a rock climber climbs down into the grand canyon at a rate of 2ft/ min. how long will it take to climb down 50 feet?

A quantity P is an exponential function of time I, such that P = 160 when t = 6 and P = 150 when I = 4. Use the given informatio

Klio2033 [76]

Answer:

k = 0.032
P0 = 131.836

Step-by-step explanation:

Perhaps you want to use the points (t, P) = (4, 150) and (6, 160) to find the parameters P0 and k in the equation ...

$P(t)=P_0\cdot e^{kt}$

We know from the given points that we can write the equation as ...

$P(t)=150\left(\dfrac{160}{150}\right)^{(t-4)/(6-4)}=150\left(\dfrac{16}{15}\right)^{\frac{t}{2}-2}\\\\=150\left(\dfrac{16}{15}\right)^{-2}\times\left(\left(\dfrac{16}{15}\right)^{\frac{1}{2}}\right)^t$

Comparing this to the desired form, we see that ...

$P_0=150\left(\dfrac{16}{15}\right)^{-2}\approx 131.836\\\\e^{k}=\left(\dfrac{16}{15}\right)^{1/2}\rightarrow k=\dfrac{1}{2}(\ln{16}-\ln{15})\approx 0.0322693$

So, the approximate equation for P is ...

$P(t)=131.836\cdote^{0.032t}$

And the parameters of interest are ...

k = 0.032
P0 = 131.836

4 0

2 years ago

Kelly walks 0.7 mile to school. write an inequality using <, >, = to compare the distances they walk to school. I need hel

Igoryamba

One inequality is 0.8>0.7>0.6. I hope it

8 0

3 years ago

Write the equation of a line passing through (-4.3) and perpendicular to -6x + 4y =-12.

sergij07 [2.7K]

Answer:

y=-2/3*x+1/3

Step-by-step explanation:

-6x+4y=-12

put into y=mx+b line equation

4y=6x-12

y=(6/4)x-(12/4)

y=(3/2)x-4

slope is 3/2

to find perpendiular line slope take the negative inverse.

-(2/3) = slope of perpendicular line

use line equation and solve for y-intercept (b)

3=(-2/3)*(-4)+b

3=8/3+b

b= 9/3-8/3 = 1/3 : 3 = 9/3 to allow for subrtaction of fractions.

3 0

3 years ago

Please help with these questions. Will mark brainliest!

andrew11 [14]

Answer:

1, pre image 2, transformation

Step-by-step explanation:

6 0

3 years ago

What is the volume of a sphere with a radius of 4 cm? Use 3. 14 for pi. Round to the nearest hundredth. 50. 24 cm³ 66. 99 cm³ 20

Nimfa-mama [501]

The volume of the sphere is 267. 95 cm³.

<h2>Given </h2>

The radius of the sphere is 4cm.

<h3>What is the volume of sphere?</h3>

The volume of a sphere is the three-dimensional space occupied by a sphere.

The volume of the sphere is determined by the following formula;

$\rm Volume = \dfrac{4}{3} \pi r^3$

Where r is the radius of the sphere.

Substitute all the values in the formula;

$\rm Volume = \dfrac{4}{3} \pi r^3\\\\\rm Volume = \dfrac{4}{3} \times (3.14) \times 4^3\\\\Volume = 4 \times 1.04 \times 64\\\\Volume = 267.95\ cm ^3$

Hence, the volume of the sphere is 267. 95 cm³.

To know more about Volume of Sphere click the link given below.

brainly.com/question/369459

4 0

2 years ago