calculate the capacity in liters of a tin 20m by 15m by 10m.​

The value of dy/dx is -cotθ, d^2y/dx^2 is -6cosec³θ, slope is -cotθ, concavity is -6cosec³θ.

Parametric Equations Point x = 6cosθ, y = 6sinθ and θ = π/4

We have to determine the value of dy/dx.

We can define dy/dx as;

dy/dx = (dy/dθ)/(dx/dθ)

We first define dy/dθ and dx/dθ.

x = 6cosθ                             y = 6sinθ

dx/dθ = -6sinθ                     dy/dθ = 6cosθ

Now put the value

dy/dx = 6cosθ/(-6sinθ)

dy/dx = -cotθ

Now we have to determine the value of d²y/dx².

d²y/dx² = d/dx(dy/dx)

We can write it as

d²y/dx² = \(\frac{\frac{d}{d\theta}(\frac{dy}{dx})}{dx/d\theta}\)

We first determine the value of d/dθ(dy/dx)

d/dθ(dy/dx) = d/dθ(-cotθ)

d/dθ(dy/dx) = cosec²θ

Now put the value

d²y/dx² = cosec²θ/(-6sinθ)

d²y/dx² = -6cosec³θ

Now we have to determine the slope.

Slope = dy/dx

Slope = -cotθ

Now we have to determine the concavity.

Concavity = d²y/dx²

Concavity = -6cosec³θ

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To solve this problem, we need to use vector addition to find the resultant velocity of Julia.

Let's assume that the east direction is the positive x-axis and the south direction is the negative y-axis.

The velocity of Julia in still water is 8 km/hr in the positive x-axis direction.

The velocity of the river is 3 km/hr in the negative y-axis direction.

To find the magnitude and direction of Julia's velocity, we need to find the resultant velocity vector, which is the vector sum of her velocity in still water and the velocity of the river.

Using the Pythagorean theorem, the magnitude of the resultant velocity can be calculated as:

|V| = √(Vx² + Vy²)

where Vx is the x-component of the resultant velocity and is equal to Julia's velocity in still water, and Vy is the y-component of the resultant velocity and is equal to the velocity of the river.

Vx = 8 km/hr

Vy = -3 km/hr

|V| = √(8² + (-3)²) = √(64 + 9) = √73 km/hr

The direction of the resultant velocity can be calculated as:

θ = tan⁻¹(Vy / Vx)

θ = tan⁻¹(-3 / 8) = -20.56°

The negative sign indicates that the resultant velocity vector makes an angle of 20.56° below the positive x-axis (east direction).

Therefore, the magnitude of Julia's velocity is approximately 8.54 km/hr, and the direction of her velocity is 20.56° below the positive x-axis (east direction).

The size of angle DAB in the quadrilateral is 48°.

The sum of the interior angles of a quadrilateral is 360°. We can say:

\(\angle \text{A} +\angle\text{B} + \angle\text{C} + \angle\text{D} = 360^\circ\)

\(\angle \text{A} +38^\circ + \angle\text{C} + 226^\circ = 360^\circ\)

\(\angle \text{A} + \angle\text{C} + 264^\circ = 360^\circ\)

\(\angle \text{A} + \angle\text{C} = 360^\circ- 264^\circ\)

\(\angle \text{A} + \angle\text{C} = 96\)

Since angles DAB and BCD are the same size. This implies ∠A  = ∠C. Thus:

\(\angle\text{A} + \angle\text{A} = 96\)

\(2\angle\text{A} = 96\)

\(\angle\text{A} = \dfrac{96}{2}\)

\(\angle\text{A} = 48^\circ\)

Therefore, the size of angle DAB is 48°.

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Answer:

y = x + 1

Step-by-step explanation:

Parallel lines have same slope.

y = x - 1

Compare with the equation of line in slope y-intercept form: y = mx +b

Here, m is the slope and b is the y-intercept.

m =1

Now, the equation is,

         y = x + b

The required line passes through (-3 ,-2). Substitute in the above equation and find y-intercept,

        -2 = -3 + b

  -2 + 3 = b

         \(\boxed{b= 1}\)

    Equation of line in slope-intercept form:

                  \(\boxed{\bf y = x + 1}\)      

The equation is :

Solution:

If two lines are parallel to each other, then their slopes are equal. The slope of y = x - 1 is 1. Hence, the slope of the line that is parallel to that line is 1.

We shouldn't forget about a point on the line : (-3, -2).

I plug that into a point-slope which is :

\(\sf{y-y_1=m(x-x_1)}\)

Slope is 1 so

\(\sf{y-y_1=1(x-x_1)}\)

Simplify

\(\sf{y-y_1=x-x_1}\)

Now I plug in the other numbers.

-3 and -2 are x and y, respectively.

