Answer:
The length of QR is approximately 18.3 cm
Step-by-step explanation:
The given parameters are;
The length of the side PR = 23 cm
The length of the side PQ = 22 cm
The measure of the angle QPR = 48°
By cosine rule, we have;
![\overline{QR}^2 = \overline{PR}^2 + \overline{PQ}^2 - 2 \times \overline{PR} \times \overline{PQ} \times cos(\angle QPR)](https://tex.z-dn.net/?f=%5Coverline%7BQR%7D%5E2%20%3D%20%5Coverline%7BPR%7D%5E2%20%2B%20%5Coverline%7BPQ%7D%5E2%20-%202%20%5Ctimes%20%5Coverline%7BPR%7D%20%20%5Ctimes%20%5Coverline%7BPQ%7D%20%5Ctimes%20cos%28%5Cangle%20QPR%29)
Plugging in the values gives;
![\overline{QR}^2 = 23^2 + 22^2 - 2 \times 23 \times 22\times cos(48^{\circ}) \approx 335.84](https://tex.z-dn.net/?f=%5Coverline%7BQR%7D%5E2%20%3D%2023%5E2%20%2B%2022%5E2%20-%202%20%5Ctimes%2023%20%20%5Ctimes%2022%5Ctimes%20cos%2848%5E%7B%5Ccirc%7D%29%20%5Capprox%20335.84)
![\therefore \overline{QR} \approx \sqrt{335.84} \approx 18.3](https://tex.z-dn.net/?f=%5Ctherefore%20%5Coverline%7BQR%7D%20%5Capprox%20%5Csqrt%7B335.84%7D%20%5Capprox%2018.3)
The length of QR ≈ 18.3 cm
Answer: There are 27 trees that Abe can plant in each row. And there are 1 pine tree and 2 oak tree in each row.
Explanation:
Since we have given that
Number of oak trees = 54
Number of pine trees = 27
According to question, we have given that Abe wants to plant the trees in rows that all have the same number of trees and are made up of only one type of tree.
So, the greatest number of trees is given by
![H.C.F\ of\ 27\ and\ 54=27](https://tex.z-dn.net/?f=H.C.F%5C%20of%5C%2027%5C%20and%5C%2054%3D27)
Hence, there are 27 trees that Abe can plant in each row.
Therefore, there are ![\frac{27}{27}=1\text{ pine tree and }\frac{54}{27}=2\text{ oak trees.}](https://tex.z-dn.net/?f=%5Cfrac%7B27%7D%7B27%7D%3D1%5Ctext%7B%20pine%20tree%20and%20%7D%5Cfrac%7B54%7D%7B27%7D%3D2%5Ctext%7B%20oak%20trees.%7D)
Step-by-step explanation:
2nd is same solution
3rd is different solution
4th is same solution
(how I did this is by simply mathematics )
+ - = -
+ += +
How do you give 15 points to Sum 1