If 1m = 3.3ft, how many cubic feet is the Kuroshio Sea Tank? Show your calculations!

For the equation ae^ct=d, solve for the variable t in terms of a,c, and d. Express your answer in terms of the natural logarithm

saveliy_v [14]

We have been given an equation $ae^{ct}=d$ . We are asked to solve the equation for t.

First of all, we will divide both sides of equation by a.

$\frac{ae^{ct}}{a}=\frac{d}{a}$

$e^{ct}=\frac{d}{a}$

Now we will take natural log on both sides.

$\text{ln}(e^{ct})=\text{ln}(\frac{d}{a})$

Using natural log property $\text{ln}(a^b)=b\cdot \text{ln}(a)$ , we will get:

$ct\cdot \text{ln}(e)=\text{ln}(\frac{d}{a})$

We know that $\text{ln}(e)=1$ , so we will get:

$ct\cdot 1=\text{ln}(\frac{d}{a})$

$ct=\text{ln}(\frac{d}{a})$

Now we will divide both sides by c as:

$\frac{ct}{c}=\frac{\text{ln}(\frac{d}{a})}{c}$

$t=\frac{\text{ln}(\frac{d}{a})}{c}$

Therefore, our solution would be $t=\frac{\text{ln}(\frac{d}{a})}{c}$ .

5 0

2 years ago

Which system of equations can be used to find the roots of the equation 4 x Superscript 5 Baseline minus 12 x Superscript 4 Base

ehidna [41]

Answer:

D. on Edg 2020

Step-by-step explanation:

You are welcome, I helped better than that other guy!!!

3 0

1 year ago

Sam is observing the velocity of a car at different times. After two hours, the velocity of the car is 50 km/h. After six hours,

Eva8 [605]

Let:
x = hours of travel
y = velocity

slope= rise/run slope=(y2-y1)/(x2-x1)
(x1,y1) = (2,50) (x2,y2) = (6,54)
sub values back into the equation m = (54-50)/(6-2) m = 1
POINT SLOPE FORMy-y1 = m(x-x1) y-50= 1(x-2) y = x -2 +50
y = x + 48

B)

the graph within the first seven hours can be obtained at point B

x = 7

y = 7+48 = 55
B(7,55)

4 0

1 year ago

The rocks near the shore between two lighthouses at points A and B make the waters unsafe. The measure of arcAXB is 300. Waters

belka [17]

As a navigator of this ship, you must consider the measure of the arc. Using the distance between the two lighthouses and the arc measurement, you can find the radius and center of the circle to set a reasonable distance in keeping the ship in safe waters.

5 0

2 years ago

Stu hiked a trail at an average rate of 3 miles per hour. He ran back on the same trail at an average rate of 5 miles per hour.

fredd [130]

Let d = the length of the trail, miles

Note that
distance = speed * time
or
time = distance / speed.

The time, t₁, to travel the trail at 3 miles per hour is
t₁ = d/3 hours
The time, t₂, to travel back at 5 miles per hour is
t₂ = d/5 hours

Because the total time is 3 hours, therefore
t₁ + t₂ = 3
d/3 + d/5 = 3
d(1/3 + 1/5) = 3
d(8/15) = 3
Multiply each side by 15.
8d = 3*15 =45
d = 45/8 = 5 5/8 miles or 5.625 miles
Total distance = 2*d = 11.25 miles or 11 1/4 miles.

t₁ = 5.625/3 = 1.875 hours or 1 hour, 52.5 minutes
t₂ = 5.625/5 = 1.125 hours or 1 hour , 7.5 minutes

Answers ;
Time to travel at 3 miles per hour = 1.875 hours (1 hour, 52.5 minutes)
Time to return at 5 miles per hour = 1.125 hours (1 hour, 7.5 minutes)
Total distance traveled = 2*d = 11.25 miles.

6 0

2 years ago

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