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2 years ago

14.

Mathematics

1 answer:

Readme [11.4K]2 years ago

8 0

The domain is t=0 to t=3.2 and range is y = 0 to 57.125 feet.

<u>What are Domain and range of a Function?</u>

The range of values that we are permitted to enter into our function is known as the domain of a function.
The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input.
After we enter an x value, the function outputs this sequence of values. The y values are those.
A function can be compared to a piece of equipment on an assembly line.
A few screws and nuts are located on one end of the assembly line, while a car is located on the other. The function is the device in the center. The domain is the screws and bolts that we insert into the machine. The car at the other can be thought of as the range.

Given function is : y = -16t^2 + 50t + 4

It hits the ground when y=0

0 = -16t^2 + 50t + 4

8t^2 -25t -2 = 0

t = 25/16 + (1/16)sqrt(625+64) = (25+26.25)/16 = 51.25/16 = 3.2 seconds

domain is t=0 to t=3.2 [3.2]

take the derivative and set it equal to zero to find maximum height

-32t +50 = 0

t = 50/32 = 25/16 = 1.5625 seconds

-16(25/16) + 50(25/16) + 4 = 34(25/16) + 64/16 = (17(25)+32)/8 = 57.125 = maximum height

range is y = 0 to 57.125 feet. the discus goes from 4 feet to 57 1/8 feet and back down to 0 feet.

Know more about Domain and Range with the help of the given link:

brainly.com/question/20349151

#SPJ4

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Answer:

The number of fringes at $d=-2$ is given as 20.

Step-by-step explanation:

Question

A Galapagos cactus finch population increases by half every decade. The number of finches is modeled by the expression

where d is the number of decades after the population was measured. Evaluate the expression for d = −2

Given :

The number of finches is modeled by the expression :

⇒ $45\cdot1.5^d$

where $d$ is the number of decades after the population was measured.

To evaluate the expression for d=-2

Solution:

In order to evaluate the given expression to find the number of finches at $d=-2$ , we will plugin $-2$ for $d$ in the expression and simplify it.