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3 years ago

13

Mathematics

1 answer:

Temka [501]3 years ago

6 0

Answer:

14 ft.

Step-by-step explanation:

78 - 25 -25 = 28

28/2 = 14

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Protease is an enzyme that breaks down proteins. What is the end product of this protein breakdown? A. amino acids B. fatty acid

mezya [45]

Answer:

A protease (also called a peptidase or ) is an enzyme an enzyme that catalyzes (increases the rate of) proteolysis, the breakdown of proteins into smaller polypeptides or single amino acids. They do this by cleaving the peptide bonproteins by hydrolysis, a reaction where water breaks bonds.

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3 years ago

A tank contains 180 gallons of water and 15 oz of salt. water containing a salt concentration of 17(1+15sint) oz/gal flows into

Stels [109]

Let A(t) denote the amount of salt (in ounces, oz) in the tank at time t (in minutes, min).

Salt flows in at a rate of

$\dfrac{dA}{dt}_{\rm in} = \left(17 (1 + 15 \sin(t)) \dfrac{\rm oz}{\rm gal}\right) \left(8\dfrac{\rm gal}{\rm min}\right) = 136 (1 + 15 \sin(t)) \dfrac{\rm oz}{\min}$

and flows out at a rate of

$\dfrac{dA}{dt}_{\rm out} = \left(\dfrac{A(t) \, \mathrm{oz}}{180 \,\mathrm{gal} + \left(8\frac{\rm gal}{\rm min} - 8\frac{\rm gal}{\rm min}\right) (t \, \mathrm{min})}\right) \left(8 \dfrac{\rm gal}{\rm min}\right) = \dfrac{A(t)}{180} \dfrac{\rm oz}{\rm min}$

so that the net rate of change in the amount of salt in the tank is given by the linear differential equation

$\dfrac{dA}{dt} = \dfrac{dA}{dt}_{\rm in} - \dfrac{dA}{dt}_{\rm out} \iff \dfrac{dA}{dt} + \dfrac{A(t)}{180} = 136 (1 + 15 \sin(t))$

Multiply both sides by the integrating factor, $e^{t/180}$ , and rewrite the left side as the derivative of a product.

$e^{t/180} \dfrac{dA}{dt} + e^{t/180} \dfrac{A(t)}{180} = 136 e^{t/180} (1 + 15 \sin(t))$

$\dfrac d{dt}\left[e^{t/180} A(t)\right] = 136 e^{t/180} (1 + 15 \sin(t))$

Integrate both sides with respect to t (integrate the right side by parts):

$\displaystyle \int \frac d{dt}\left[e^{t/180} A(t)\right] \, dt = 136 \int e^{t/180} (1 + 15 \sin(t)) \, dt$

$\displaystyle e^{t/180} A(t) = \left(24,480 - \frac{66,096,000}{32,401} \cos(t) + \frac{367,200}{32,401} \sin(t)\right) e^{t/180} + C$

Solve for A(t) :

$\displaystyle A(t) = 24,480 - \frac{66,096,000}{32,401} \cos(t) + \frac{367,200}{32,401} \sin(t) + C e^{-t/180}$

The tank starts with A(0) = 15 oz of salt; use this to solve for the constant C.

$\displaystyle 15 = 24,480 - \frac{66,096,000}{32,401} + C \implies C = -\dfrac{726,594,465}{32,401}$

So,

$\displaystyle A(t) = 24,480 - \frac{66,096,000}{32,401} \cos(t) + \frac{367,200}{32,401} \sin(t) - \frac{726,594,465}{32,401} e^{-t/180}$

Recall the angle-sum identity for cosine:

$R \cos(x-\theta) = R \cos(\theta) \cos(x) + R \sin(\theta) \sin(x)$

so that we can condense the trigonometric terms in A(t). Solve for R and θ :

