Peter bought a special pen as a birthday present for an artist friend. He has a sturdy box that he wants to use to mail the pen. The box is 4 inches wide, 2 inches deep, and 8 inches high. The pen is 10 inches long. Peter knows he will have to place it in the box along the “long” diagonal AB, as shown in the diagram. Will the pen fit in the box? (Ignore the thickness of the pen.) Give the length of the long diagonal and explain how you found your answer. The box is 4 inches wide, 2 inches deep, and 8 inches high. The pen is 10 inches long. Peter knows he will have to place it in the box along the “long” diagonal AB, as shown in the diagram. Will the pen fit in the box? (Ignore the thickness of the pen.) Give the length of the long diagonal and explain how you found your answer. Peter bought a special pen as a birthday present for an artist friend. He has a sturdy box that he wants to use to mail the pen. The box is 4 inches wide, 2 inches deep, and 8 inches high. The pen is 10 inches long. Peter knows he will have to place it in the box along the “long” diagonal AB, as shown in the diagram. Will the pen fit in the box? (Ignore the thickness of the pen.) Give the length of the long diagonal and explain how you found your answer. Begin by finding the length of AC using right triangle ADC. Then use the fact that angle ACB is a right angle. You may want to use a shoe box or another box-shaped object to help you picture the situation.
PythBox1 2. Generalize your findings from Questions 1 and 2 to a box with dimensions p, q, and r units. In other words, find the length from U to V, as shown in the diagram?

Asap 25 pts brainliest to right best/answer

Using the side-splitter theorem, daniel wrote a proportion for the segment formed by luke segment de. what is ec?

Airplane speeds are measured in three different ways: (1) indicated speed, (2) true speed, and (3) ground speed. the indicated airspeed is the airspeed given by an instrument called an airspeed indicator. a plane’s indicated airspeed is different from its true airspeed because the indicator is affected by temperature changes and different altitudes of air pressure. the true airspeed is the speed of the airplane relative to the wind. ground speed is the speed of the airplane relative to the ground. for example, a plane flying at a true airspeed of 150 knots into a headwind of 25 knots will have a ground speed of 125 knots. the problems below refer to static and dynamic pressure. static pressure is used when a body is in motion or at rest at a constant speed and direction. dynamic pressure is used when a body in motion changes speed or direction or both. a gauge compares these pressures, giving pilots an indicated airspeed. in problem #s 1 and 2, use the following information. the indicated airspeed s (in knots) of an airplane is given by an airspeed indicator that measures the difference p (in inches of mercury) between the static and dynamic pressures. the relationship between s and p can be modeled by s=136.4p√+4.5. 1. find the differential pressure when the indicated airspeed is 157 knots. 2. find the change in the differential pressure of an airplane that was traveling at 218 knots and slowed down to195 knots. in problem #s 3 and 4, use the following information. the true airspeed t (in knots) of an airplane can be modeled by t=(1+a50,000) ⋅ s, where a is the altitude (in feet) and s is the indicated airspeed (in knots). 3. write the equation for true airspeed t in terms of altitude and differential pressure p. 4. a plane is flying with a true airspeed of 280 knots at an altitude of 20,000 feet. estimate the differential pressure. explain why you think your estimate is correct.