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Roman55 [17]
3 years ago
11

What is the diameter of circle C?

Mathematics
1 answer:
Ganezh [65]3 years ago
5 0

Answer:

d=2\sqrt{34}

Step-by-step explanation:

Applying Pythagoras theorem on right angle triangle

radius=r=\sqrt{(3)^2+(5)^2}

r=\sqrt{34}

Diameter=2 x radius

d=2r=2\sqrt{34}

You might be interested in
Determine whether the data described below are qualitative or quantitative and explain why.The shoe sizes left parenthesis such
Igoryamba

Answer:

B.The data are quantitative because they consist of they consist of counts or measurements.

Step-by-step explanation:

Qualitative data are those data which does not include any number. The data which has characteristic is known as Qualitative data.

Quantitative data are those data which include numbers.

Since the data of shoe sizes include numerical value. Thus it is Quantitative Data.

7 0
2 years ago
(GIVING BRAINLIEST) A company rents out 11 food booths and 26 game booths at the county fair. The fee for a food booth is $50 pl
bogdanovich [222]
The answer is 2500+215d

Hope that helps
5 0
2 years ago
8 + 8a - 2a - 4<br> Pls help
PIT_PIT [208]

Answer:

that would 6a+4

Step-by-step explanation:

8a - 2a , 8 - 4

5 0
2 years ago
Read 2 more answers
- The temperature of a hot liquid is 100 degrees. The liquid is placed in a refrigerator
oee [108]

Answer:

PLZ GIVE BRAINLESISET

Calculus Newton's Law of Cooling

Sources: #1 – 5: Smith/Minton Calculus 4th ed. #6 – 8: Thomas/Finney Calculus 9th ed.

Use Newton's Law of Cooling T −TS = (TO −TS )e−kt

( ) to solve the following. Round temperature

answers to the nearest tenth of a degree, and time (duration) answers to the nearest hundredth of a

minute.

1) A cup of fast-food coffee is 180°F when freshly poured. After 2 minutes in a room at 70°F, the coffee has

cooled to 165°F. Find the time that it will take for the coffee to cool to 120°F.

165− 70 = (180 − 70)e−2 k

95 =110e−2 k

e−2 k = 95

110

k =

ln

95

110

"

#

$ %

&

'

−2

120 − 70 = (180 − 70)e

−

ln 95

110

"

#

$ %

&

'

−2

"

#

$

$

$

$

%

&

'

'

'

'

t

50 =110e

ln 95

110

!

"

# $

%

&

2

!

"

#

#

#

#

$

%

&

&

&

&

t

e

ln 95

110

!

"

# $

%

&

2

!

"

#

#

#

#

$

%

&

&

&

&

t

= 50

110

t =

ln

50

110

!

"

# $

%

&

ln

95

110

!

"

# $

%

&

2

!

"

#

#

#

#

$

%

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&

&

&

≈10.76 minutes

2) A bowl of porridge at 200°F (too hot) is placed in a 70°F room. One minute later the porridge has cooled to

180°F. When will the temperature be 120°F (just right)?

180 − 70 = (200 − 70)e−k

110 =130e−k

e−k = 11

13

k = −ln

11

13

"

#

$ %

&

'

120 − 70 = (200 − 70)e

ln 11

13

!

"

# $

%

&t

50 =130e

ln 11

13

!

"

# $

%

&t

e

ln 11

13

!

"

# $

%

&t

= 50

130

t =

ln

5

13

!

"

# $

%

&

ln

11

13

!

"

# $

%

&

≈ 5.72 minutes

3) A smaller bowl of porridge served at 200°F cools to 160°F in one minute. What temperature (too cold) will

this porridge be when the bowl of exercise 2 has reached 120°F (just right)?

160 − 70 = (200 − 70)e−k

90 =130e−k

e−k = 9

13

k = −ln

9

13

"

#

$ %

&

'

T − 70 = (200 − 70)e

ln 9

13

"

#

$ %

&

'(5.72)

T =130e

ln 9

13

"

#

$ %

&

'(5,72)

+ 70

T ≈ 85.9°

4) A cold drink is poured out at 50°F. After 2 minutes of sitting in a 70°F room, its temperature has risen to

56°F.

A) What will the temperature be after 10 minutes?

B) When will the drink have warmed to 66°F?

