A number x more than −13

A solid object is dropped into a pond with a temperature of 20 degrees Celsius. The function f(t)=Ce(−kt)+20 represents the situ

LenaWriter [7]

Answer:

The initial temperature of the object was 37.6 degrees Celsius

The initial temperature of the object was 37.6 (without units)

Step-by-step explanation:

we have

$f(t)=Ce^{(-kt)} +20$

where

f(t) represent the temperature of the object in degree Celsius

t is the time in minutes

<em>Find the value of the constant C</em>

we have the ordered pair (4,35)

substitute in the equation and solve for C

$35=Ce^{(-0.0399*4)} +20$

$Ce^{(-0.0399*4)}=15$

$C=15/e^{(-0.0399*4)}$

$C=17.6$

Find the initial value of the object

we know that

The initial temperature is the value of f(t) when the value of t is equal to zero

so

For t=0

$f(0)=(17.6)e^{(-k*0)} +20$

$f(0)=17.6 +20$

$f(0)=37.6\ degrees\ Celsius$

therefore

The initial temperature of the object was 37.6 degrees Celsius

The initial temperature of the object was 37.6 (without units)

3 0

3 years ago

Let a=<-4,-3,5> Find a unit vector in the same direction as having positive first coordinate.

Rashid [163]

Answer:

The value is $u = < \frac{2\sqrt{2}}{10} , \frac{3\sqrt{2}}{10} , - \frac{\sqrt{2}}{2}>$

Step-by-step explanation:

From the question we are told that

The vector is a=<-4,-3,5>

Generally the unit vector is $u = ay$

Here y represent the y-coordinate

So

$u =y$

=> $u =$

Generally the resultant of a unit vector is 1

So

$|u| = \sqrt{ (-4y)^2 + (-3y)^2 + (5y)^2} = 1$

Hence

$|u| = \sqrt{ 16y^2 + 9y^2 + 25y^2} = 1$

Taking the square of both sides

$16y^2 + 9y^2 + 25y^2 = 1$

=> $50y^2 = 1$

=> $y = \pm \frac{1}{\sqrt{50}}$

=> $y = \pm \frac{1}{5 \sqrt{2}}$

Rationalizing

=> $y = \pm \frac{\sqrt{2}}{10}$

Given that the first coordinate is positive

$y = - \frac{\sqrt{2}}{10}$

Hence the unit vector is

$u =$

=> $u = < \frac{2\sqrt{2}}{10} , \frac{3\sqrt{2}}{10} , - \frac{\sqrt{2}}{2}>$

4 0

3 years ago

A number is selected at random from the set {2, 3, 4, … 10}. Which event, by definition, covers the entire sample space of this

PolarNik [594]

Let's do process of elimination

a) 2 is part of the set and 2 is not greater than 2. NO

b) 5 and 10 in the set are divisible by 5. NO

c) 2,4,6,8,10 are even but the rest are odd ( BUT note the word "or"). the rest are less than 12. YES

d) 0 and 1 are the only numbers that are neither prime nor composite (they're not even part of the set). NO

e) the square root of 9 is 3 so the maximum number is 9 (but what happened to 10?) NO

6 0

4 years ago

Point K is between points H and J, HK=x-5, KJ=5x-12, and HJ=25. Find the value of x

bija089 [108]

X-5 + 5x-12 = 25
combine like terms
6x-17 = 25
add 17
25 + 17 =42
6x + 42
x = 7

7 0

3 years ago

What is the answer for 2m + 3m + 8 + 6

Leokris [45]

Answer:

5m+14

Step-by-step explanation:

5 0

3 years ago