Ask question

Ask question

All categories

3 years ago

12

At the moment a hot iron rod is plunged into freezing water, the difference between the rod's and the water's temperatures is 10

0\degree100°100, degree Celsius. This causes the iron to cool and the temperature difference drops by 60\%60%60, percent every second. Write a function that gives the temperature difference in degrees Celsius, D(t)D(t)D, left parenthesis, t, right parenthesis, ttt seconds after the rod was plunged into the water.

2 answers:

Papessa [141]3 years ago

0 0

Answer:

$D(t)=100(0.4)^t$

Step-by-step explanation:

The temp is 100 at time t = 0

After 1 sec, the temp difference would be:

$100-(\frac{100-60}{100})$

After 2 sec, the temp difference would be:

$100-(\frac{100-60}{100})^2$

Similarly for 3 seconds, 4 seconds etc.

We notice that the parenthesis part is 40% of it, so we can also write:

100(40%)^t,

where

t is the time

40% can be written as 40/100 = 0.4

SO, the function is:

$d(t)=100(0.4)^t$

Artist 52 [7]3 years ago

0 0

Answer:

$D(t)=100*0.4^t$

Step-by-step explanation:

Initially, the difference between the rod's and the water's temperatures is 100°

i.e D(t)=100 When t=0

After 1 seconds, the temp drops by 60%.

Therefore, the new value of D will be the old value multiplied by (100-60)%.

D(1)=100 X (100%-60%) = 100*0.4

After 2 seconds, the temp difference would be:

D(2)=100*0.4*0.4= $100*0.4^2$

We notice that for any t, the percentage at which the difference is reduced is raised to the power of t.

Therefore, temperature difference in degrees Celsius, D(t), t seconds after the rod was plunged into the water is given as:

$D(t)=100*0.4^t$

You might be interested in

A truck can travel 1200 miles on 80 gallons of gasoline. how far can it travel on 240 gallons of gasoline ? Show your work

pogonyaev

Answer:

3600 miles on 240 gal

Step-by-step explanation:

80 gal can go 1200

160 gal can go 2400

240 gal can go 3600

7 0

2 years ago

Read 2 more answers

Mystery Boxes: Breakout Rooms

ollegr [7]

Answer:

$\begin{array}{ccccccccccccccc}{1} & {3} & {4} & {12} & {15} & {18}& {18 } & {26} & {29} & {30} & {32} & {57} & {58} & {61} \\ \end{array}$

Step-by-step explanation:

Given

$\begin{array}{ccccccccccccccc}{1} & {[ \ ]} & {4} & {[ \ ] } & {15} & {18}& {[ \ ] } & {[ \ ]} & {29} & {30} & {32} & {[ \ ]} & {58} & {[ \ ]} \\ \end{array}$

Required

Fill in the box

From the question, the range is:

$Range = 60$

Range is calculated as:

$Range = Highest - Least$

From the box, we have:

$Least = 1$

So:

$60 = Highest - 1$

$Highest = 60 +1$

$Highest = 61$

The box, becomes:

$\begin{array}{ccccccccccccccc}{1} & {[ \ ]} & {4} & {[ \ ] } & {15} & {18}& {[ \ ] } & {[ \ ]} & {29} & {30} & {32} & {[ \ ]} & {58} & {61} \\ \end{array}$

From the question:

$IQR = 20$ --- interquartile range

This is calculated as:

$IQR = Q_3 - Q_1$

$Q_3$ is the median of the upper half while $Q_1$ is the median of the lower half.

So, we need to split the given boxes into two equal halves (7 each)

<u>Lower half:</u>

$\begin{array}{ccccccc}{1} & {[ \ ]} & {4} & {[ \ ] } & {15} & {18}& {[ \ ] } \\ \end{array}$

<u>Upper half</u>

<u></u> $\begin{array}{ccccccc}{[ \ ]} & {29} & {30} & {32} & {[ \ ]} & {58} & {61} \\ \end{array}$ <u></u>

The quartile is calculated by calculating the median for each of the above halves is calculated as:

$Median = \frac{N + 1}{2}th$

Where N = 7

So, we have:

$Median = \frac{7 + 1}{2}th = \frac{8}{2}th = 4th$

So,

$Q_3$ = 4th item of the upper halves

$Q_1$ = 4th item of the lower halves

From the upper halves

<u></u> $\begin{array}{ccccccc}{[ \ ]} & {29} & {30} & {32} & {[ \ ]} & {58} & {61} \\ \end{array}$ <u></u>

<u></u>

We have:

$Q_3 = 32$

$Q_1$ can not be determined from the lower halves because the 4th item is missing.

