Answer:
32/12
Step-by-step explanation:
To calculate the tangent you need to divide the opposite side by the adjacent side: 70/24=35/12
Answer:
Step-by-step explanation:
48 ÷ 9 = 5·33333333333 Reoccurring
So you will need 6 packets of to cover the ·3333333333
Answer:
11 17/21
Step-by-step explanation:
![\bf \qquad \textit{initial velocity}\\\\ \begin{array}{llll} \qquad \textit{in feet}\\\\ h(t) = -16t^2+v_ot+h_o \end{array} \quad \begin{cases} v_o=\textit{initial velocity of the object}\\ h_o=\textit{initial height of the object}\\ h=\textit{height of the object at "t" seconds} \end{cases}\\\\ -------------------------------\\\\](https://tex.z-dn.net/?f=%5Cbf%20%5Cqquad%20%5Ctextit%7Binitial%20velocity%7D%5C%5C%5C%5C%0A%5Cbegin%7Barray%7D%7Bllll%7D%0A%5Cqquad%20%5Ctextit%7Bin%20feet%7D%5C%5C%5C%5C%0Ah%28t%29%20%3D%20-16t%5E2%2Bv_ot%2Bh_o%0A%5Cend%7Barray%7D%20%0A%5Cquad%20%0A%5Cbegin%7Bcases%7D%0Av_o%3D%5Ctextit%7Binitial%20velocity%20of%20the%20object%7D%5C%5C%0Ah_o%3D%5Ctextit%7Binitial%20height%20of%20the%20object%7D%5C%5C%0Ah%3D%5Ctextit%7Bheight%20of%20the%20object%20at%20%22t%22%20seconds%7D%0A%5Cend%7Bcases%7D%5C%5C%5C%5C%0A-------------------------------%5C%5C%5C%5C)
![\bf h(t)=7+29t-16t^2\qquad h(t)=19\implies 19=7+29t-16t^2 \\\\\\ 16t^2-29t+12=0\impliedby \textit{now, let's use the quadratic formula} \\\\\\ t=\cfrac{-(-29)\pm\sqrt{(-29)^2-4(16)(12)}}{2(16)}\implies t=\cfrac{29\pm\sqrt{841-768}}{32} \\\\\\ t=\cfrac{29\pm\sqrt{73}}{32}\implies t\approx \begin{cases} 1.17\\ 0.64 \end{cases}](https://tex.z-dn.net/?f=%5Cbf%20h%28t%29%3D7%2B29t-16t%5E2%5Cqquad%20h%28t%29%3D19%5Cimplies%2019%3D7%2B29t-16t%5E2%0A%5C%5C%5C%5C%5C%5C%0A16t%5E2-29t%2B12%3D0%5Cimpliedby%20%5Ctextit%7Bnow%2C%20let%27s%20use%20the%20quadratic%20formula%7D%0A%5C%5C%5C%5C%5C%5C%0At%3D%5Ccfrac%7B-%28-29%29%5Cpm%5Csqrt%7B%28-29%29%5E2-4%2816%29%2812%29%7D%7D%7B2%2816%29%7D%5Cimplies%20t%3D%5Ccfrac%7B29%5Cpm%5Csqrt%7B841-768%7D%7D%7B32%7D%0A%5C%5C%5C%5C%5C%5C%0At%3D%5Ccfrac%7B29%5Cpm%5Csqrt%7B73%7D%7D%7B32%7D%5Cimplies%20t%5Capprox%20%0A%5Cbegin%7Bcases%7D%0A1.17%5C%5C%0A0.64%0A%5Cend%7Bcases%7D)
so hmm check the picture below, thus the ball hits 19 feet of height twice, once on the way up, and once on the way down, at about 0.64 seconds and at 1.17 seconds.