The height in feet of a rocket after t seconds is given by h(t) = 160t - 16t^2.

find the maximum height the rocket attains in feet

Step-by-step explanation:

h(t)=160t-16t^2=-16(t²-10t+25-25)

=-16(t-5)²+400

max. height reached=400 ft

The maximum height 400 feet is attained at t = 5 seconds.

Step-by-step explanation:

All powers of in the equation for are integers that are greater than or equal to zero. Additionally, the greatest power of is two. Hence, is a quadratic equation about .

In this case,

The question is asking for the maximum value of this equation. Start by finding the (time) that would maximize the value of the polynomial.

The graph of a quadratic equation looks like a parabola. Additionally, since the coefficient of is less than zero, the parabola opens downward. The maximum value of the parabola would be at its vertex. Additionally, at the vertex,

.

In other words, the rocket is at its maximum height when time is equal to 5 seconds.

To find that height, let and evaluate :

.

That is: the maximum height of the rocket would be 400 feet.

3x + 4y -25 =0 represents the amount of change sianna should recieve

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.