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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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If speed varies inversely as the time it takes to drive and Kris takes 5 hours driving at 55 mph, what speed will Martin need to

Fudgin [204]

Answer:

55mph . None of the options are correct

Step-by-step explanation:

If the speed varies inversely as the time it takes to drive, then v ∝ 1/t. where;

v is the speed

t is the time taken

Hence;

v = k/t with k being the constant of proportionality.

Since it takes Kris 5 hours when driving at 55 mph, we will substitute v = 55mph and t = 5 hours. into the equation above to get the value of k as shown:

55 = k/5

Cross multiply

k = 55*5

k = 275

Hence, to calculate the speed it will Martin to drive for 5 hours, we will substitute k = 275 and t = 5 into the original equation v = k/t as shownl

v = 275/5

v = 55 mph

Hence, we can conclude that Martin will also need to drive at a speed of 55mph if he wants to take 5hours.

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2 years ago

You just measured a sugar cube and obtained the following information: mass = 3.48 g height = length = width = 1.3 cm Determine

nignag [31]

Answer: Volume of sugar cube=2.20 cm³

Density of sugar cube = 1.60 g/cm³.

The sugar cube will sink.

Step-by-step explanation:

Given : Mass of cube = 3.48 g

Also, dimension of sugar cube :

height = length = width = 1.3 cm

Since , the volume of cube = (side)³

Volume of sugar cube=(1.3) ³= 2.197 ≈ 2.20 cm³

Also, Density = $\dfrac{\text{Mass}}{\text{Volume}}$

⇒ Density of sugar cube = $\dfrac{3.48}{2.2}=1.5818\approx1.60\ g/cm^3$

∴ Density of sugar cube = 1.60 g/cm³.

It is known that the density of water is 1 g/cm³.

Here , density of sugar cube > density of water

⇒ The sugar cube will sink .

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2 years ago

The triangles shown below must be congruent. True or false

Alex777 [14]

The correct answer to your question is false. this is because congruent triangles must have the same 3 angles and the same 3 sides, and while these triangles have the same angles, they dont have the same sides.
let me know if you have any other questions
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2 years ago

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Martin's car had 86,456 miles on it. Of that distance, Martin's wife drove 24,901 miles,

navik [9.2K]

Answer:

Martin drove 53,558 miles.

Step-by-step explanation:

If you add up the amount of miles his son and wife drove, you get 32,898. To get the answer, you would subtract that from the total number of miles to get 53,558.

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2 years ago

James knows that when h walks, he takes about 120 steps per minute and that each step is 2.75 feet long. Which calculation is mo

Luba_88 [7]

Answer:

120*2.75*60/5280

= 3.75

Step-by-step explanation:

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