What's the volume of the cone?

The temperature, H, in degrees Celsius, of a cup of coffee placed on the kitchen counter is given by H = f(t), where t is in min

Deffense [45]

Answer:

a

f'(t) is negative

b

The unit is degC/min

c

At 35 minutes after the coffee was put on the counter, its temperature is 68 and will decrease by about 0.75 in the next 30 seconds.

Step-by-step explanation:

From the question we are told we are told that

The equation for the temperature of a cup of coffee place on a counter is

$H= f(t)$

Here t is the time in minutes the coffee was put on the counter

Generally f(t)' is the derivative of f(t) at it represents the change of the temperature of the cup of coffee with respect to time

Generally for the coffee placed on the counter after a couple of minutes the temperature will decrease hence f(t)' is negative

Generally the unit of the temperature is in degrees Celsius while that of time is in minutes

So the change in temperature with time f(35)' will be in degrees Celsius/minutes (i.e degC/min)

From the question we are told that

$|f(35)'| = 1.5$

i.e the rate of change of temperature after 35 minutes is 1.5

and

$|f(35)| = 68$

i.e the temperature of the cup of coffee after 35 minutes is 67 degC

Now after another t= 30 seconds = $\frac{30}{60}= 0.5 \ minutes$ the rate of change of the temperature of the cup of coffee is

$R = |f(35)'| * t$

=> $R = 1.5 * 0.5$

=> $R = 0.75$

So

At 35 minutes after the coffee was put on the counter, its temperature is 68 and will decrease by about 0.75 in the next 30 seconds.

5 0

3 years ago

I need help with this so could you give me the answers with an explanation if you can.

Katarina [22]

Answer:

$2.44745763 \times {10}^{6}$

Step-by-step explanation:

$R = \frac{ {x}^{2} }{y} \\ \\ = \frac{ {(3.8 \times {10}^{5}) }^{2} }{5.9 \times {10}^{4} } \\ \\ = \frac{14.44 \times {10}^{10} }{5.9 \times {10}^{4} } \\ \\ = 2.44745763 \times {10}^{10 - 4} \\ = 2.44745763 \times {10}^{6}$

4 0

3 years ago

Last question please

MatroZZZ [7]

Let's try an make a formula to make things easy.

_________________________________________________

Look at Andrew's pattern, it goes up 6 every time. Lets look at the 6 times table

6 times table: 6, 12, 18, 24, ...

____________________________________

First think, how would you work out the 7th term in the 6th times table?

You would do 6 times 7.

So the formula for the 6th times table is:

6n (where n is the term you want to find out)

_______________________________________

So to get the 9th term in the 6 times table, you would replace the n with 9, like so:

9th term in 6 times table = 6 x 9 = 54

______________________________________

Now lets compare the 6 times table to Andrew's pattern:

6 times table: 6, 12, 18, 24,

Andrew's pattern: 3, 9, 15, 21,

_____________________________________

If you look, you can see that Andrew's pattern is the 6 times table minus 3!

So what would be the formula for Andrew pattern?

---> it would be: 6n - 3 (since it's the 6 times table but minus 3)

_____________________________________

We can use this formula to easily work out the 20th term in Andrew's pattern!:

20th term = 6 x 20 - 3 = 120 - 3 = 117 (remember, replace the n with 20)

______________________________________

Now let's make a formula for Ben's pattern!

Ben's pattern goes up in 5s, so lets compare it to the 5 times table:

5 times table: 5, 10, 15, 20

Ben's pattern: 3, 8, 13, 18,

The formula for the 5 times table is 5n, and Ben's pattern is the 5 times table but minus 2.

So the formula for Ben's pattern is: 5n - 2

__________________________________

Now swap out the n for 20 (to get the 20th term):

20th term = 5 x 20 - 2 = 100 - 2 = 98

_________________________________________

So Andrew's 20th term is 117, and Ben's 20th term is 98.

All we do now is subtract them to find the difference:

117 - 98 = 19

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Answer:

Ben's 20th term is smaller by 19!

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5 0

3 years ago

What is .93 divided to 19.43 to the nearest whole number

Brrunno [24]

I got 20.89, and nearest to the whole number would be 20.

5 0

3 years ago

The correlation in error terms that arises when the error terms at successive points in time are related is termed _____.

n200080 [17]

Answer:

auto correlation is the answer to the question

7 0

2 years ago