Answer:
The two possible distance are 147.5km and 64.4km
Step-by-step explanation:
Given
<em>See Attachment for Illustration</em>
Required
Determine the possible distance of ship A from the boat
The distress is represented by X;
So, the question requires we calculate distance AX;
This will be done using cosine formula as follows;
![a^2 = b^2 + x^2 - 2bxCosA](https://tex.z-dn.net/?f=a%5E2%20%3D%20b%5E2%20%2B%20x%5E2%20-%202bxCosA)
In this case;
a = 70;
b = ??
x = 120
A = 28 degrees
Substitute these values in the formula above
![70^2 = b^2 + 120^2 - 2 * b * 120 Cos28](https://tex.z-dn.net/?f=70%5E2%20%3D%20b%5E2%20%2B%20120%5E2%20-%202%20%2A%20b%20%2A%20120%20Cos28)
![4900 = b^2 + 14400 - 2 * b * 120 * 0.8829](https://tex.z-dn.net/?f=4900%20%3D%20b%5E2%20%2B%2014400%20-%202%20%2A%20b%20%2A%20120%20%2A%200.8829)
![4900 = b^2 + 14400 - 211.9b](https://tex.z-dn.net/?f=4900%20%3D%20b%5E2%20%2B%2014400%20-%20211.9b)
Subtract 4900 from both sides
![b^2 + 14400 - 4900 - 211.9b = 0](https://tex.z-dn.net/?f=b%5E2%20%2B%2014400%20-%204900%20-%20211.9b%20%3D%200)
![b^2 + 9500 - 211.9b = 0](https://tex.z-dn.net/?f=b%5E2%20%2B%209500%20-%20211.9b%20%3D%200)
![b^2 - 211.9b + 9500 = 0](https://tex.z-dn.net/?f=b%5E2%20-%20211.9b%20%2B%209500%20%20%3D%200)
Solve using quadratic formula
![\frac{-b\±\sqrt{b^2 - 4ac}}{2a}](https://tex.z-dn.net/?f=%5Cfrac%7B-b%5C%C2%B1%5Csqrt%7Bb%5E2%20-%204ac%7D%7D%7B2a%7D)
Substitute 1 for a; -211.9 for b and 9500 for c
![b = \frac{-(211.9)\±\sqrt{(211.9)^2 - 4 * 1 * 9500}}{2 * 1}](https://tex.z-dn.net/?f=b%20%3D%20%5Cfrac%7B-%28211.9%29%5C%C2%B1%5Csqrt%7B%28211.9%29%5E2%20-%204%20%2A%201%20%2A%209500%7D%7D%7B2%20%2A%201%7D)
![b = \frac{211.9\±\sqrt{44901.61 - 38000}}{2}](https://tex.z-dn.net/?f=b%20%3D%20%5Cfrac%7B211.9%5C%C2%B1%5Csqrt%7B44901.61%20-%2038000%7D%7D%7B2%7D)
![b = \frac{211.9\±\sqrt{6901.61}}{2}](https://tex.z-dn.net/?f=b%20%3D%20%5Cfrac%7B211.9%5C%C2%B1%5Csqrt%7B6901.61%7D%7D%7B2%7D)
![b = \frac{211.9\±83.08}{2}](https://tex.z-dn.net/?f=b%20%3D%20%5Cfrac%7B211.9%5C%C2%B183.08%7D%7B2%7D)
This can be splitted to
or ![b = \frac{211.9-83.08}{2}](https://tex.z-dn.net/?f=b%20%3D%20%5Cfrac%7B211.9-83.08%7D%7B2%7D)
or ![b = \frac{128.82}{2}](https://tex.z-dn.net/?f=b%20%3D%20%5Cfrac%7B128.82%7D%7B2%7D)
or ![b = 64.41](https://tex.z-dn.net/?f=b%20%3D%2064.41)
![b = 147.5km\ or\ b = 64.4km](https://tex.z-dn.net/?f=b%20%3D%20147.5km%5C%20or%5C%20b%20%3D%2064.4km)
<em>Hence, the two possible distance are 147.5km and 64.4km</em>
Answer:
19
Step-by-step explanation:
Add the numbers:
![9+10=19](https://tex.z-dn.net/?f=9%2B10%3D19)
Therefore, 9 + 10 = 19
Answer: she walks 3 feet per second
Step-by-step explanation: If she walks 180 per minute and there is 60 seconds in a minute then just divide 180 by 60 and you will get 3 which is the answer.
Hope this helps
Step-by-step explanation:
25 questions, 2 points each.
that means there were 25×2 = 50 points in total.
Gideon got 42 out of the 50.
100% = 50
1% = 100%/100 = 50/100 = 0.5
42 is how many % ? as many as 1% (0.5) fits into 42.
so,
42/0.5 = 42×2 = 84%
he scored 84%.