So, we make use of:

$IQR = Q_3 - Q_1$

Where $Q_3 = 32$ and $IQR = 20$

So:

$20 = 32 - Q_1$

$Q_1 = 32 - 20$

$Q_1 = 12$

So, the lower half becomes:

<u>Lower half:</u>

$\begin{array}{ccccccc}{1} & {[ \ ]} & {4} & {12 } & {15} & {18}& {[ \ ] } \\ \end{array}$

From this, the updated values of the box is:

$\begin{array}{ccccccccccccccc}{1} & {[ \ ]} & {4} & {12} & {15} & {18}& {[ \ ] } & {[ \ ]} & {29} & {30} & {32} & {[ \ ]} & {58} & {61} \\ \end{array}$

From the question, the median is:

$Median = 22$ and $N = 14$

To calculate the median, we make use of:

$Median = \frac{N + 1}{2}th$

$Median = \frac{14 + 1}{2}th$

$Median = \frac{15}{2}th$

$Median = 7.5th$

This means that, the median is the average of the 7th and 8th items.

The 7th and 8th items are blanks.

However, from the question; the mode is:

$Mode = 18$

Since the values of the box are in increasing order and the average of 18 and 18 do not equal 22 (i.e. the median), then the 7th item is:

$7th = 18$

The 8th item is calculated as thus:

$Median = \frac{1}{2}(7th + 8th)$

$22= \frac{1}{2}(18 + 8th)$

Multiply through by 2

$44 = 18 + 8th$

$8th = 44 - 18$

$8th = 26$

The updated values of the box is:

$\begin{array}{ccccccccccccccc}{1} & {[ \ ]} & {4} & {12} & {15} & {18}& {18 } & {26} & {29} & {30} & {32} & {[ \ ]} & {58} & {61} \\ \end{array}$

From the question.

$Mean = 26$

Mean is calculated as:

$Mean = \frac{\sum x}{n}$

So, we have:

$26= \frac{1 + 2nd + 4 + 12 + 15 + 18 + 18 + 26 + 29 + 30 + 32 + 12th + 58 + 61}{14}$

Collect like terms

$26= \frac{ 2nd + 12th+1 + 4 + 12 + 15 + 18 + 18 + 26 + 29 + 30 + 32 + 58 + 61}{14}$

$26= \frac{ 2nd + 12th+304}{14}$

Multiply through by 14

$14 * 26= 2nd + 12th+304$

$364= 2nd + 12th+304$

This gives:

$2nd + 12th = 364 - 304$

$2nd + 12th = 60$

From the updated box,

$\begin{array}{ccccccccccccccc}{1} & {[ \ ]} & {4} & {12} & {15} & {18}& {18 } & {26} & {29} & {30} & {32} & {[ \ ]} & {58} & {61} \\ \end{array}$

We know that:

<em>The 2nd value can only be either 2 or 3</em>

<em>The 12th value can take any of the range 33 to 57</em>

Of these values, the only possible values of 2nd and 12th that give a sum of 60 are:

$2nd = 3$

$12th = 57$

i.e.

$2nd + 12th = 60$

$3 + 57 = 60$

So, the complete box is:

$\begin{array}{ccccccccccccccc}{1} & {3} & {4} & {12} & {15} & {18}& {18 } & {26} & {29} & {30} & {32} & {57} & {58} & {61} \\ \end{array}$

6 0

2 years ago

10 subtracted from a number is 15.

Vlada [557]

When negative five is subtracted from a number the result is 10. The number is 5.
x - (-5) = 10
x + 5 = 10
x = 10 - 5
x = 5

8 0

3 years ago

Find x. <br><br> See attached picture.

Serhud [2]

The value of x will be equal to 4√6. The correct option is B.

<h3>What is trigonometry?</h3>

The branch of mathematics sets up a relationship between the sides and the angles of the right-angle triangle termed trigonometry.

Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions. There are numerous distinctive trigonometric identities that relate to a triangle's side length and angle.

The value of side x will be calculated by using the angle properties.

SIn( 45 ) = P / H

Sin (45) = 12 / H

H = 12 / ( 1 / √2) = 12√2

Again using the angle property for finding the value of x.

tan30 = P / B

x = tan30 x B

x = ( 1 / √3 ) x 12√2

x = 4√6

Therefore, the value of x will be equal to 4√6. The correct option is B.

To know more about Trigonometry follow

brainly.com/question/24349828

#SPJ1

3 0

1 year ago

What is the result when the number 40 is decreased by 10%?

choli [55]

Answer:

it would be 36

Step-by-step explanation:

8 0

3 years ago