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If x+7x+7 is a factor of the polynomial function gg, what is the value of g(7)g(7) ?

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The graphs of the functions f(x)=sin⁡(x) f(x)=\sin (x) and g(x)=12 g(x)=\frac{1}{2} intersect at 22 points on the interval 0<x<π 0<x<\pi .\newlineWhat is the area of the region bound by the graphs of f(x) f(x) and g(x) g(x) between those points of intersection ?\newlineChoose 11 answer:\newline(A) π3 \frac{\pi}{3} \newline(B) π2 \frac{\pi}{2} \newline(C) 2−π2 2-\frac{\pi}{2} \newline(D) 3−π3 \sqrt{3}-\frac{\pi}{3}
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What is the area of the region between the graphs of f(x)=x2+12x f(x)=x^{2}+12 x and g(x)=3x2+10 g(x)=3 x^{2}+10 from x=1 x=1 to x=4 x=4 ?\newlineChoose 11 answer:\newline(A) 7777\newline(B) 643 \frac{64}{3} \newline(C) 1818\newline(D) 4545
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Consider the curve given by the equation 3x2+y4+6x=253 3 x^{2}+y^{4}+6 x=253 . It can be shown that dydx=−6(x+1)4y3. \frac{d y}{d x}=\frac{-6(x+1)}{4 y^{3}}. \newlineWrite the equation of the horizontal line that is tangent to the curve and is above the x x -axis.
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The learning rate for new skills is proportional to the difference between the maximum potential for learning that skill, M M , and the amount of the skill already learned, L L .\newlineWhich equation describes this relationship?\newlineChoose 11 answer:\newline(A) L(t)=k(M−L) L(t)=\frac{k}{(M-L)} \newline(B) L(t)=k(M−L) L(t)=k(M-L) \newline(C) dLdt=k(M−L) \frac{d L}{d t}=k(M-L) \newline(D) dLdt=k(M−L) \frac{d L}{d t}=\frac{k}{(M-L)}
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What is the value of ddx(1x) \frac{d}{d x}\left(\frac{1}{x}\right) at x=6 x=6 ?
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What is the value of ddx(x) \frac{d}{d x}(\sqrt{x}) at x=9 x=9 ?
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A curve in the plane is defined parametrically by the equations \newlinex=t3+tx=t^{3}+t and \newliney=t4+2t2y=t^{4}+2t^{2}. An equation of the line tangent to the curve at \newlinet=1t=1 is\newline(A) y=2x\text{(A)}\ y=2x\newline(B) y=8x\text{(B)}\ y=8x\newline(C) y=2x−1\text{(C)}\ y=2x-1\newline(D) y=4x−5\text{(D)}\ y=4x-5\newline(E) y=8x+13\text{(E)}\ y=8x+13
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A pendulum is swinging next to a wall.\newlineThe distance D(t) D(t) (in cm \mathrm{cm} ) between the bob of the pendulum and the wall as a function of time t t (in seconds) can be modeled by a sinusoidal expression of the form a⋅sin⁡(b⋅t)+d a \cdot \sin (b \cdot t)+d .\newlineAt t=0 t=0 , when the pendulum is exactly in the middle of its swing, the bob is 5 cm 5 \mathrm{~cm} away from the wall. The bob reaches the closest point to the wall, which is 3 cm 3 \mathrm{~cm} from the wall, 11 second later.\newlineFind D(t) D(t) .\newlinet t should be in radians.\newlineD(t)=□ D(t)=\square
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Pluto's distance P(t) P(t) (in billions of kilometers) from the sun as a function of time t t (in years) can be modeled by a sinusoidal expression of the form a⋅sin⁡(b⋅t)+d a \cdot \sin (b \cdot t)+d .\newlineAt year t=0 t=0 , Pluto is at its average distance from the sun, which is 66.99 billion kilometers. In 6666 years, it is at its closest point to the sun, which is 44.44 billion kilometers away.\newlineFind P(t) P(t) .\newlinet t should be in radians.\newlineP(t)= P(t)=
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