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$23-36=$ Find the critical numbers of the function.$$f(x)=x^{-2} \ln x$$
In Exercises $1-6,$ use the figures to find the exact value of each trigonometric function. $$\cos 2 \theta$$
In Exercises $1-6,$ use the figures to find the exact value of each trigonometric function. $$\sin 2 \alpha$$
In Exercises $1-6,$ use the figures to find the exact value of each trigonometric function. $$\tan 2 \alpha$$
In Exercises $7-14,$ use the given information to find the exact value of each of the following: $$\begin{array}{llll}{a, \sin 2 \theta} & {\text { b. } \cos 2 \theta} & {\text { c. } \tan 2 \theta}\end{array}$$$\sin \theta=\frac{12}{13}, \theta$ lies in quadrant II.
In Exercises $7-14,$ use the given information to find the exact value of each of the following: $$\begin{array}{llll}{a, \sin 2 \theta} & {\text { b. } \cos 2 \theta} & {\text { c. } \tan 2 \theta}\end{array}$$$\cos \theta=\frac{40}{41}, \theta$ lies in quadrant IV.
An 200g apple is hanging in a tree, 10 ft off the ground. Whatis the gravitational potential energy (gravity = 9.8m/s2) of the apple?A golf ball has a mass of 0.046 kg. It is dropped and has 1.1 Jof gravitational potential energy (gravity = 9.8 m/s2).What height was it dropped from?If a ball has a kinetic energy of 450 J, what must its mass beif it is traveling through the air at 30 m/s?
A system consists of three particles, each ofmass 6.10 g, located at the corners of an equilateraltriangle with sides of 39.0 cm.(a) Calculate the gravitational potential energy of thesystem.(b) Assume the particles are released simultaneously. Describethe subsequent motion of each. Will any collisions take place?Explain.
Lewis Hamilton is driving his car weighing 1000 kg at the top of a hill, traveling at 20 m/s. He puts the transmission in neutral and, using the brakes, he comes to a stop at a point 15 m below its start position. If the brake discs have a mass of 5 kg each, how hot do they get? Assume the specific heat for mild steel is 500 J/kg°C.
When using a pencil eraser, you exert a downward force of 5.5 N at a distance of 1.9 cm from the hardwood-eraser joint. The pencil has a 2.2 mm radius and is held at an angle of 21° to the horizontal. The shear modulus of wood is 1.00 × 10^10 N/m^2 and the strain modulus is 1.50 × 10^10 N/m^2.
f = 5.5 Nd = 1.9 cmr = 2.2 mmθ = 21°
By how much does the wood flex perpendicular to its length in meters?How much is it compressed lengthwise in meters?
A positron is an elementary particle identical to an electron except that its charge is +e. An electron and a positron can rotate about their center of mass as if they were a dumbbell connected by a massless rod.What is the orbital frequency in rev/s for an electron and a positron 1.60 nm apart?
The lab experiment is repeated with the same two glass platesbut with a different human hair. The sodium vapor lamp is replacedby a monochromatic light source that produces light of wavelengthλair = 630 nm. The separation between adjacent dark fringes ismeasured to be 0.465 mm. Calculate the diameter of the hair. (Thelength of the plates is 12.0 cm.)
