How long would it take a traveler to get from Lake Superior (Minnesota) to the Puget Sound?

NASA launches a rocket at t=0 seconds. Its height, in meters above sea-level, as a function of time is given by h(t)=−4.9t2+121t

Alenkasestr [34]

NASA launches a rocket at t = 0 seconds. Its height, in meters above sea-level, as a function of time is given by

$h(t)=-4.9t^2+121t+283$

The sea level is represented by h = 0, therefore, to find the corresponding time when h splashes into the ocean we have to solve for t the following equation:

$h(t)=0\implies-4.9t^2+121t+283=0$

Using the quadratic formula, the solution for our problem is

$\begin{gathered} t=\frac{-(121)\pm\sqrt{(121)^2-4(-4.9)(283)}}{2(-4.9)} \\ =\frac{121\pm142.083778...}{9.8} \\ =\frac{121+142.083778...}{9.8} \\ =26.8452834694... \end{gathered}$

The rocket splashes after 26.845 seconds.

The maximum of this function happens at the root of the derivative. Differentiating our function, we have

$h^{\prime}(t)=-9.8t+121$

The root is

$-9.8t+121=0\implies t=\frac{121}{9.8}=12.347$

Then, the maximum height is

$h(12.347)=1029.99$

1029.99 meters above sea level.

6 0

1 year ago

Which of the following rules should be use to find the area of a triangle?

lbvjy [14]

The area of a triangle is half the product of the base and the height.

Since multiplication is commutative, the following expressions are equivalent:

$A=(bh)\cdot \dfrac{1}{2} = \dfrac{b}{2}\cdot h = \dfrac{h}{2}\cdot b$

So, option D is correct

4 0

3 years ago

you have 3.75 to spend at a vending machine. You want to buy at least three health bars. Regualr health bars cost 0.75 each and

DedPeter [7]

Answer:

Let x be the number of regular health bars you buy and y the number of strawberry health bars you buy. Then:

0.75x+1.25y=3.75

x+y>=3

Step-by-step explanation:

For the first equation, we have to assume that you will spend all of your money, otherwise it becomes an inequation. The money you spend on regular bars is 0.75x dollars and the money you spend on strawberry bars is 1.25y, so if you spend your 3.75 dollars on the bars, then 0.75x+1.25y=3.75.

For the second, you will always buy x+y health bars, regular and strawberry. There isn't enough information to make this into a equation, the only thing we can deduce is the inequation x+y>=3.

If we also assume that x and y are integers (we can't buy half-bars or one-fourth of a bar) then the minimum number of bars we can buy is 3 (3 strawberry bars) and the maximum is 5 bars (5 regular bars). x+y must be an integer too, so the possibilities for the second equation are x+y=3, x+y=4 and x+y=5. There is a finite number of solutions in any case.

4 0

2 years ago

Big ideas math 1.2 Practice A number 19

slega [8]

By applying Segment Addition Postulate, segment FH is equal to 24 units.

<h3>What is a point?</h3>

A point can be defined as a zero dimensional geometric object and it is generally represented by a dot.

<h3>What is a line segment?</h3>

A line segment can be defined as the part of a line in a geometric figure such as a triangle, circle, quadrilateral, etc., that is bounded by two (2) distinct points and it typically has a fixed length.

<u>Given the following data:</u>

Line segment FG = 37.

Segment HG = 13.

Since point H lies on line segment FG, we would apply Segment Addition Postulate to determine segment FH as follows:

FG = HG + FH

37 = 13 + FH

FH = 37 - 13

FH = 24 units.

Read more on line segment here: brainly.com/question/17617628

#SPJ1

Complete Question:

Given that line segment FG = 37 and segment HG = 13, find segment FH.

4 0

1 year ago

Find the volume of a 2by2

STALIN [3.7K]

Answer:

24

Step-by-step explanation:

2+2+2 = 6*2 = 12*2 = 24

3 0

2 years ago