A motorboat travels 244 kilometers in 4 hours going upstream and 665
kilometers in 7 hours going downstream. What is the rate of the boat in still water and what is the rate of the current?

Answer:

3 is 20% of 15

Step-by-step explanation:

Answer:

D) ASA

Step-by-step explanation:

Solution :

Along the edge [tex]$C_1$[/tex]

The parametric equation for [tex]$C_1$[/tex] is given :

[tex]$x_1(t) = 9t , y_2(t) = 0 \ \ for \ \ 0 \leq t \leq 1$[/tex]

Along edge [tex]$C_2$[/tex]

The curve here is a quarter circle with the radius 9. Therefore, the parametric equation with the domain [tex]$0 \leq t \leq 1 $[/tex] is then given by :

[tex]$x_2(t) = 9 \cos \left(\frac{\pi }{2}t\right)$[/tex]

[tex]$y_2(t) = 9 \sin \left(\frac{\pi }{2}t\right)$[/tex]

Along edge [tex]$C_3$[/tex]

The parametric equation for [tex]$C_3$[/tex] is :

[tex]$x_1(t) = 0, \ \ \ y_2(t) = 9t \ \ \ for \ 0 \leq t \leq 1$[/tex]

Now,

x = 9t, ⇒ dx = 9 dt

y = 0, ⇒ dy = 0

[tex]$\int_{C_{1}}y^2 x dx + x^2 y dy = \int_0^1 (0)(0)+(0)(0) = 0$[/tex]

And

[tex]$x(t) = 9 \cos \left(\frac{\pi}{2}t\right) \Rightarrow dx = -\frac{7 \pi}{2} \sin \left(\frac{\pi}{2}t\right)$[/tex]

[tex]$y(t) = 9 \sin \left(\frac{\pi}{2}t\right) \Rightarrow dy = -\frac{7 \pi}{2} \cos \left(\frac{\pi}{2}t\right)$[/tex]

Then :

[tex]$\int_{C_1} y^2 x dx + x^2 y dy$[/tex]

[tex]$=\int_0^1 \left[\left( 9 \sin \frac{\pi}{2}t\right)^2\left(9 \cos \frac{\pi}{2}t\right)\left(-\frac{7 \pi}{2} \sin \frac{\pi}{2}t dt\right) + \left( 9 \cos \frac{\pi}{2}t\right)^2\left(9 \sin \frac{\pi}{2}t\right)\left(\frac{7 \pi}{2} \cos \frac{\pi}{2}t dt\right) \right]$[/tex]

[tex]$=\left[-9^4\ \frac{\cos^4\left(\frac{\pi}{2}t\right)}{\frac{\pi}{2}} -9^4\ \frac{\sin^4\left(\frac{\pi}{2}t\right)}{\frac{\pi}{2}} \right]_0^1$[/tex]

= 0

And

x = 0,  ⇒ dx = 0

y = 9 t,  ⇒ dy = 9 dt

[tex]$\int_{C_3} y^2 x dx + x^2 y dy = \int_0^1 (0)(0)+(0)(0) = 0$[/tex]

Therefore,

[tex]$ \oint y^2xdx +x^2ydy = \int_{C_1} y^2 x dx + x^2 x dx+ \int_{C_2} y^2 x dx + x^2 x dx+ \int_{C_3} y^2 x dx + x^2 x dx $[/tex]

                        = 0 + 0 + 0

Applying the Green's theorem

[tex]$x^2 +y^2 = 81 \Rightarrow x \pm \sqrt{81-y^2}$[/tex]

[tex]$\int_C P dx + Q dy = \int \int_R\left(\frac{\partial Q}{\partial x} - \frac{\partial P}{\partial y}\right) dx dy $[/tex]

Here,

[tex]$P(x,y) = y^2x \Rightarrow \frac{\partial P}{\partial y} = 2xy$[/tex]

[tex]$Q(x,y) = x^2y \Rightarrow \frac{\partial Q}{\partial x} = 2xy$[/tex]

[tex]$\left(\frac{\partial Q}{\partial x}-\frac{\partial P}{\partial y} \right) = 2xy - 2xy = 0$[/tex]

Therefore,

[tex]$\oint_Cy^2xdx+x^2ydy = \int_0^9 \int_0^{\sqrt{81-y^2}}0 \ dx dy$[/tex]

                            [tex]$= \int_0^9 0\ dy = 0$[/tex]

The vector field F is = [tex]$y^2 x \hat i+x^2 y \hat j$[/tex]  is conservative.

