Given : A heated piece of metal cools according to the function $c(x)=(0.5)^{x-7}$ , where x is measured in hours and then a cooling device id added that aids in cooling according to the function $h(x)=-x-2$

We have to determine the temperature of the metal after two hours.

Let w(x) denotes the temperature of metal .

Thus, w(x) can be given by function c(x) + h (x) = [c + h](x)

Thus, $w(x)=[c+h](x)\\\\w(x)=(0.5)^{x-7}+(-x-2)\\\\$ , where x is measured in hours.

Thus, after two hours that is when x = 2

the temperature of metal is given by w(2)

$w(x)=(0.5)^{x-7}+(-x-2)\\\\ w(2)=(0.5)^{2-7}+(-2-2)$

Solving , we get,

$w(2)=(0.5)^{2-7}+(-2-2)\\\\ w(2)=(0.5)^{-5}+(-4)\\\\ w(2)=32-4=28$

Thus, the temperature of the metal after two hours is 28 Celsius.

Hence, Option (b) is correct.

7 0

2 years ago

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6*10^5 is how many times as large as 3*10^3

fenix001 [56]

Answer: 200 times larger

Explanation (6*10^5)/(3*10^3)=2*10^2

2*100=200

The other answer was wrong because in order of operations (PEMDAS), exponents come before multiplication.

8 0

2 years ago

Charlie can type faster than any of his classmates. He took a test that showed he can type 700 words in 5 minutes (WPM). The fas

BartSMP [9]

Answer: B

Step-by-step explanation:

If you divide the word by minutes for each one you get 216 which is for the record speed and if you divided how fast Charlie typed it would be 140 which mean that Charlie types slower then the record speed

6 0

3 years ago

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