A car is traveling at \( 112 km / h \) due south at a point \( \frac { 4 } { 5 } \) kilometer north of an intersection. A police car is traveling at \( 96 km / h \) due west at a point \( \frac { 2 } { 5 } kilometer \) due east of the same intersection. At that instant, the radar in the police car measures the rate at which the distance between the two cars is changing. What does the radar gun register? Round your answer to three decimal places.
Question
Answer
143.11 km/h
Related Questions
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What is the distance from Kareem to the house?
Kareem and Amy are standing on a riverbank, \( 150 \) meters apart, at points \( A \) and \( B \) respectively. (See the figure below.) They want to know the distance from Kareem to a house located across the river at point \( C \) . Kareem measures angle \( A \) (angle \( B A C \) ) to be \( 55 ^ { \circ } \) , and Amy measures angle \( B \) (angle \( A B C \) ) to be \( 74 ^ { \circ } \) . What is the distance from Kareem to the house? Round your answer to the nearest tenth of a meter.
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Suppose a projectile is fired from a cannon with velocity \( v _ { 0 } \) and angle of elevation \( \theta \) . The horizontal distance \( R ( \theta ) \) it travels (in feet) is given by the following.
\( R ( \theta ) = \frac { ( v _ { 0 } ) ^ { 2 } \sin 2 \theta } { 32 } \)
If \( v _ { 0 } = 80 ft \) /s, what angle \( 0 \) (in radians) should be used to hit a target on the ground \( 118 \) feet in front of the cannon?
Q:
Consider the derivation of an alternate form of the cosine double angle identity.
1. \( \cos ( 2 x ) = \cos ^ { 2 } ( x ) - \sin ^ { 2 } ( x ) \)
2. \(= \cos ^ { 2 } ( x ) - ( 1 - \cos ^ { 2 } ( x ) ) \)
3. \(= \cos ^ { 2 } ( x ) - 1 - \cos ^ { 2 } ( x ) \)
4. \(= 2 \cos ^ { 2 } ( x ) - 1\)
What is the error in this derivation?
In step \( 1 , \cos ( 2 x ) \) is equal to \( \cos ^ { 2 } ( x ) + \sin ^ { 2 } ( x ) \) .
In step \( 2 , \sin ^ { 2 } ( x ) \) should have been replaced with \( 1 + \) \( \cos ^ { 2 } ( x ) \) .
In step \( 3 , \cos ^ { 2 } ( x ) - 1 - \cos ^ { 2 } ( x ) \) should be \( \cos ^ { 2 } ( x ) - 1 \) \( + \cos ^ { 2 } ( x ) \)
In \( \operatorname { step } 4 , 2 \cos ^ { 2 } ( x ) - 1 \) should be \( 1 - 2 \cos ^ { 2 } ( x ) \)
Q:
Suppose \( A B C \) is a right triangle with sides a, b, and c and right angle at C. Use the Pythagorean theorem to find the unknown s the denominators when apolicable. nide length. Then find the values of the six trigonometric functions for angle B. Rationalize the denominators when applicable. \(a = 3 , b = 4\)
What is the length of side c? (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)
\(\sin B = ?\)
Q:
Write the ratios for \( \sin M , \cos M , \) and \( \tan M \) . Give the exact value and a four-decimal approximation.
\(\sin M = \square \)
(Type an exact answer in simplified form. Type an integer or a fraction.) Type the decimal approximation of the answer rounded to four decimal places.
\( \sin M = \square \)
(Round the final answer to four decimal places as needed.)