Helen is organising a party and she needs party plates and straws their 30 party place in a pack there are 120 straws in a pack
2 answers:
Answer:
4 packs of party plates and one pack of straws.
Step-by-step explanation:
We have been given that there are 30 plates in a pack and 120 straws in a pack she needs exactly the same number of plates as straws.
To solve our given problem, we will convert find least common multiple of 30 and 120.
Multiples of 30: 30, 60, 90, 120,150,
Multiples of 120: 120, 240,...
We can see that least common multiple of 30 and 120 is 120.
Therefore, Helen should buy 4 packs of party plates and one pack of straws.
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Solution:
Consider the Given Isosceles Triangle
Considering the Possibilities
Case 1. When two equal angles are of 70°
Let the third angle be x.
Keeping in mind , that sum of Interior angles of Triangle is 180°.
70° + 70° + x= 180°
140° +x= 180°
x= 180°- 140°
x= 40°
Case 2:
When an angle measures 70°, and two equal angles measure x°.
Keeping the same property of triangle in mind, that is sum of interior angles of triangle is 180°.
70° + x° + x° = 180°
⇒ 70° + 2 x° = 180°
⇒ 2 x° = 180° - 70°
⇒ 2 x° = 110°
Dividing both sides by 2, we get
x= 55°
Answer:
5 trees should be planted to maximize the yield per acre,
The maximum yield would be 1250
Step-by-step explanation:
Given,
The original number of trees per acre = 20,
Average pounds of nuts by a tree = 60,
Let x be the times of increment in number of trees,
So, the new number of trees planted per acre = 20 + x
∵ for each additional tree planted per acre, the average yield per tree drops 2 pounds,
So, the new number of pounds of nut = (60 - 2x)
Thus, the total yield per acre,
Differentiating with respect to t ( time ),
Again differentiating with respect to t,
For maxima or minima,
⇒ 20 - 4x = 0
⇒ 20 = 4x
⇒ x = 5,
For x = 5, Y''(x) = negative,
Hence, Y(x) is maximum for x = 5,
And, maximum value of Y(x) = (20+5)(60 - 10) = 25(50) = 1250,
i.e. 5 trees should be planted to maximize the yield per acre,
and the maximum yield would be 1250 pounds