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Rachel is standing atop a 13 ft ladder. The ladder is leaning against a vertical wall. The ladder starts sliding away from the wall at a rate of 3 ft/sec. How fast is the ladder sliding down the wall when the tip of the ladder is 5 ft high?

• 3 ft/sec
• -7.2 ft/sec
• 7.2 ft/sec
• 12

Tags

CCSS.8.G.B.8

Rachel is standing atop a 13 ft ladder. The ladder is leaning against a vertical wall. The ladder starts sliding away from the wall at a rate of 3 ft/sec.  How fast is the angle between the tip of the ladder and the house changing when the ladder is 5 ft high? Hint: Use a trig function.

• 1 deg/sec
• -.5 deg/sec
• .6 deg/sec
• The angle is not changing.

Tags

CCSS.HSG.SRT.C.6

CCSS.HSG.SRT.C.8

Rachel is standing atop a 13ft ladder. The ladder is leaning against a vertical wall. The ladder starts sliding away from the wall at a rate of 3ft/sec.  How fast is the angle changing between the base of the ladder and the ground when the ladder is 5 ft high?

• -1.44 deg/sec
• 1.5 deg/sec
• .5 deg/sec
• .65 deg/sec

Tags

CCSS.HSG.SRT.C.6

CCSS.HSG.SRT.C.8

CCSS.HSG.SRT.D.11

The radius r of a sphere is increasing at a rate of 2 inches per minute.  Find the rate of change of the volume when r=6 inches.

• C=2πr
• A=πr²
• V=(4/3)πr³
• S=4πr²

Tags

CCSS.HSG.GMD.A.3

Oil spilling from a ruptured tanker spreads in a circle on the surface of the ocean. The radius of the spill increases at a rate of 5 m/min. How fast is the area of the spill increasing when the radius is 5 m?

• 50π m²/min

• 47π m²/min

• 52π m²/min

• 40π m²/min

Tags

CCSS.7.G.B.4

A spherical snowball melts so that its radius decreases at a rate of 4 in/sec. At what rate is the volume of the snowball changing when the radius is 4 in?

• -262π in³/sec

• -247π in³/sec

• -256π in³/sec

• -263π in³/sec

Tags

CCSS.HSG.GMD.A.3

CCSS.8.G.C.9

A 5 ft ladder is leaning against a wall and sliding towards the floor. The top of the ladder is sliding down the wall at a rate of 2 ft/sec. How fast is the base of the ladder sliding away from the wall when the base of the ladder is 3 ft from the wall?

• 4/3 ft/sec

• 8/7 ft/sec

• 1 ft/sec

• 8/3 ft/sec

Tags

CCSS.8.G.B.8

Water leaking onto a floor forms a circular pool. The radius of the pool increases at a rate of 4 cm/min. How fast is the area of the pool increasing when the radius is 10 cm?

• 86π cm²/min

• 89π cm²/min

• 80π cm²/min

• 71π cm²/min

Tags

CCSS.7.G.B.4

An observer stands 2400 ft away from a launch pad to observe a rocket launch. The rocket blasts off and maintains a velocity of 200 ft/sec. Assume the scenario can be modeled as a right triangle. How fast is the observer to rocket distance changing when the rocket is 700 ft from the ground?

• 56 ft/sec

• 57 ft/sec

• 52 ft/sec

• 61 ft/sec

Tags

CCSS.8.G.B.8

Oil spilled from a tanker spreads in a circle whose circumference increases at a rate of 40 ft/sec. How fast is the area of the spill increasing when the circumference of the circle is 100π ft?

What equation(s) should be used?

• $A=πr^2\ \ and\ \ C=2πr$

• $C=2πr$

• $A=πr^2$

• $A=πr^2\ \ and\ \ \ C\ =πd$

Tags

CCSS.HSA.CED.A.2

CCSS.HSG.GMD.A.1