Solve for x.
1 answer:
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Answer:
t = 2.11 seconds
Step-by-step explanation:
A toy rocket is launched from the top of a 48 foot hill. The rockets initial upward velocity is 32 feet per second and its height h at any given second t is modeled by the equation:
Let us assume that we need to find the time by it to reach the ground. It means h = 0
The above is a quadratic equation. The value of t is given by :
So, it will take 2.11 seconds to reach the ground.
For the first circle, let's use the pythagorean theorem
now, it just so happen that the hypotenuse on that triangle, is actually 17, but we used the pythagorean theorem to find it, and the pythagorean theorem only works for right-triangles.
so if the hypotenuse is actually 17, that means that triangle there is actually a right-triangle, meaning that the radius there, and the outside line there, are both meeting at a right-angle.
when an outside line touches the radius line, and they form a right-angle, the outside line is indeed a tangent line, since the point of tangency is always a right-angle with the radius.
now, let's check for second circle
well, low and behold, we didn't get our hypotenuse as 16 after all, meaning, that triangle is NOT a right-triangle, and that outside line is not touching the radius at a right-angle, therefore is NOT a tangent line.
let's check the third circle
this time, we did get our hypotenuse to 65, the triangle is a right-triangle, so the outside line is indeed a tangent line.
now, it just so happen that the hypotenuse on that triangle, is actually 17, but we used the pythagorean theorem to find it, and the pythagorean theorem only works for right-triangles.
so if the hypotenuse is actually 17, that means that triangle there is actually a right-triangle, meaning that the radius there, and the outside line there, are both meeting at a right-angle.
when an outside line touches the radius line, and they form a right-angle, the outside line is indeed a tangent line, since the point of tangency is always a right-angle with the radius.
now, let's check for second circle
well, low and behold, we didn't get our hypotenuse as 16 after all, meaning, that triangle is NOT a right-triangle, and that outside line is not touching the radius at a right-angle, therefore is NOT a tangent line.
let's check the third circle
this time, we did get our hypotenuse to 65, the triangle is a right-triangle, so the outside line is indeed a tangent line.
Answer:
Initial temperature;
432.76
Common ratio;
-0.067
Equation;
Step-by-step explanation:
In this scenario, the time in minutes represents the independent variable x while the temperature of the pizza represents the dependent variable y.
The analysis is performed in Ms. Excel. The first step is to obtain a scatter plot of the data then finally inserting an exponential trend line to obtain the required equation.
The Ms. Excel output is shown in the attachment below. To obtain the initial temperature we substitute x = 0 in the equation. On the other hand, the common ratio is the exponent in the equation.
