3. Jane and Brittany have been saving up for their summer vacation. After how many days will

Please help i will give brainliest and thanks !!!!

Juliette [100K]

Answer:

6 trees and 12 bushes

Step-by-step explanation:

6 trees will be 474

12 bushes will be 276

474+276=750

6+12=18

hope this helps

6 0

3 years ago

The concentration C of certain drug in a patient's bloodstream t hours after injection is given by

frozen [14]

Answer:

a) The horizontal asymptote of $C(t)$ is $c = 0$ .

b) When t increases, both the numerator and denominator increases, but given that the grade of the polynomial of the denominator is greater than the grade of the polynomial of the numerator, then the concentration of the drug converges to zero when time diverges to the infinity. There is a monotonous decrease behavior.

c) The time at which the concentration is highest is approximately 1.291 hours after injection.

Step-by-step explanation:

a) The horizontal asymptote of $C(t)$ is the horizontal line, to which the function converges when $t$ diverges to the infinity. That is:

$c = \lim _{t\to +\infty} \frac{t}{3\cdot t^{2}+5}$ (1)

$c = \lim_{t\to +\infty}\left(\frac{t}{3\cdot t^{2}+5} \right)\cdot \left(\frac{t^{2}}{t^{2}} \right)$

$c = \lim_{t\to +\infty}\frac{\frac{t}{t^{2}} }{\frac{3\cdot t^{2}+5}{t^{2}} }$

$c = \lim_{t\to +\infty} \frac{\frac{1}{t} }{3+\frac{5}{t^{2}} }$

$c = \frac{\lim_{t\to +\infty}\frac{1}{t} }{\lim_{t\to +\infty}3+\lim_{t\to +\infty}\frac{5}{t^{2}} }$

$c = \frac{0}{3+0}$

$c = 0$

The horizontal asymptote of $C(t)$ is $c = 0$ .

b) When t increases, both the numerator and denominator increases, but given that the grade of the polynomial of the denominator is greater than the grade of the polynomial of the numerator, then the concentration of the drug converges to zero when time diverges to the infinity. There is a monotonous decrease behavior.

c) From Calculus we understand that maximum concentration can be found by means of the First and Second Derivative Tests.

First Derivative Test

The first derivative of the function is:

$C'(t) = \frac{(3\cdot t^{2}+5)-t\cdot (6\cdot t)}{(3\cdot t^{2}+5)^{2}}$

$C'(t) = \frac{1}{3\cdot t^{2}+5}-\frac{6\cdot t^{2}}{(3\cdot t^{2}+5)^{2}}$

$C'(t) = \frac{1}{3\cdot t^{2}+5}\cdot \left(1-\frac{6\cdot t^{2}}{3\cdot t^{2}+5} \right)$

Now we equalize the expression to zero:

$\frac{1}{3\cdot t^{2}+5}\cdot \left(1-\frac{6\cdot t^{2}}{3\cdot t^{2}+5} \right) = 0$

$1-\frac{6\cdot t^{2}}{3\cdot t^{2}+5} = 0$

$\frac{3\cdot t^{2}+5-6\cdot t^{2}}{3\cdot t^{2}+5} = 0$

$5-3\cdot t^{2} = 0$

$t = \sqrt{\frac{5}{3} }\,h$

$t \approx 1.291\,h$

The critical point occurs approximately at 1.291 hours after injection.

Second Derivative Test

The second derivative of the function is:

$C''(t) = -\frac{6\cdot t}{(3\cdot t^{2}+5)^{2}}-\frac{(12\cdot t)\cdot (3\cdot t^{2}+5)^{2}-2\cdot (3\cdot t^{2}+5)\cdot (6\cdot t)\cdot (6\cdot t^{2})}{(3\cdot t^{2}+5)^{4}}$

$C''(t) = -\frac{6\cdot t}{(3\cdot t^{2}+5)^{2}}- \frac{12\cdot t}{(3\cdot t^{2}+5)^{2}}+\frac{72\cdot t^{3}}{(3\cdot t^{2}+5)^{3}}$

$C''(t) = -\frac{18\cdot t}{(3\cdot t^{2}+5)^{2}}+\frac{72\cdot t^{3}}{(3\cdot t^{2}+5)^{3}}$

If we know that $t \approx 1.291\,h$ , then the value of the second derivative is:

$C''(1.291\,h) = -0.077$

Which means that the critical point is an absolute maximum.

The time at which the concentration is highest is approximately 1.291 hours after injection.

5 0

3 years ago

Which equation best represents the line?

erica [24]

y = mx + b, where m = slope, and b = y-intercept.

y = 3x + 3

y = 1/2x - 3

y = 1/2x + 3

y = 3x + 1/2

we can eliminate 2 and 4 since the y-intercept in the graph is shown as (0, 3)

This leaves us with

y = 3x + 3 and y = 1/2x+3

m = change in y / change in x

We take any two points on the line to find the slope.

I chose (2, 4), (0, 3)

change in x: 2 - 0 = 2

change in y: 4 - 3 = 1

m = 1/2

This leaves us with the only answer that has the slope of 1/2 and the y-intercept of 3.

option: 3

y = 1/2x + 3

7 0

3 years ago

Can someone solve this problem for me

Aleks [24]

Answer:

(C) 90 $in^{2}$

Step-by-step explanation:

The figure is a combination of two parallelograms. So, to find the area of the whole figure, all you have to do is find the area of each parallelogram separately (they happen to be the same in this problem) and then add them up. The formula for the area of a parallelogram is A = base*height. In each parallelogram, the base is 15 in., and the height is 3 in. Therefore, the area of each parallelogram is 45 $in^{2}$ and the area of the whole figure is 90 $in^{2}$ .

Hope this helps :)

3 0

2 years ago

Which number is an irrational number? o 2 0 - 3 02.56 O 16

Agata [3.3K]

Answer:

2.56 is the correct answer because -3 can be turned into a rational number

and 2 an 16 are rational number

6 0

3 years ago