A particle is moving with acceleration \( a(t)=18 t+12 \). its position at time \( t=0 \) is \( s(0)=12 \) and its velocity at time \( t=0 \) is \( v(0)=3 \). What is its position at time \( t=7 \) ?

Consider the parametric curve \( x=\cos \theta \) and \( y=\sin \theta \). Determine whether this curve is concave up, down, or neither at \( \theta=\frac{\pi}{6} \) A) upward B) downward C) neither D) All answers a b

4. DETERMINDR \( \quad \int^{\sqrt{4-x^{2}}} d x \).

If the point \( (1,2) \) is an inflection point of the curve of the function \( f \) where \( f^{\prime}(x)=4 x^{3}-\mathrm{k} x^{2} \), then \( \mathrm{k}=\ldots \ldots \) (a) 24 (b) 6 (c) 4 (d) 12

Al resolver la integral doble \( \int_{1}^{2} \int_{1-x}^{\sqrt{x}} x^{2} y d y d x \) obtenemos: a. 402 b. 170 c. 170 d. \( 163 / 120 \)

Evaluate the improper integral: \( \int_{1}^{\infty} \frac{1}{x^2} \, dx \)