I really need help with this trigonometric function, i am struggling and it would mean a lot.

Answer:

[tex]dA(t)/dt = -\frac{3}{7}e^{-t/70}[/tex] g/min

Step-by-step explanation:

The mass flow rate dA(t)/dt = mass flowing in - mass flowing out

Since water is pumped in at a rate of 3 L/min, and it contains no salt, the concentration in is thus 0 g/L. the mass flow in is thus 0 g/L × 3 L/min = 0 g/min.

Let A(t) be the mass present at any time, t. The concentration at any time ,t is thus A(t)/volume = A(t)/210. Since water flows out at a rate of 3 L/min, the mass flow out is thus, A(t)/210 g/L × 3 L/min = A(t)/70 g/min.

So, dA(t)/dt = mass flowing in - mass flowing out

dA(t)/dt = 0 g/min - A(t)/70 g/min

dA(t)/dt =  - A(t)/70 g/min

 Since the tank initially contains 30 g of salt, the initial mass of salt in the tank is 30 g. So A(0) = 30

So, the initial value problem is thus  

dA(t)/dt =  - A(t)/70 , A(0) = 30

Separating the variables, we have

dA(t)/A(t) = -dt/70

Integrating both sides, we have

∫dA(t)/A(t) = ∫-dt/70

㏑A(t) = -t/70 + C

taking exponents of both sides, we have

A(t) = exp(-t/70 + C)

A(t) = exp(-t/70)expC

[tex]A(t) = e^{-t/70}e^{C}\\A(t) = Ce^{-t/70} whereC = e^{C}[/tex]

A(0) = 30, So

[tex]A(0) = Ce^{-0/70}\\30 = Ce^{0}\\C = 30[/tex]

[tex]A(t) = 30e^{-t/70}[/tex]

The rate at which the number of grams of salt in the tank is changing at time t is

[tex]dA(t)/dt = \frac{d30e^{-t/70} }{dt} \\dA(t)/dt = -\frac{30e^{-t/70} }{70}\\dA(t)/dt = -\frac{3}{7}e^{-t/70}[/tex]

So, the rate at which the number of grams of salt in the tank is changing at time t is

[tex]dA(t)/dt = -\frac{3}{7}e^{-t/70}[/tex] g/min

Answer:

5

Step-by-step explanation:

25 / ( 12-7)  = 25 / 5 = 5

I hope im right!!

Answer:

72 cm²

Step-by-step explanation:

Given:

m<ABC = 44°

x = 16 cm

y = 13 cm

Required:

Area of the triangle

Solution:

Formula for finding area of a triangle using the Side-Angle-Side method is given as:

Area = ½*ab*sin C

where,

a = 16

b = 13

C = 44°

Plug in the values

Area = ½(16*13)*sin 44

Area = 72.2444705 ≈ 72 cm²

Answer:

1,050

Step-by-step explanation:

3.5x

12x

25

=

1,050

Answer:

1st, third and last options are correct answers

Step-by-step explanation:

e + 3 + e + 3

2e + 6

2(e + 3)

Answer:

10

Step-by-step explanation:

5 x 8 / 4

40/4=10

Answer:

Bottom left graph, ∠a + ∠b = 180°, ∠a + ∠b = 90°, ∠a + ∠b = 90°

Step-by-step explanation:

For the first problem, we can look at the slope. The slope of the equation is negative. The line has to be similar to the bottom slant of the letter "K".

There are two lines that are similar and have the same y-intercept, so it's just a matter of which slope matches.

The slope is -1, so that means to find a different point we go down 1 and right 1.

The only point that's the same on the two lines are (0, 3).

When go down 1 and right 1, the point should be: (1,2)

The only line that satisfy this is the bottom left graph.

For problem 2, ∠a and ∠b must add up to 180°.

So the equation for problem 2 is: ∠a + ∠b = 180°

For problem 3, ∠a and ∠b are equal because they're opposite angles.

So the equation for problem 3 is: ∠a = ∠b

For problem 4, ∠a and ∠b must add up to 90°.

So the equation for problem 4 is: ∠a + ∠b = 90°

For problem 5, ∠a and ∠b must add up to 90°, since the other angle is 90°, which is half to 180°.

So the equation for problem 5 is: ∠a + ∠b = 90°

Answer:

Ignore los puntos.

Ignore the points.

