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3 years ago

Find the distance between (-4,0) and (8,-3)

Mathematics

1 answer:

Dennis_Churaev [7]3 years ago

3 0

Answer:

12.3693

Step-by-step explanation:

use distance formula

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A roast turkey is taken from an oven when its temperature has reached 185 degrees F and is placed on a table in a room where the

Vedmedyk [2.9K]

(a) Using Newton's Law of Cooling, $\dfrac{dT}{dt} = k(T - T_s)$ , we have $\dfrac{dT}{dt} = k(T - 75)$ where T is temperature after T minutes.
Separate by dividing both sides by T - 75 to get $\dfrac{dT}{T - 75} = k dt$ . Integrate both sides to get $\ln|T - 75| = kt + C$ .

Since $T(0) = 185$ , we solve for C:
$|185 - 75| = k(0) + C\ \Rightarrow\ C = \ln 110$
So we get $\ln|T - 75| = kt + \ln 110$ . Use T(30) = 150 to solve for k:
$\ln| 150 - 75 | = 30k + \ln 110\ \Rightarrow\ \ln 75 - \ln 110= 30k \Rightarrow \\ k= \frac{1}{30}\ln (75/110) = \frac{1}{30}\ln(15/22)$

So

$\ln|T - 75| = kt + \ln 110 \Rightarrow |T - 75| = e^{kt + \ln110} \Rightarrow \\ \\
|T - 75| = 110e^{kt} \Rightarrow T - 75 = \pm110e^{(1/30)\ln(15/22)t} \Rightarrow \\
T = 75 \pm110e^{(1/30)\ln(15/22)t}$

But choose Positive because T > 75. Temp of turkey can't go under.

$T(t) = 75 + 110e^{(1/30)\ln(15/22)t} \\
T(45) = 75 + 110e^{(1/30)\ln(15/22)(45)} = 136.929 \approx 137{}^{\circ}F$

(b)

$T(t) = 75 + 110e^{(1/30)\ln(15/22)t} = 75 + 110(15/22)^{t/30} \\
100 = 75 + 110(15/22)^{t/30} \\
25 = 110(15/22)^{t/30} 
\frac{25}{110} = (15/22)^{t/30} \\
\ln(25/110) / ln(15/22) = t/30 \\
t = 30\ln(25/110) / ln(15/22) \approx 116\ \mathrm{min}$

Dogs of the AMS.

4 0

3 years ago

Four students about to purchase concert tickets for $20.00 for each ticket discover that they may purchase a block of 5 tickets

CaHeK987 [17]

Answer:

Each student's contribution = $17

Each student will save $ 3

Step-by-step explanation:

Cost of the block of 5 tickets is $85.00.

Dividing the $ 85 by 5 would give the equal amount each would have to contribute.

$ 85/5=$ 17

Each will have to pay $ 17 to buy a block of 5 tickets for $85.00.

We can find the amount each will save by subtracting the amount to be shared by the 5 students from the amount paid by the 4 students.

They will save

$ 20-$17=

Each of them will save $3 if they can get a fifth person to join them and the 5 people equally divide the price of the 5-ticket block.

5 0

3 years ago

A rectangle length was 4 feet longer than triple the length of it width

wlad13 [49]

Length is 48 ft

The perimeter of a rectangle is equal to the sum of all side’s.
2(lengths)+2(widths)= perimeter
Length=3x+4
Now given the perimeter of 140
3(3x+4)+3(x)=140
9x+12+3x=140
12x+12=140
12x=128
X= 10.7
10.7 is the width

Length=3x+4
Length =3(10.6)+4
Length=31.8+4
Length=35.8
Answer = 35.8
This can only be answered if you were given a perimeter.

4 0

3 years ago

Solve for x. Assume that lines which appear tangent are tangent.

Orlov [11]

Answer:

Period. Segment Lengths in Circles. Solve for x . Assume that lines which appear tangent are tangent. 1). 154 2 9 (249). 425 = 9481. 90-144.

7 0

3 years ago

Round 125.3546 to 1 decimal place

Gekata [30.6K]

There are maybe like 1% of 125.3546

3 0

3 years ago