Devin jumped off a cliff into the ocean in Acapulco while vacationing with his family. His height as a function of time could be modeled by the function h(t)= -16t square root 2 +16t +96, where T is the time in seconds and H is the time in feet. How many seconds until Devon hit the water? Around to the nearest tenth is necessary.

3 seconds

Step-by-step explanation:

Given the height modelled by the function

h(t) = -16t² + 16t + 96

The hit the water at h(t) = 0

0 = -16t² + 16t + 96

Divide through b y -16

0 = t² - t - 6

t² - t - 6 = 0

t² - 3t+2t - 6 = 0

t(t-3)+2(t-3) = 0

t+ 2 = 0 and t - 3 = 0

t = -2 secs and t = 3secs

Since t can't be negative, hence;

t = 3 secs

hence it will take 3 seconds until Devon hit the water

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.

step-by-step explanation:

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.