Answer:

1

Step-by-step explanation:

9 - 3  ÷ 1/3 + 1

first do division

3 ÷ 1/3 = 9

9 - 9 + 1 = 1

The value of the principal investment would be = $12,500.75

A principal investment is defined as the capital amount of money that is being deposited into an account with the purpose of receiving interest for a particular period of time.

The years of investment (t) = 9 years

The annual interest rate (r) = 3.9% = 3.9/100= 0.039

The total worth of the investment (A) = $17,757.16

Then, solve the equation for P

P = A / ert

P = 17,757.16 / e(0.039*9)

P = $12,500.75

Therefore, the principal amount that is needed which can be compounded continuously to get the total amount given = $12,500.75

Learn more about simple interest here:

https://brainly.com/question/25793394

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answer:

h

Step-by-step explanation:

if there is more blues and green cards than purple there is a lower chance of getting purple

Answer:

[tex]K)~\frac{3}{16+x}[/tex]

Step-by-step explanation:

[tex]green~ cards=4[/tex]

[tex]blue ~cards=9[/tex]

[tex]purple~ cards=3[/tex]

[tex]pink ~cards=x[/tex]

[tex]total:-[/tex] 4×9×3×x

→ [tex]16+x[/tex]

[tex]p(x)=\frac{3}{16+x}[/tex]

[tex]Answer:K[/tex]

[tex]------------[/tex]

hope it helps...

have a great day!!

Answer:

0.2

Step-by-step explanation:

1/10 = 0.1

10/100 = 0.1

0.1+0.1 = 0.2

Answer:

The equation of the line is: [tex]y = 0.6x + 0.6[/tex]

Step-by-step explanation:

Equation of a line:

The equation of a line has the following format:

[tex]y = mx + b[/tex]

In which m is the slope and b is the y-intercept.

Two points:

We have these following two points in this exercise:

x = -6, y = -3, so (-6,-3)

x = 4, y = 3, so (4,3)

Finding the slope:

Given two points, the slope is given by the change in y divided by the change in x.

Change in y: 3 - (-3) = 3 + 3 = 6

Change in x: 4 - (-6) = 4 + 6 = 10

So

[tex]m = \frac{6}{10} = 0.6[/tex]

Then

[tex]y = 0.6x + b[/tex]

Finding b:

We replace one of the points in the equation to find b. I will use (4,3).

[tex]y = 0.6x + b[/tex]

[tex]3 = 0.6*4 + b[/tex]

[tex]2.4 + b = 3[/tex]

[tex]b = 0.6[/tex]

The equation of the line is: [tex]y = 0.6x + 0.6[/tex]

Answer:

y=x-2

Step-by-step explanation:

I graphed the equations on desmos and saw which one had those ordered pairs on the line.

Answer:

the average no of customers in the system is 0.9

Step-by-step explanation:

Given that

The average number of arrivals is 6 per minute

And, the average service rate of a single server is 10 minutes

We need to find out the average no of customers in the system

So,

Lq = rho^2 / 1 ÷ rho

= (6 ÷ 10)^2 ÷ (1 - 6 ÷ 10)

= 36 ÷ 100  ×  10 ÷ 4

= 0.9

Hence, the average no of customers in the system is 0.9

Answer:

Step-by-step explanation:

Let's solve for x.

2x+3y=9

Step 1: Add -3y to both sides.

2x+3y+−3y=9+−3y

2x=−3y+9

Step 2: Divide both sides by 2.

2x/ 2 = −3y+9/ 2

x= −3/ 2 y+ 9/ 2

Answer:

x= −3/ 2 y+ 9/ 2

Answer:

Since [tex]P(A)P(B) \neq P(A \cap B)[/tex], these two events are not independent.