\(\sf{y-(-2)=x-(-3)}\)

Simplify

\(\sf{y+2=x+3}\)

We're almost there, the objective is to have an equation in y = mx + b form.

So now I subtract 2 from each side

\(\sf{y=x+1}\)

Answer:

y = 4\(\sqrt{5}\) , ? = 10

Step-by-step explanation:

using Pythagoras' identity on the smallest right triangle

x² = 4² + 2² = 16 + 4 = 20 ( take square root of both sides )

x = \(\sqrt{20}\) = \(\sqrt{4(5)}\) = \(\sqrt{4}\) × \(\sqrt{5}\) = 2\(\sqrt{5}\)

using Pythagoras' identity on the middle right triangle

y² = 8² + 4² = 64 + 16 = 80 ( take square root of both sides )

y = \(\sqrt{80}\) = \(\sqrt{16(5)}\) = \(\sqrt{16}\) × \(\sqrt{5}\) = 4\(\sqrt{5}\)

using Pythagoras' identity on the largest right triangle

?² = x² + y² = (2\(\sqrt{5}\) )² + (4\(\sqrt{5}\) )² = 20 + 80 = 100

Take square root of both sides

? = \(\sqrt{100}\) = 10

Answer:

b= = - 7/4 or -1.75

Step-by-step explanation:

14b +21 -2b=0

12b +21=0

12b= -21

b= -21/12

b= - 7/4 or -1.75

Answer:

i dont know what you neccesarily want but here are two answers b=-7/4 or -1 3/4 other answer is 12b+21

Step-by-step explanation:

first, you have to set this question equal to 0.

7(2b+3)-2b=0

now you have to distribute the 7 to everything inside the parentheses.

14b+21-2b=0

combine like terms

12b+21=0

you can stop here and take this answer if this is the one you want

now subtract each side by 21

12b=-21

divide each side by 12

b=-21/12

simplify

b=-7/4

hope this helps! have a nice day :)

Answer: 8.06 Inches

The area of the circle is 28.26 ft². 3. The diameter of the circle is 8.06 inches.

Answer:

I hope this helps!

Answer:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

y-2*x-(6)=0

STEP

1

:

Equation of a Straight Line

1.1 Solve y-2x-6 = 0

Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).

"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.

Answer:

Los números son 23 y 35.

Step-by-step explanation:

Q: The sum of two numbers is 58. If one of the numbers is 12 more than the other number, what are the numbers?

Set the numbers as x and y. Using the given information, we have two equations:

x+y=58

x=y+12

Solving using substitution, we have:

y+y+12=58 -> y=23

Substituting, x=23+12=35

The numbers are 23 and 35.

Answer:

$1.79 per gallon, I believe.

Step-by-step explanation:

Answer:

False

Step-by-step explanation:

1. The inverse function should have c(n) isolated
2. When finding the inverse of a function, the variables c(n) and n are interchanged (and then c(n) is isolated).
It would look like this --->c(n)=50+4n--->n=50+4(c(n)) ---> c(n)=(n-50)/4

The probability of rolling a die and getting a 2, then a 5, is 1/36.

To determine the probability of rolling a die and getting a 2, then a 5, we need to multiply the probabilities of each event happening.

First, let's consider the probability of rolling a die and getting a 2. Since there are six equally likely outcomes when rolling a fair six-sided die (numbers 1 to 6), the probability of rolling a 2 is 1/6.

Now, let's consider the probability of rolling a die and getting a 5. Again, there are six equally likely outcomes, so the probability of rolling a 5 is also 1/6.

To find the probability of both events happening, we multiply the probabilities:

Probability of rolling a 2 and then a 5 = (1/6) * (1/6) = 1/36.

Therefore, the probability of rolling a die and getting a 2, then a 5, is 1/36.

It's important to note that each roll of the die is an independent event, meaning that the outcome of one roll does not affect the outcome of the next roll. Therefore, the probability of rolling a 2 and then a 5 remains constant at 1/36 regardless of previous rolls or the order in which they occur.

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The volume of the shape is 490cm³

A prism is a solid shape that is bound on all its sides by plane faces. prism is named after the shape of these bases.

The base of this prism is rectangular. The volume of a prism is expressed as;

V = base area × height

base area = 7 × 10 = 70cm²

height = 7cm

the volume of the shape = 70× 7 = 490cm²

therefore the volume of the shape is 490cm³.

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a) The dot product of v and -v is -1.

b) The dot product of v + w and v – w is 2v.w

c) The dot product of v – 2w and v + 2w is 4||w||^2 - 4v.w

(a) For any unit vector v, the dot product of v and -v can be found as follows:

v · -v = ||v||||-v||cos(θ) = ||v||||v||cos(180°) = -||v||^2 = -1, where ||v|| represents the magnitude of the vector v and θ is the angle between the vectors.

