Mathematics, 19.03.2020 04:17 mat1413

Write the equation of the cosecant function with domain All real numbers except pi/2 + pi/3 k, k∈Z and range (−[infinity],−3]∪[5,[infinity]) and a y-intercept at (0,5). Leave your answer in factored form.

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Answer from: Quest

the furthest the dog can be is 508 meters away from the house, and the closest he can be is 492 meters away from the house.

Answer from: Quest

the speed is $135$ miles per hour > is false

step-by-step explanation:

we know that

a relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form $y/x=k$ or $y=kx$

in a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

the graph shown in the figure represent a direct variation

the slope of the line represent the speed

$y/x=k$

for the point $(1.5,90)$

substitute the values of x and y

$k=90/1.5=60\ miles/hour$

the linear equation is equal to

$y=60x$

statements

case a) it takes $2$ hours to go $120$ miles

the statement is true

because

substitute

for $x=2$

find the value of y in the linear equation

$y=60(2)=120\ miles$ > is correct

case b) the speed is $135$ miles per hour

the statement is false

because the speed is $60\ miles/hour$

case c) the unit rate for the trip is $60\ miles/hour$

the statement is true

because the speed is equal to the slope of the linear equation

case d) it took $20$ minutes to go the first $20$ miles

the statement is true

because

substitute

for $x=20\ minutes=(1/3)\ hour$

find the value of y in the linear equation

$y=60(1/3)=20\ miles$ > is correct

Answer from: Quest

answer-

the equation that models this pattern is $y=32000(0.5)^x$

solution-

a researcher placed a petri dish with 32,000 bacterial cells. one hour after being placed in the vacuum chamber, the number of cells in the petri dish had halved. another hour later, the number of cells had again halved.

this can be represented as exponential decreasing function,

$y=a(1 - r)^x$

where,

a = starting amount = 32000r = rate = 50% = 0.5 as the sample becomes halved in each hour x = hours

putting the values,

$\rightarrow y=32000(1 - 0.5)^x$

$\rightarrow y=32000(0.5)^x$

y-intercept means, where x=0, so

$\rightarrow y=32000(0.5)^0\\\\\rightarrow y=32000\times 1=32000$

the coordinate of this poin will be (0, 32000)

this means when x=0 or at the starting of the research, the number of bacteria cells was 32000.

after 3 hours, number of bacteria cells will be,

$\rightarrow y=32000(0.5)^3$

$\rightarrow y=32000\times 0.125$

$\rightarrow y=4000$

the coordinate of this point will be (3, 4000)

Answer from: Quest

well it says right there your brother is 13; "your age". so lets keep it simple. you are 13 years old and there is no way to put this into any kind of equation without wanting to tear your hair out. who came up with this?

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Write the equation of the cosecant function with domain All real numbers except pi/2 + pi/3 k, k∈Z a...