Step-by-step explanation:

Independent events:

Two events, A and B, are independent if:

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

In this question:

Event A: Male

Event B: Independent

Probability of male:

20 + 15 + 17 = 52 out of (20 + 15 + 17 + 18 + 12 + 7) = 89.

So

[tex]P(A) = \frac{52}{89}[/tex]

Probability of favoring independent:

20 + 18 = 38 out of 89. So

[tex]P(B) = \frac{38}{89}[/tex]

Probability of male and favoring independent:

20 out of 89. So

[tex]P(A \cap B) = \frac{20}{89}[/tex]

Test if they are independent:

[tex]P(A)P(B) = \frac{52}{89}*\frac{38}{89} = \frac{52*38}{89*89} = 0.24946[/tex]

[tex]P(A \cap B) = \frac{20}{89} = 0.22472[/tex]

Since [tex]P(A)P(B) \neq P(A \cap B)[/tex], these two events are not independent.

Answer:

78

Step-by-step explanation:

a + 8b = 6 + 8 x 9 = 6 + 72 = 78

Answer: 78

Step-by-step explanation:

value of a=6

value of b=9

a+8b= 6+8*9

as the 8 will be multiplied by 9

6+8*9= 6+72

6+72 = 78

Answer:

-85º

Step-by-step explanation:

275 - 360 = -85

Answer:

40 Balcony/15 floor

Step-by-step explanation:

A and C are out instantly cause the amount of tickets sold doesnt equal 55 and B is out cause 50x5=250 and 5x10=50 which totals to 300 not 350

Answer: -3√3

Step-by-step explanation: Factor out the square roots from each term

2√54 -> 6√6

√27 -> 3√3

3√24 -> 6√6

The equation becomes 6√6 - 3√3 - 6√6

By combining like terms we can eliminate 6√6

This leaves us with -3√3 as the simplified solution

Answer:

-3√3

Step-by-step explanation:

do the hcf method to get all the values outside

hcf of 54= 2, 3, 3, 3

hcf of 27 = 3, 3, 3

hcf of 24 = 2,2,3,3

2✓2×3×3×3 - √3,3,3 - 3√2,2,3,3

take out the common factor and multiply it with the value we have outside leave it if it doesnt have a number

2×3√2×3 - 3✓3 -3×2×3

6√6 - 3√3 - 3×2×3

6×3 - 3√3 - 3×2×3

18-18 - 3✓3

-3√3

Answer:

Step-by-step explanation:

B im pretty sure hope its right

Answer:

2/3

Step-by-step explanation:

4/9 divided by 2/3 = 4/9 times 3/2

= 2/3

Answer:

1. 29. Solve for the variable and graph the solution on a number line: –2x < –10 30. Solve for the variable and graph the solution on a number line: 9 + c > –2 31. Solve for the variable and graph the solution

2.  v – 4 ≥ 3 (6 + 2v

3. The last term, "the constant", is -5 Step-1 : Multiply the coefficient of the first term by the constant 4 • -5 = -20 Step-2 : Find two factors of -20 whose sum equals the coefficient of the middle term, which is -8

4.The first term is, 4p 2 its coefficient is 4 . The middle term is, -8p its coefficient is -8 . The last term, "the constant", is -5 Step-1 : Multiply the coefficient of the first term by the constant 4 • -5 = -20

Step-by-step explanation:

the rest is up to you, and u better say thanks and give me brainliest this took ages to explain

Answer:

Rounding to tenths

E: 56.8 %

F: 48.8 %

G: 44.9 %

H: 50.4 %

Step-by-step explanation:

Hope this helps!

Answer:

50.4 percent is f

Step-by-step explanation:

and the steps is calculate it

Answer:

Step-by-step explanation:

8.4

Answer:

$8.4

Step-by-step explanation:

[tex]3.36*2.5[/tex]

Answer:

m = 2

Step-by-step explanation:

[tex]\frac{13-5}{6-2}=\frac{8}{4} =\boxed{2}[/tex]

Hope this helps.

Answer:

90

Step-by-step explanation:

A regular quadrilateral is a square.

The sum of the exterior angles of a polygon is always

360 degrees

Therefore a quadrilateral has four exterior angles making the individual exterior angles

360 over 4=90 degrees

Hope this helps plz like and brainly :D

much would be appreciated <3