Answer: .012

Step-by-step explanation: 6*2 is 12, and you can simply use the number of decimal points on the smaller term to get .012

Answer:

should be .12

Step-by-step explanation:

.06 multiplied by 2 is .12

Answer:

9,-7 hope this helps :))))))))

Answer:

g

Step-by-step explanation:

gggg

Answer:

r=-0.23684

Step-by-step explanation:

Answer:

1.57

Step-by-step explanation:

Answer:

1.57

Step-by-step explanation:

Circumference = 2pi(r) = 2(3.14)1 = 6.28

1/4x6.28=1.57

Answer:

.9x 6.2= $5.58

.............

I think 710 is the answer

266+266+89+89= 710

Answer:

y = 18

a = -2

Step-by-step explanation:

Hello There!

For the first one we need to create an equation to solve for y

23+7=y+12

30=y+12

isolate the variable using inverse operations

subtract 12 from each side

30-12=18

we're left with y = 18

for the second one we need to create an equation to solve for a

3+15+a=8+8+8

3+15=18

8+8+8=16

16=18+a

step 1 subtract each side by 18

16-18=-2

we're left with a = -2

Answer:

C. 48.

Step-by-step explanation:

If the mean is 12, then 12 must be 2x, 3x, 4x, and 3x divided by 4.

      --> [tex]\frac{2x+3x+4x+3x}{4}=12[/tex]

      --> [tex]\frac{12x}{4}=12[/tex]

      --> [tex]\\3x=12[/tex]

      --> x=4

Add: 2x+3x+4x+3x=8+12+16+12=48

Answer:

B

Step-by-step explanation:

Answer:

0.2308 = 23.08% probability that this person made a day visit

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Visitor made a purchase

Event B: Made a day visit

Probability that a visitor made a purchase:

30% of 20%(day visitors)

10% of 50%(one-night)

50% of 30%(two-night)

So

[tex]P(A) = 0.3*0.2 + 0.1*0.5 + 0.5*0.3 = 0.26[/tex]

Probability of a purchase with a day visit:

30% of 20%. So

[tex]P(A \cap B) = 0.3*0.2 = 0.06[/tex]

How likely is it that this person made a day visit?

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.06}{0.26} = 0.2308[/tex]

0.2308 = 23.08% probability that this person made a day visit

Answer:

Check image

Step-by-step explanation:

Answer:

√13

Yes you are right

Step-by-step explanation:

The law of cos again

BC^2 = 18 + 25 - 2 * 3√2 * 5 cos(45 degrees)

= 13

==>

BC = √13

Answer:

yes the answer is correct

Answer:

1000 = n

Step-by-step explanation:

Answer:

Step 1:  Determine why circle 1 is similar to circle 2

The reason why circle 1 is similar to circle 2 is that they both expand at the same rate.  While x grows larger, both circle 1 and circle 2 grow at a proportional rate.  Circle 2 grows is 5 times bigger than circle 1 given any value 5.

When x = 3:  circle 1 = 6 and circle 2 = 30

When x = 10:  circle 1 = 20 and circle 2 = 100

Answer:

Circle 2 is a dilation of circle 1 with a scale factor of 5.

Step-by-step explanation:

Took the quiz and got a perfect score :)

Answer:

11x

Step-by-step explanation:

To find it, you can simply expand the expression

(3x + 5)(4x - 3)

= 3x(4x - 3) + 5(4x - 3)

= 12x² - 9x + 20x - 15

= 12x² + 11x - 15

division is 1.92307692308

multiply is 325

Answer:

Balance stretching is giving equal attention to stretching all parts of your body. It is also important to stretch opposite muscles in equal amounts. For example, you need to stretch your hamstrings as much as your quads, and you need to stretch your right arm as much as your left arm.

or

Balanced stretching refers to performing stretching exercises across the entire body. Stretching the entire body balances the fitness benefits across all muscle groups instead of limiting the benefits to a single or limited number of muscle groups.

Step-by-step explanation:

just took the test on edge

Good Luck!

Balanced stretching can be defined as the process of performing physical exercises to stretch the whole body which gives the body a complete balance and fitness.

This means an activity which is done physically to improve health and fitness.

Many stretching exercises to help the body balance itself.

Alternating knee raises with each step as you walk.

Without using your hands, getting out of a chair and standing up.

Giving each portion of your body equal attention while stretching is known as balance stretching. Stretching opposing muscles equally is also essential. For instance, you should extend your right arm as much as your left arm and your hamstrings as much as your quads.

Learn more about physical exercise here:

brainly.com/question/1744272

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