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sleet_krkn [62]
3 years ago
14

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]3 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

<u>Solving the i part;</u>

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

<u>Solving the j part;</u>

\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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-5= -5x-10

Plus 10 from both sides

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A population of rabbits on a farm grows by 12% each year. Assume that this increase occurs as new baby rabbits at the beginning
jolli1 [7]

Answer:

a) r₁₂ = 104.36

In general, rₙ = arⁿ⁻¹

b)

- rabbit food consumed during the 10th year is approximately 832 pounds

- rabbit food consumed in total for the 1st through 10th years is approximately 5265 pounds

Step-by-step explanation:

Given that:

r1 = 30 and a farm grows by 12%

a = 30 and the common ratio r = 1.12

now

n           r

1        30.00

2       33.60

3       37.63

4       42.15

5       47.21

6       52.87

7       59.21

8       66.32

9       74.28

10      83.19

11       93.18

12      104.36

Therefore r₁₂ = 104.36

In general, rₙ = arⁿ⁻¹

b)

if each rabbit consume 10 lbs of rabbit food each year

n           r                food consumed(lbs)

1        30.00               300

2       33.60               336

3       37.63                376

4       42.15                422

5       47.21                472

6       52.87               529

7       59.21                592

8       66.32               663

9       74.28               743

10      83.19                832

total                          5265

Therefore, the rabbit food consumed during the 10th year is approximately 832 pounds

And the rabbit food consumed in total for the 1st through 10th years is approximately 5265 pounds

6 0
2 years ago
In 2008, the price of gasoline was $2.79 per gallon. In 2009, the price of gasoline was
ikadub [295]

Answer:

36%

Step-by-step explanation:

line up $ and % data like this:

$2.79 represents 100%

$3.79 represents  X%

cross multiply

X*2.79 = 3.79*100

divide both sides by 2.79

X= 3.79*100 / 2.79 ≈ 136%

so it increased 36%

7 0
2 years ago
Find three consecutive whose sum 237
Nina [5.8K]

Answer:

78 79 80

Step-by-step explanation:

Let the smallest number = x

Let the next number = x + 1

Let the largest number = x + 2

x + x + 1 + x + 2 = 237      Add together to get the equation

3x + 3 = 237                     Subtract 3 from both sides.

3x + 3 - 3 = 237 - 3          Combine the right

3x = 234                           Divide by 3

x = 234/3

x = 78

The smallest number is 78

The next number 79

The highest number is 80

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enyata [817]
Hello,

3(2x-5)+2(4-x)
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7 0
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