1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Nat2105 [25]
2 years ago
8

The Law and Order detectives enter a house at 11:30 am and found a man on the floor murdered. They take his body temperature fin

ding to be 91.8 F. The body is taken to the morgue and at 12:30 pm the body temperature is 84.4 F. Using an exponential model for the body temperature, to the nearest minute, what time was he killed. Normal body temperature is 98.6.
Mathematics
1 answer:
taurus [48]2 years ago
7 0

Answer:

Time of murder = 10:39 am

Step-by-step explanation:

Let the equation of exponential function representing the final temperature of the body after time 't' is,

f(t) = a(e)^{nt}

Here, a = Initial temperature

n = Constant for the change in temperature

t = Duration

At 11:30 am temperature of the body was 91.8°F.

91.8 = 98.6(e)^{nt} --------(1)

Time to reach the body to the morgue = 12:30 pm

Duration to reach = 12:30 p.m. - 11:30 a.m.

                              = 1 hour

Therefore, equation will be,

84.4 = 91.8(e)^{n\times 1}

eⁿ = \frac{84.4}{91.8}

ln(eⁿ) = ln(0.9194)

n = -0.08403

From equation (1),

91.8 = 98.6(e)^{-0.08403t}

(e)^{0.08403t}=\frac{98.6}{91.8}

ln[(e)^{0.08403t}]=ln[\frac{98.6}{91.8}]

0.08403t = 0.07146

t = 0.85 hours

t ≈ 51 minutes

Therefore, murder was done 51 minutes before the detectives arrival.

Time of murder = 11:30 - 00:51

                          = 10:90 - 00:51

                          = 10:39 am

You might be interested in
Find the slop of the line that passes Thur each pair of points
LuckyWell [14K]

7 - -5 = 12  delta y
-3 - 4 = -7   delta x
12 divided by negative 7= the slope
6 0
3 years ago
Can someone help me with this question please
rusak2 [61]
The correct answer is c
6 0
3 years ago
The two lines below intersect as shown What is the value of x?
Rufina [12.5K]

Answer:

x = 6

Step-by-step explanation:

because we know the lines intersect we also know the 2 angles are vertical meaning they are equal to each other

Knowing the angles are equal to each other you can make the equation

2x + 29 = 9x - 13

then you solve for x in this equation

2x + 29 = 9x - 13

(subtract 2x from both sides)

29 = 7x - 13

(add 13 to both sides)

42 = 7x

(divide by 7 on both sides)

6 = x

x = 6

6 0
3 years ago
Given the system of equations: 2x – y = –2 x = 14 2y
SSSSS [86.1K]
If you would like to solve the system of equations, you can do this using the following steps:

2x - y = -2
x = 14 + 2y
__________
<span>2x - y = -2
</span>2 * (14 + 2y) - y = -2
28 + 4y - y = -2
28 + 3y = -2
3y = -2 - 28
3y = -30    /3
y = -30/3
y = -10

<span>x = 14 + 2y = 14 + 2 * (-10) = 14 - 20 = -6
</span>
(x, y) = (-6, -10)

The correct result would be <span>(-6, -10).</span>
5 0
3 years ago
Montoya Construction needs to borrow $375,000 to build a road to install utilities in a small subdivision. It borrows the funds
MissTica

Step 1

Given;

\begin{gathered} \text{Principal(p)= \$375000} \\ \text{First rate = 8\%=}\frac{8}{100}=0.08 \\ \text{Second rate = 20\%= }\frac{20}{100}=0.2 \\ \text{Time}=\frac{90}{365}=\frac{18}{73} \end{gathered}

Required; To find the difference in interest between the two periods.

Step 2

State the formula for simple interest

A=P(1+rt)

Step 3

Find the interest when the rate is 8%

\begin{gathered} A=375000(1+(0.08\times\frac{18}{73}) \\ A=375000(1+\frac{36}{1825}) \\ A=\text{\$}382397.26 \end{gathered}

Therefore the interest is given as;

A-P=382397.26-375000=\text{\$}7397.26

Step 4

Find the interest in 1980 with a 20% rate

\begin{gathered} A=375000(1+(0.2\times\frac{18}{73}) \\ A=\text{\$}393493.15 \end{gathered}

The interest is given as;

A-p=393493.15-375000=\text{\$}18493.15\text{ }

Step 5

Find the difference in interest between the two rates.

\text{\$}18493.15-\text{\$}7397.26=\text{\$}11095.89

Hence, the difference in interest between the two rates = $11095.89

4 0
1 year ago
Other questions:
  • 1/3 x 20/9 can you help me please
    9·2 answers
  • Which equations have the same value of x as 2/3(6x+12)=-24 Select two options.
    5·2 answers
  • What do all the ratios in part (<br> a. have in common in ace 15b?
    10·1 answer
  • Simplifying rational expressions
    7·1 answer
  • Make a the subject of V^2+U^2+2as
    9·1 answer
  • Use a calculator to find angle theta for which tan theta = 2. Round to the nearest hundredth.
    9·1 answer
  • Evaluate the expression 10−5a+(18−b), where a=2 and b=11.
    14·1 answer
  • 0) Craig buys a ring for $500. He sells it for $750.
    6·2 answers
  • In the diagram,m&lt;1= (4x+10) and m&lt;2=(c+20) the value of x is
    8·1 answer
  • What does -(-3) equal?
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!