1.A wedding planner uses 72 ivy stems for 18 centerpieces. When she arrives at the venue, she realizes she will only need 16 centerpieces. How many ivy stems should she use so that the ratio of ivy stems to centerpieces stays the same?

64 ivy stems.

Step-by-step explanation:

Given:

A wedding planner uses 72 ivy stems for 18 centerpieces.

When she arrives at the venue, she realizes she will only need 16 centerpieces.

Question asked:

How many ivy stems should she use so that the ratio of ivy stems to centerpieces stays the same?

Solution:

As wedding planner uses 72 ivy stems for 18 centerpieces:

Ratio of ivy stems to centerpieces =

As she realizes that she needs only 16 centerpieces:

Let ivy stems should be used to stays the ratio same =

Now, to do the ratio same:-

Old ratio =

New ratio =

To do the ratio same:-

By cross multiplication:

Dividing both sides by 18

Therefore, 64 ivy stems she should use so that the ratio of ivy stems to centerpieces stays the same.

intensity of the vector is v= √37 ≈ 6.08 units and make angle ∡α ≈ 9.46° with east direction

step-by-step explanation:

required vector is consists of the two componentsvx= 2+4=6 units   and vy= 1 unit and vx ⊥ vywe will use pythagorian theorem to find intensity of the vector vv∧2 = vx∧2 + vy∧2 => v = √vx∧2 + vy∧2 = √6∧2 + 1∧2 = √36+1 = √37 ≈ 6.08 unitsthe angle ∡α between vector and east direction we wil find with tanαtanα = 1/6 => α = arc tanα = arc 1/6 => α ≈ 9.46°

hope this

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step-by-step explanation:

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