$R \cos(\theta) = -\dfrac{66,096,000}{32,401}$

$R \sin(\theta) = \dfrac{367,200}{32,401}$

Recall the Pythagorean identity and definition of tangent,

$\cos^2(x) + \sin^2(x) = 1$

$\tan(x) = \dfrac{\sin(x)}{\cos(x)}$

Then

$R^2 \cos^2(\theta) + R^2 \sin^2(\theta) = R^2 = \dfrac{134,835,840,000}{32,401} \implies R = \dfrac{367,200}{\sqrt{32,401}}$

and

$\dfrac{R \sin(\theta)}{R \cos(\theta)} = \tan(\theta) = -\dfrac{367,200}{66,096,000} = -\dfrac1{180} \\\\ \implies \theta = -\tan^{-1}\left(\dfrac1{180}\right) = -\cot^{-1}(180)$

so we can rewrite A(t) as

$\displaystyle A(t) = 24,480 + \frac{367,200}{\sqrt{32,401}} \cos\left(t + \cot^{-1}(180)\right) - \frac{726,594,465}{32,401} e^{-t/180}$

As t goes to infinity, the exponential term will converge to zero. Meanwhile the cosine term will oscillate between -1 and 1, so that A(t) will oscillate about the constant level of 24,480 oz between the extreme values of

$24,480 - \dfrac{267,200}{\sqrt{32,401}} \approx 22,995.6 \,\mathrm{oz}$

and

$24,480 + \dfrac{267,200}{\sqrt{32,401}} \approx 25,964.4 \,\mathrm{oz}$

which is to say, with amplitude

$2 \times \dfrac{267,200}{\sqrt{32,401}} \approx \mathbf{2,968.84 \,oz}$

6 0

2 years ago

Find the perimeter of a regular pentagon with each side measuring 6cm.

Black_prince [1.1K]

Answer:

30cm

Step-by-step explanation:

Perimeter of a Pentagon=5L

P=5×6cm=30cm

6 0

3 years ago

1. During October, William Korth worked 160 regular time hours at $9.28 an hour and 18 overtime hours at time-

Vanyuwa [196]

Answer:

Kindly check explanation

Step-by-step explanation:

1.) regular time hours = 160

Overtime hours = 18

Gross pay = (9.28 * 160) + (1.5 * 9.28 * 18) = $1735.36

2.) Last year, Ida Zolen worked 2,000 hours at regular time pay of $8.20 an hour. She also worked 75 hours over time at double his regular rate. What was Ida’s gross pay last year?

Gross pay:

(2000 * 8.20) + (2 * 8.20 * 75) = $17,630

3. Alan Kirbaum works on an 8-hour day basis and is paid $8 an hour for regular time work and time-and-a half for overtime work. Last week he worked these hours: Monday:9 ; Tuesday:6 ; Wednesday:11 ; Thursday:8 ; Friday:9.

A) How many regular hours did he work?

Regular hours = (8 + 6 + 8 + 8 + 8).= 38 hours

B) How many overtime?

Overtime = (1 + 3 + 1). = 5 hours

C) What is his overtime rate?

2.5 * $8 = $20

D) What is his overtime pay?

$20 * 5 = $100

E) Find Alan’s gross pay.

(38 * $8) + $100 = $404

4. Stephen Woll’s regular pay is $20 an hour. He is paid time and a half for overtime work beyond 40 hours a week. He

worked: Monday:11 ; Tuesday:10 ; Wednesday:10 ; Friday:12. Find Stephen

Total Hour = (11 + 10 + 10 + 12) = 43 hours

8 0

3 years ago

Which expression is equivalent to the following complex fraction?

Sergeu [11.5K]

Answer:

(-2y+5x) / (3x - 2y)

Step-by-step explanation:

If we write this sentence, we have:

((-2/x) + (5/y)) / ((3/y) - (2/x))

If we do LCM in the denominators of each fraction, we have:

((-2y+5x)/xy) / ((3x - 2y)/xy)

We can cut the 'xy' in the numerator and denominator of the whole fraction:

(-2y+5x) / (3x - 2y)

The final expression we have is (-2y+5x) / (3x - 2y)

3 0

3 years ago

Read 2 more answers