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Ne4ueva [31]
3 years ago
5

There are 4 semi-trailer trucks parked in a line at the rest stop. After the first truck, each truck in the line weighs 2 tons m

ore than the truck before it. The trucks weigh a total of 32 tons. How many pounds does each truck weigh?
Mathematics
2 answers:
butalik [34]3 years ago
4 0
Let the weight of the first truck be represented by w.

total weight = w + (2 + w) + (2 + 2 + w) + (2 + 2 + 2 + w)
32 = 4w + 12
20 = 4w
w = 5

Therefore, the first truck weighs 5 tons, the second weighs 7 tons, the third weighs 9 tons and the fourth weighs 11 tons.
white boy
3 years ago
boooooo
Xelga [282]3 years ago
3 0

Answer:

The weights of the trucks are 5, 7, 9 and 11 tons respectively.

Step-by-step explanation:

Let the weight of first truck = x ( in tons ).

It is given that the weight of the trucks is increasing by 2 tons after the first truck.

So, we get,

Truck                     Weight

1                                 x

2                                x+2

3                                x+2+2 = x+4

4                                x+4+2 = x+6

Since, the total weights of the trucks is 32 tons. We get,

x+(x+2)+(x+4)+(x+6)=32

i.e. 4x+12=32

i.e. 4x=20

i.e. x= 5

So, the weight of the first truck is 5 tons.

Then, we have,

The weight of 2nd truck = 5+2 = 7 tons

The weight of 2nd truck = 5+4 = 9 tons

The weight of 2nd truck = 5+6 = 11 tons

Hence, the weights of the trucks are 5, 7, 9 and 11 tons respectively.

white boy
3 years ago
boooo stupid noon
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5 0
3 years ago
find the angle between the vectors. (first find the exact expression and then approximate to the nearest degree. ) a=[1,2,-2]. B
SashulF [63]

Answer:

\theta = cos^{-1} (\frac{10}{\sqrt{9} \sqrt{25}})=cos^{-1} (\frac{10}{15}) = cos^{-1} (\frac{2}{3}) = 48.190

Since the angle between the two vectors is not 180 or 0 degrees we can conclude that are not parallel

And the anfle is approximately \theta \approx 48

Step-by-step explanation:

For this case first we need to calculate the dot product of the vectors, and after this if the dot product is not equal to 0 we can calculate the angle between the two vectors in order to see if there are parallel or not.

a=[1,2,-2], b=[4,0,-3,]

The dot product on this case is:

a b= (1)*(4) + (2)*(0)+ (-2)*(-3)=10

Since the dot product is not equal to zero then the two vectors are not orthogonal.

Now we can calculate the magnitude of each vector like this:

|a|= \sqrt{(1)^2 +(2)^2 +(-2)^2}=\sqrt{9} =3

|b| =\sqrt{(4)^2 +(0)^2 +(-3)^2}=\sqrt{25}= 5

And finally we can calculate the angle between the vectors like this:

cos \theta = \frac{ab}{|a| |b|}

And the angle is given by:

\theta = cos^{-1} (\frac{ab}{|a| |b|})

If we replace we got:

\theta = cos^{-1} (\frac{10}{\sqrt{9} \sqrt{25}})=cos^{-1} (\frac{10}{15}) = cos^{-1} (\frac{2}{3}) = 48.190

Since the angle between the two vectors is not 180 or 0 degrees we can conclude that are not parallel

And the anfle is approximately \theta \approx 48

3 0
3 years ago
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