What is the limit of ln(15/t) as t approaches 15e?

Jamie is hiking up a small mountain. He climbs up at a constant rate of 300 feet/hour until he reaches the peak at 1,500 feet. A

aleksandr82 [10.1K]

Answer:

a. d = 1500 - 300t. b. after 2 hours and after 4 hours

Step-by-step explanation:

a. Since Jamie hikes up the mountain at a rate of 300 ft/hr, and the mountain is 1500 ft high, his distance, d from the peak of the mountain at any given time,t is given by

d = 1500 - 300t.

b.If Jamie distance d = 900 ft, then the equation becomes,

900 = 1500 - 300t

900 - 1500 = -300t

-600 = -300t

t = -600/-300

t = 2 hours

The equation d = 1500 - 300t. also models his distance from the peak of the mountain if he hikes down at a constant rate of 300 ft/hr

At d = 900 ft, the equation becomes

900 = 1500 - 300t

900 - 1500 = -300t

-600 = -300t

t = -600/-300

t = 2 hours

So, on his hike down the mountain, it takes him another 2 hours to be 900 ft from the peak of the mountain.

So, he is at 900 ft on his hike down after his start of hiking up the mountain at time t = (2 + 2) hours = 4 hours. Since it takes 2 hours to climb to the peak of he mountain and another 2 hours to climb down 900 ft from the peak of the mountain.

4 0

3 years ago

Solve the two-step equation.-0.45x + 0.33 = -0.66What is the solution?x = -2.2x = -1.4x = 1.4x = 2.2f

Softa [21]

Answer:

x = 2.2

Step-by-step explanation:

-0.45x + 0.33 = -0.66

Subtract .33 from each side

-0.45x + 0.33-.33 = -0.66-.33

-.45x = -.99

Divide each side by -.45

-.45x./-.45 = -.99/-.45

x = 11/5

x = 2.2

8 0

3 years ago

For the following amount at the given interest rate compounded continuously, find (a) the future value after 9 years, (b) the

Stella [2.4K]

Answer:

(a) The future value after 9 years is $7142.49.

(b) The effective rate is $r_E=4.759 \:{\%}$ .

(c) The time to reach $13,000 is 21.88 years.

Step-by-step explanation:

The definition of Continuous Compounding is

If a deposit of $P$ dollars is invested at a rate of interest $r$ compounded continuously for $t$ years, the compound amount is

$A=Pe^{rt}$

(a) From the information given

$P=4700$

$r=4.65\%=\frac{4.65}{100} =0.0465$

$t=9 \:years$

Applying the above formula we get that

$A=4700e^{0.0465\cdot 9}\\A=7142.49$

The future value after 9 years is $7142.49.

(b) The effective rate is given by

$r_E=e^r-1$

Therefore,

$r_E=e^{0.0465}-1=0.04759\\r_E=4.759 \:{\%}$

(c) To find the time to reach $13,000, we must solve the equation

$13000=4700e^{0.0465\cdot t}$

$4700e^{0.0465t}=13000\\\\\frac{4700e^{0.0465t}}{4700}=\frac{13000}{4700}\\\\e^{0.0465t}=\frac{130}{47}\\\\\ln \left(e^{0.0465t}\right)=\ln \left(\frac{130}{47}\right)\\\\0.0465t\ln \left(e\right)=\ln \left(\frac{130}{47}\right)\\\\0.0465t=\ln \left(\frac{130}{47}\right)\\\\t=\frac{\ln \left(\frac{130}{47}\right)}{0.0465}\approx21.88$

3 0

3 years ago

The only way to identify an intercept is as an ordered pair.<br><br> True<br> False

artcher [175]

False because there are other ways to identify an intercept

5 0

3 years ago

Paul is three times as old as Mary and Peter is four times as old as Mary,If the sum of their ages is 64, how old are Peter,Paul

uysha [10]

Let Mary's age be x.

Paul is three times as old as Mary, so Paul's age would be 3x.

Peter is four times as old as Mary, so Peter's age would be 4x.

The sum of their ages is 64
⇒ Paul's age+ Peter's age+ Mary's age= 64
⇒ 3x+ 4x+ x= 64
⇒ 8x= 64
⇒ x= 64/8
⇒ x= 8

Paul's age is: 3x= 3*8= 24

Peter's age is: 4x= 4*8= 32

Final answer: Paul is 24 years old.
Peter is 32 years old.
Mary is 8 years old.

Hope this helps~

7 0

3 years ago