Answer:
u = x tan(A) - sec(A) sqrt(x^2 + y^2 - (x cos(A) + y sin(A))^2) or u = sec(A) sqrt(x^2 + y^2 - (x cos(A) + y sin(A))^2) + x tan(A)
Step-by-step explanation:
Solve for u:
(x sin(A) - u cos(A))^2 + (x cos(A) + y sin(A))^2 = x^2 + y^2
Subtract (x cos(A) + y sin(A))^2 from both sides:
(x sin(A) - u cos(A))^2 = x^2 + y^2 - (x cos(A) + y sin(A))^2
Take the square root of both sides:
x sin(A) - u cos(A) = sqrt(x^2 + y^2 - (x cos(A) + y sin(A))^2) or x sin(A) - u cos(A) = -sqrt(x^2 + y^2 - (x cos(A) + y sin(A))^2)
Subtract x sin(A) from both sides:
-u cos(A) = sqrt(x^2 + y^2 - (x cos(A) + y sin(A))^2) - x sin(A) or x sin(A) - u cos(A) = -sqrt(x^2 + y^2 - (x cos(A) + y sin(A))^2)
Divide both sides by -cos(A):
u = x tan(A) - sec(A) sqrt(x^2 + y^2 - (x cos(A) + y sin(A))^2) or x sin(A) - u cos(A) = -sqrt(x^2 + y^2 - (x cos(A) + y sin(A))^2)
Subtract x sin(A) from both sides:
u = x tan(A) - sec(A) sqrt(x^2 + y^2 - (x cos(A) + y sin(A))^2) or -u cos(A) = -x sin(A) - sqrt(x^2 + y^2 - (x cos(A) + y sin(A))^2)
Divide both sides by -cos(A):
Answer: u = x tan(A) - sec(A) sqrt(x^2 + y^2 - (x cos(A) + y sin(A))^2) or u = sec(A) sqrt(x^2 + y^2 - (x cos(A) + y sin(A))^2) + x tan(A)
Answer: Rahul walks 2.7 km more than Vansh.
Step-by-step explanation:
The options include:
a. Vansh walks 7.2 km more than Rahul.
b. Vansh walks 2 km more than Rahul.
c. Rahul and Vansh both cover the same distance.
d. Rahul walks 2.7 km more than Vansh.
Distance covered by Rahul weekly = 9km
Distance covered by Vansh weekly = 900m × 7 = 6300m = 6300/1000 = 6.3km
From the above, we can see that Rahul walk (9km - 6.3km) = 2.7km more than Vansh.
Note: 1000 meters = 1 kilometers
Given:
JK is tangent to a circle with center H
To find:
The length of HK.
Solution:
The image is attached below.
JK = 8 mi, HJ = 15 mi
JK is tangent to a circle.
The tangent is always perpendicular to the radius.
Therefore, m∠J = 90°
Using Pythagoras theorem:
HK² = JK² + HJ²
HK² = 8² + 15²
HK² = 64 + 225
HK² = 289
HK² = 17²
Taking square root on both sides.
HK = 17
The length of HK is 17 mi.
Answer:
2
Step-by-step explanation:
there is 2: 3<u> 1 </u>
4
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