Since v and -v are unit vectors, their magnitudes are equal to 1, so ||v||^2 = 1. Thus, the dot product of v and -v is -1.

(b) For any unit vectors v and w, the dot product of v + w and v – w can be found as follows:

(v + w) · (v – w) = ||v + w||||v – w||cos(θ) = (||v||||v|| + 2v · w + ||w||||w||)cos(θ) = 2v · w

where θ is the angle between the vectors v + w and v – w, and v · w is the dot product of v and w.

(c) For any unit vectors v and w, the dot product of v – 2w and v + 2w can be found as follows:

(v – 2w) · (v + 2w) = ||v – 2w||||v + 2w||cos(θ) = (||v||||v|| + 4||w||||w|| - 4v · w)cos(θ) = 4||w||^2 - 4v · w

where θ is the angle between the vectors v – 2w and v + 2w, and v · w is the dot product of v and w.

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Answer: its protein channels

Step-by-step explanation:

Answer:

100

Step-by-step explanation:

Rs500-Rs400=Rs100.

Answer:

#3 1.92599941856

Step-by-step explanation:

P Q P V Q P ^ Q P -> Q -P -Q -P V -Q -P -> Q -P -> -Q P <-> Q

T T T T T F F F F F T    T

F T T F F T T T T T F    F

P F T F F T T T T T F     F

-P T T F F T T T T T F     F

-Q T T T T F T F F F T     T

-P V -Q T T F F T T T T T F

-P -> Q T T F F T T T T T F

-P -> -Q T T F F T T T T T F

P <-> Q T T T T F T T T T F

Here is a more detailed explanation of how I filled out the table:

P | Q : This column is simply the truth value of P and Q. If P and Q are both true, then the entry in this column is T. If P is true and Q is false, then the entry in this column is F. If P is false and Q is true, then the entry in this column is F. And if P and Q are both false, then the entry in this column is T.

P V Q : This column is the truth value of P or Q. If P is true, then the entry in this column is T. If Q is true, then the entry in this column is T. And if P and Q are both false, then the entry in this column is F.

P ^ Q : This column is the truth value of P and Q. If P and Q are both true, then the entry in this column is T. And if P and Q are both false, then the entry in this column is F.

P -> Q : This column is the truth value of P implies Q. If P is true and Q is false, then the entry in this column is F. And if P is false or Q is true, then the entry in this column is T.

-P : This column is the negation of P. If P is true, then the entry in this column is F. And if P is false, then the entry in this column is T.

-Q : This column is the negation of Q. If Q is true, then the entry in this column is F. And if Q is false, then the entry in this column is T.

-P V -Q : This column is the truth value of not P or not Q. If P and Q are both true, then the entry in this column is F. If P and Q are both false, then the entry in this column is T. And if P or Q is true, then the entry in this column is T.

-P -> Q : This column is the truth value of not P implies Q. If P is true and Q is false, then the entry in this column is T. And if P is false or Q is true, then the entry in this column is F.

-P -> -Q : This column is the truth value of not P implies not Q. If P and Q are both true, then the entry in this column is T. If P is false or Q is false, then the entry in this column is T. And if P is true and Q is true, then the entry in this column is F.

P <-> Q : This column is the truth value of P if and only if Q. If P and Q are both true or P and Q are both false, then the entry in this column is T. And if P and Q have different truth values, then the entry in this column is F.

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The radius of the gear should be approximately 2.8644 inches.It is important to note that when making calculations involving units, we need to make sure that all units are consistent and convert them when necessary. In this case, we converted the answer from feet to inches to match the given unit.

To find the radius of the gear that will pull a chain at 60 ft/min when rotating at 40 rev/min, we can use the formula:

chain speed = 2 x pi x radius x rotational speed

where pi is a mathematical constant approximately equal to 3.14.

We know that the chain speed is 60 ft/min and the rotational speed is 40 rev/min, so we can substitute those values into the formula:

60 = 2 x 3.14 x radius x 40

Simplifying the equation, we get:

radius = 60 / (2 x 3.14 x 40)

radius = 0.2387 ft

To convert feet to inches, we can multiply the answer by 12:

radius = 0.2387 x 12 = 2.8644 inches.

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Answer:

your answer will be 6.64

Step-by-step explanation:

hope this helps have a nice day :)

Answer:

19.13

Step-by-step explanation:

You take 342.98 and you minus 323.85

Answer:

  $18,527.74

Step-by-step explanation:

Each year, the fund amount is multiplied by 1+8% = 1.08. After 10 years, it will have been multiplied by that factor 10 times, 1.08^10. For some principal P deposited now, we want ...

  P(1.08^10) = $40,000

  P = $40,000/1.08^10 ≈ $18,527.74