and - 4i + +9j + 6k

A( 0,7,10), B( -1,6,6) C(-4,9,6)

AB⁻ = OB-OA = -I+6j+6k-(7j+10k) = -I-j-4k

AB = $\sqrt{1+1+16} = \sqrt{18}$

BC = OC-OB = -4i+9j+6k-(-I+6j+6k) = -3i+3j

BC= $\sqrt{9+9} =\sqrt{18}$

CA = OA-OC = 7j+10k - (- 4i + +9j + 6k ) = 4i-2j+4k

CA = $\sqrt{16+4+16} =\sqrt{36} =4$

Since AB²+BC² = CA²

And AB=BC

Therefore it follows that ΔABC is a right angled isosceles triangle

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Answer:

$h=1.99 miles$

Step-by-step explanation:

Let's call $h$ the balloon's height above the ground and $b$ the horizontal distance between the balloon and the first milepost.

If the angle of the depression of this milepost is 24 degrees, we can say the following:

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$b=\frac{h}{tan(24)}$ (equation 1)

For the next milepost, the horizontal distance between the balloon and tihs milepost will be $(b+1)miles$ and the angle of depression will be 20 degrees, so we can say the following

$tan(20)=\frac{h}{b+1}$

$b+1=\frac{h}{tan(20)}$

$b=\frac{h}{tan20}-1$

then, replacing from equation 1

$\frac{h}{tan(24)} =\frac{h}{tan(20)}-1$

$1 =\frac{h}{tan(20)}-\frac{h}{tan(24)}$

$1 =h*(\frac{1}{tan(20)}-\frac{1}{tan(24)})$

$h=\frac{1}{(\frac{1}{tan(20)}-\frac{1}{tan(24)})}$

Resolving, we'll find the value of $h$

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2 years ago

A stadium asked for $760,000 for naming rights. During a bidding war for the stadium naming rights, one company bid 7% more than

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Answer:

$\$\ 829464$

Step-by-step explanation:

Bid of first company:

Bid is $7\%$ more

$7\%$ of $760000=\frac{7}{100}\times760000=53200$

Bid of first $=760000+53200=813200$

Bid of second company:

Bid of second is $2\%$ greater than that of first

$2\%$ of first bid $=\frac{2}{100}\times 813200=16264$

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2 years ago

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olga55 [171]

Hello. 

-------
Let 2003 be the zero year; then 2005 is the three year, and 2008 the 5 year.
---------------
P = ab^x
---
P(3) = ab^3 = 800000
P(0) = ab^0 = 900000

---
a = 900000
Solve for "b"::
b^3 = 8/9
b = 2/cbrt(9)
----
Equation::
P(x) = 900000^x
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Ans: P(5) = 900000

Have a nice day

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2 years ago

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Answer:

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Step-by-step explanation:

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From internet I found that approx lenght of a bike ( bicycle) is = 68 inches.

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