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Chapter 3: Problem 17
If \(\frac{(C+x)}{x-3}=\frac{x+8}{3}\), which of the following could be an expression of \(C\) in terms of \(x\) ? A) \(3(1+x)\) B) \(x^2+2 x-24\) C) \(\frac{1}{3}(x+6)(x-4)\) D) \(\frac{1}{3}(x-3)(x+8)\)
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(A) NO CHANGE B) The echolocation, sonar, of the bat's weaponry is its main curiosity. C) The bat has a curious weaponry, main among which is its echolocation and sonar. D) The bat's weaponry is mainly curious in its use of echolocation of sonar.
A) NO CHANGE B) novel, Uncle Tom's Cabin, C) novel Uncle Tom's Cabin, D) novel Uncle Tom's Cabin
Students in a physics class are studying how the angle at which a projectile is launched on level ground affects the projectile's hang time and horizontal range. Hang time can be calculated using the formula \(t=\frac{2 v \cdot \sin (\theta)}{g}\), where \(t\) is the hang time in seconds, \(v\) is the initial launch velocity, \(\theta\) is the projectile angle with respect to level ground, and \(g\) is the acceleration due to gravity, defined as \(9.8 \mathrm{~m} / \mathrm{s}^2\). Horizontal range can be calculated using the formula \(R=\frac{v^2 \sin (2 \theta)}{g}\), where \(R\) is the distance the projectile travels from the launch site, in feet. Which of the following gives the value of \(v\), in terms of \(R, t\), and \(\theta\) ? A) \(v=\frac{t \sin (\theta)}{2 R \sin (\theta)}\) B) \(v=\frac{2 t \sin (\theta)}{R \sin (\theta)}\) C) \(v=\frac{2 R \sin (\theta)}{t \sin (2 \theta)}\) D) \(v=\frac{2 R \sin (2 \theta)}{t \sin (\theta)}\)
If the radius of the circle above is \(x, \angle A O B=120^{\circ}\), and \(O\) is the center of the circle, what is the length of chord \(A B\), in terms of \(x\) ? A) \(\sqrt{2} x\) B) \(\sqrt{3} x\) C) \(\frac{x}{\sqrt{2}}\) D) \(\frac{x}{\sqrt{3}}\)
Which of the following is a possible equation for a circle that is tangent to both the \(x\)-axis and the line \(x=4\) ? A) \((x+2)^2+(y+2)^2=4\) B) \((x+2)^2+(y-2)^2=4\) C) \((x-2)^2+(y+4)^2=4\) D) \((x-6)^2+(y-2)^2=4\)
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