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2 years ago

Ramon wants to plant cucumbers and tomatoes in his garden. He has room for

Mathematics

2 answers:

yarga [219]2 years ago

6 0

Answer:

Number of Cucumbers = 12

Number of Tomatoes = 4

Step-by-step explanation:

Let number of cucumber be c and number of tomatoes be t

Since he has room for 16 plants, we can write:

c + t = 16

He wants to plant 3 times as many cucumbers as tomatoes. We can write:

c = 3t

We can substitute this in 1st equation and solve for t:

c + t = 16

3t + t = 16

4t = 16

t = 16/4 = 4

And c = 3t

c = 3(4) = 12

Number of Cucumbers = 12

Number of Tomatoes = 4

babunello [35]2 years ago

3 0

Answer:

The correct answer is he should plant 12 cucumbers and 4 tomatoes.

Step-by-step explanation:

First we must start by analyzing the information we have:

We know that in total Ramon can only plant 16 plants.

We know that the amount of cucumbers he wants to plant is 3 times greater than the amount of tomatoes.

But what <u>we don't know is the amount of tomatoes</u> that he is going to plant, and that is what we are going to find out.

As we do not know this number, we will assign the incognita x.

So:

Total: 16

Number of cucumbers 3 times greater than tomatoes: 3x

Tomatoes: x

Now we just have to put together the equation:

$x + 3 x = 16$

Now we just have to solve to determine the amount of tomatoes :

$4 x = 16\\x= 16 : 4\\x= 4$

Knowing that the number of tomatoes is 4, we should only subtract that number from the total number of plants that Ramon can plant, and so we will obtain the amount of cucumbers:

16 - 4 = 12

In this way we can say that the correct answer is he should plant 12 cucumbers and 4 tomatoes.

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Step-by-step explanation:

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2 years ago

Two forces, F1 and F2, are represented by vectors with initial points that are at the origin. The first force has a magnitude of

Strike441 [17]

Answer:

Step-by-step explanation:

The two force F1 and F2 are represented by vectors with initial points that are at the origin.

the terminal point of the vector is point P(1, 1, 0)

Therefore, the direction of the vector force is

$v_1=(1-0)\hat i+(1-0)\hat j +(0-0)\hat k\\\\=1\hat i+1\hat j+0\hat k\\\\=\hat i + \hat j$

The unit vector in the direction of force will be

$\frac{v_1}{|v_1|} =\frac{\hat i+ \hat j}{\sqrt{1^2+1^2+0^2} } \\\\=\frac{1}{\sqrt{2} (\hat i +\hat j)}$

The magnitude of the force is 40lb, so the force will be

$F_1=40\times \frac{1}{\sqrt{2} } (\hat i+\hat j)\\\\=20\sqrt{2} (\hat i+\hat j)$

The terminal point of its vector is point Q(0, 1, 1)

Therefore, the direction of the vector force is

$v_2=(0-0)\hat i+(1-0)\hat j +(1-0)\hat k\\\\=0\hat i+1\hat j+1\hat k\\\\=\hat j + \hat k$

$\frac{v_2}{|v_2|} =\frac{\hat j+ \hat k}{\sqrt{0^2+1^2+1^2} } \\\\=\frac{1}{\sqrt{2} (\hat j +\hat k)}$

The magnitude of the force is 60lb, so the force will be

$F_2=60\times \frac{1}{\sqrt{2} } (\hat j+\hat k)\\\\=30\sqrt{2} (\hat j+\hat k)$

The resultant of the two forces is

$F=F_1+F_2\\\\=[20\sqrt{2} (\hat i+\hat j)]+[30\sqrt{2} (\hat j +\hat k)]\\\\=20\sqrt{2} \hat i+20\sqrt{2} \hat j +30\sqrt{2} \hat j+30\sqrt{2} \hat k\\\\=20\sqrt{2} \hat i+50\sqrt{2} \hat j+30\sqrt{2} \hat k$