Find scale factor, solve for x, and solve for y.

Mathematics

1 answer:

snow_tiger [21]2 years ago

6 0

Answer:

Part 1) The scale factor is 3

Part 2) The value of x is 36 in

Part 3) The value of y is 26 in

Step-by-step explanation:

step 1

Find the scale factor

we know that

If two figures are similar then the ratio of its corresponding sides is proportional and this ratio is called the scale factor

In this problem

Let

z-----> the scale factor

$z=(10+5)/5=3$

step 2

Find the value of x

To find the value of x, multiply the length of 12 by the scale factor

$x=(12)(3)=36\ in$

step 3

Find the value of y

we know that

$(13)(3)=13+y$

$y=39-13=26\ in$

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you place a cup of 200f coffee on a table in a room that is 67f and 10 minutes later it is 195f. approximately how long will it

kompoz [17]

Newton's law of cooling says the rate of change of temperature is proportional to the difference between the object's temperature and the temperature of the environment.

Here, the object starts out at 200 °F, which is 133 °F greater than the environment temperature. 10 minutes later, the object is 195 °F, so is 128 °F greater than the environment. In other words, the temperature difference has decayed by a factor of 128/133 in 10 minutes.

The solution to the differential equation described by Newton's Law of Cooling can be written as the equation
T(t) = 67 + 133*(128/133)^(t/10)
where T is the object's temperature in °F and t is the time in minutes from when the object was placed in the 67 °F environment.

The equation
T(t) = 180
can be solved analytically, but it can be a bit easier to solve it graphically. A graphing calculator shows it takes 42.528 minutes for the temperature of the coffee to reach 180 °F.