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2 years ago

Given the vectors, a=3i+4j, b=-2i+5j, c=10i-j, d=-1/3i+5/2j, find -0.4a-0.3b+0.2d=?

Mathematics

1 answer:

sveta [45]2 years ago

6 0

Answer:

$-\frac{2}{3}i - \frac{13}{5}j$

Step-by-step explanation:

-0.4(3i + 4i) - 0.3(-2i + 5j) + 0.2(- $\frac{1}{3}i$ + $\frac{5}{2}$ j)

-1.2i - 1.6j + 0.6i - 1.5j - $\frac{0.2}{3}$ i + 0.5j

Converting to fraction form;

$-\frac{6}{5}i + \frac{3}{5}i - \frac{1}{15}i - \frac{8}{5}j - \frac{3}{2}j + \frac{1}{2} j$

Solving the i part;

$\frac{-18i + 9i - i}{15}$ = $-\frac{2}{3}i$

Solving the j part;

$\frac{-16j-15j+5j}{10} = -\frac{13}{5}$ j

So -0.4a - o.3b + 0.2d = $-\frac{2}{3}i$ - $\frac{13}{5}j$

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Two components of a minicomputer have the following joint pdf for their useful lifetimes X and Y: f(x, y) = xe−x(1 + y) x ≥ 0 an

Yuri [45]

Answer:

For the given explanation we see that two life times are not independent

Step-by-step explanation:

probability for X (for x≥ 0)

$\int\limits^\infty_0 {xe^-^x^(^1^+^y^)} \, dy$

$-e^-^x\int\limits^\infty_0 {de^-^x^y} \,$

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Probability for X exceed 3

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= $e^-^3$

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$\int\limits^\infty_0 {xe^-^x^(^1^+^y^)} \, dx \\$

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3 0

2 years ago

A customer at a store paid $64 for 3 large candles and 4 small candles. At the same store, a second customer paid $4 more than t

belka [17]

system of equations can be used to find the price in dollars of each large candle, x, and each small candle, y is $x+8y=68$ and $3x+4y=64$ .

Step-by-step explanation:

Here we have , A customer at a store paid $64 for 3 large candles and 4 small candles. At the same store, a second customer paid $4 more than the first customer for 1 large candle and 8 small candles. The price of each large candle is the same, and the price of each small candle is the same. We need to find Which system of equations can be used to find the price in dollars of each large candle, x, and each small candle, y . Let's find out:

Let the price in dollars of each large candle, x, and each small candle, y .So

A customer at a store paid $64 for 3 large candles and 4 small candles

Equation is :

⇒ $3x+4y=64$ .....(1)

At the same store, a second customer paid $4 more than the first customer for 1 large candle and 8 small candles.

Equation is :

⇒ $x+8y=68$ .......(2)

3(2)-(1) i.e.

⇒ $3(x+8y)-(3x+4y)=68(3)-64$

⇒ $20y=140$

⇒ $y=7$

So , $x+8y=68$

⇒ $x+8(7)=68$

⇒ $x=12$

Therefore , system of equations can be used to find the price in dollars of each large candle, x, and each small candle, y is $x+8y=68$ and $3x+4y=64$ .

7 0

2 years ago

$290, 12.5%, 6 months

Veronika [31]

The information shown here only shows a principal sum, a rate of interest and a period or time. There is no question as to what is needed. But suppose the need is for simple interest, then we calculate using the given information and the formula: I = PRT where I is simple interest, P is the principal, R is the rate per year, and T is time P = 290, T is 6 months which is 0.5 years, R = 12.5 % which is written as 0.125 in decimal fraction. I = 290 × 0.125 x 0.5 → I = 18.125 Therefore after 6 months , the interest earned will be 18. 125 dollars

3 0

2 years ago

(b) The train is 61 cm long and travels at a speed of 18 cm/s.

xz_007 [3.2K]

Answer:

It goes 18 cm every second:

18 x 4 = 72 cm

The bridge is 72 cm long.

Hope this helps!

3 0

2 years ago

Read 2 more answers

Devon purchased a new car valued at $16,000 that depreciated continuously at a rate of 35%. Its current value is $2,000. The equ

irga5000 [103]

I hope the equation will be 2000=16000(1-r)^t because t is missing in the equation which we need to find.

Given rate: r= 35%= 0.35.

So, first step is to plug in 0.35 for r in the given formula to get the value of t.

Hence, the equation will be:

2000=16000(1-0.35)^t

2000=16000(0.65)^t (By subtraction)

2000/16000= 16000(0.65)^t /16000 (Dividing each sides by 16000)

0.125 = 0.65^t (By simplifying).

log 0.125 = log 0.65^t (Taking log each sides to isolate t).

log 0.125 = t log 0.65 (By applying the log property).

$\frac{log 0.125}{log 0.65} =t$ (Dividing each sides by log 0.65)

-0.903/-0.187 =t

t= 4.83

t= 5 ( Rounded to nearest integers)

So, Devon's car is 5 years old.

7 0

2 years ago