A)

56 − 70 = (50 − 70)e−2 k

−14 = −20e−2 k

e−2 k = 7

10

k =

ln

7

10

"

#

$ %

&

'

−2

T − 70 = (50 − 70)e

ln 7

10

!

"

# $

%

&

2 (10)

T = 70 +(−20)e

ln 7

10

!

"

# $

%

&

2 (10)

≈ 66.6°F

B)

66 − 70 = (50 − 70)e

ln(0.7)

2 t

−4 = −20e

ln(0.7)

2 t

e

ln(0.7)

2 t

= 4

20

t = ln(0.2)

ln(0.7)

2

≈ 9.02 minutes after it is poured.

5) At 10:07 pm, you find a secret agent murdered. Next to him is a martini that got shaken before he could stir

it. Room temperature is 70°F. The martini warms from 60°F to 61°F in the 2 minutes from 10:07 pm to

10:09 pm. If the secret agent's martinis are always served at 40°F, what was the time of death (rounded to the

nearest minute)?

61− 70 = (60 − 70)e−2 k

−9 = −10e−2 k

e−2 k = 9

10

k = ln(0.9)

−2

60 − 70 = (40 − 70)e

ln(0.9)

2 t

−10 = −30e

ln(0.9)

2 t

e

ln(0.9)

2 t

= 1

3

t =

ln

1

3

!

"

# $

%

&

ln(0.9)

2

≈ 20.85 minutes

The agent was murdered

at approx. 9:46 pm.

6) A hard-boiled egg at 98°C is put into a sink of 18°C water. After 5 minutes, the egg's temperature is 38°C.

Assuming that the surrounding water has not warmed appreciably, how much longer will it take the egg to

reach 20°C?

38−18 = (98−18)e−5k

20 = 80e−5k

e−5k = 20

80

k = ln(0.25)

−5

20 −18 = (38−18)e

ln(0.25)

5 t

2 = 20e

ln(0.25)

5 t

e

ln(0.25)

5 t

= 2

20

t = ln(0.1)

ln(0.25)

5

≈ 8.30 minutes

7) Suppose that a cup of soup cooled from 90°C to 60°C after 10 minutes in a room whose temperature

was 20°C.

A) How much longer would it take the soup to cool to 35°C?

60 − 20 = (90 − 20)e−10 k

40 = 70e−10 k

e−10 k = 40

70

k =

ln

4

7

!

"

# $

%

&

−10

35− 20 = (90 − 20)e

ln 4

7

!

"

# $

%

&

10 t

15 = 70e

ln 4

7

!

"

# $

%

&

10 t

e

ln 4

7

!

"

# $

%

&

10 t

= 15

70

t =

ln

3

14

!

"

# $

%

&

ln

4

7

!

"

# $

%

&

10

≈ 27.53 minutes

B) Instead of being left to stand in the room, the cup of 90°C soup is placed in a freezer whose temperature

is -15°C, and it took 5 minutes to cool to 60°C. How long will it take the soup to cool from 90°C

to 35°C?

60 −(−15) = (90 −(−15))e−5k

75 =105e−5k

e−5k = 75

105

k =

ln

5

7

!

"

# $

%

&

−5

35−(−15) = (90 −(−15))e

ln 5

7

!

"

# $

%

&

5 t

50 =105e

ln 5

7

!

"

# $

%

&

5 t

e

ln 5

7

!

"

# $

%

&

5 t

= 50

105

t =

ln

10

21

!

"

# $

%

&

ln

5

7

!

"

# $

%

&

5

≈11.03 minutes

8) A pan of warm water (46°C) was put into a refrigerator. Ten minutes later, the water's temperature was 39°C.

10 minutes after that it was 33°C. Use Newton's Law of Cooling to estimate the temperature of the

refrigerator.

39 −TS = (46 −TS )e−10 k ⇒ e−10 k = 39 −TS

46 −TS

33−TS = (39 −TS )e−10 k ⇒ e−10 k = 33−TS

39 −TS

39 −TS

46 −TS

= 33−TS

39 −TS

(39 −TS )

2

= (33−TS )(46 −TS )

1521− 78TS +TS

2 =1518− 79TS +TS

2

TS = −3°C

5 0
3 years ago
Please help me on this question hery hard 5x5=
konstantin123 [22]

Answer:

25

Step-by-step explanation:

7 0
2 years ago
Read 2 more answers
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