If sinø =2/3 and second<0, find cosø and tanø

1 milligram = 0.001 gram

x milligrams = 6 grams

By crossmultiplying, it becomes

0.001 * x = 6 * 1

0.001x = 6

x = 6/0.001

x = 6000

The mass in milligrams is 6000 milligrams

Answer:

See below

Step-by-step explanation:

Given sequence is:

\(7,\: \frac{28}{3},\:\frac{112}{9},\:\frac{448}{27},\:\frac{1792}{81}\:\)

Here,

First term \(a=7\)

Common ratio \(r=\frac{28}{7\times 3}=\frac{4}{3}\)

Formula for nth term of geometric sequence is given as:

\(a(k) =ar^{k-1}\)

Plugging the values of a and r in the above formula, we find:

\(\huge{\purple{a(k) =(7)\bigg(\frac{4}{3}\bigg)^{k-1}}}\)

This is the required explicit formula for the given geometric sequence.

The only triple integral that has all constant bounds when written in cylindrical coordinates is the second one, i.e., ∭x2 + y2 dV.

In cylindrical coordinates, a triple integral is given by ∭f(r, θ, z) r dz dr dθ.

To have constant bounds, the limits of integration must not contain any of the variables r, θ, or z. Let's see which of the given triple integrals satisfy this condition.

The given triple integrals are:

a) ∭xyz dVb) ∭x2 + y2 dVc) ∭(2 + cos θ) r dVd) ∭r3 sin2 θ cos θ dV

To determine which of these integrals have all constant bounds, we must express them in cylindrical coordinates.

1) For the first integral, we have xyz = (rcosθ)(rsinθ)(z) = r2cosθsinθz.

Hence, ∭xyz dV = ∫[0,2π]∫[0,R]∫[0,H]r2cosθsinθzdzdrdθ.

The limits of integration depend on all three variables r, θ, and z.

So, this integral doesn't have all constant bounds.

2) The second integral is given by ∭x2 + y2 dV.

In cylindrical coordinates, x2 + y2 = r2, so the integral becomes ∫[0,2π]∫[0,R]∫[0,H]r2 dzdrdθ.

The limits of integration don't contain any of the variables r, θ, or z.

Hence, this integral has all constant bounds.

3) For the third integral, we have (2 + cos θ) r = 2r + rcosθ. Hence, ∭(2 + cos θ) r dV = ∫[0,2π]∫[0,R]∫[0,H](2r + rcosθ)r dzdrdθ.

The limits of integration depend on all three variables r, θ, and z. So, this integral doesn't have all constant bounds.

4) The fourth integral is given by ∭r3 sin2θ cosθ dV. In cylindrical coordinates, sinθ = z/r, so sin2θ = z2/r2.

Also, cosθ doesn't depend on r or z. Hence, the integral becomes ∫[0,2π]∫[0,R]∫[0,H]r3z2cosθ dzdrdθ.

The limits of integration depend on all three variables r, θ, and z. So, this integral doesn't have all constant bounds.

Therefore, the only triple integral that has all constant bounds when written in cylindrical coordinates is the second one, i.e., ∭x2 + y2 dV.

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The shape of the graph changes qualitatively at k = ± 2 and

\(k=\sqrt{(2)\).

The given function is f(x,y) = y-x²+y²+kxy.

The critical points of the function are found by taking the partial derivatives and equating them to zero:

∂f/∂x = -2x + ky = 0

y = 2x/k

∂f/∂y = 2y + kx = 0

y = -kx/2

Substituting y from the first equation into the second equation gives

x = k²x/4, so k² = 4 and k = ± 2.

Therefore, the critical points are (0,0), (2,4), and (-2,4)

We will now examine the critical points to see when the shape of the graph changes qualitatively.

There are two cases to consider:

Case 1: (0,0)At (0,0), the Hessian matrix is

H = [∂²f/∂x² ∂²f/∂x∂y;∂²f/∂y∂x ∂²f/∂y²]

=[ -2 0;0 2].

The determinant of the Hessian matrix is -4, which is negative.

Therefore, (0,0) is a saddle point and the graph changes qualitatively as k increases for all values of k.

Case 2: (±2,4)At (2,4) and (-2,4), the Hessian matrix is

H = [∂²f/∂x² ∂²f/∂x∂y;∂²f/∂y∂x ∂²f/∂y²]

=[ -2k 2k;2k 2].

The determinant of the Hessian matrix is 4k²+8, which is positive when k is greater than √(2).

Therefore, the critical points (2,4) and (-2,4) are local minima when

k > √(2).

Thus, the shape of the graph changes qualitatively at k = ± 2 and

k = √(2).

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The probability of rain tomorrow is the same regardless of whether it has rained in the past two days or not. Therefore, we cannot use the given information to make a prediction about the weather tomorrow.

In example 4.4, we are given a situation where it has not rained in the past two days. The question asks for the probability of rain tomorrow. This type of question falls under the category of conditional probability. In conditional probability, we find the probability of an event given that another event has already occurred.
To solve this problem, we can use Bayes' theorem. Bayes' theorem states that the probability of an event A given that event B has occurred is equal to the probability of event B given that event A has occurred multiplied by the probability of event A divided by the probability of event B.
Let us define the events in this problem as follows:
A = It will rain tomorrow
B = It has not rained in the past two days
Using the given information, we know that P(B) = 0.75 (since there are four possible outcomes: rain yesterday, rain day before yesterday, rain both days, no rain both days, and we are given that the latter has occurred). We need to find P(A|B).
To find P(A|B), we need to find P(B|A), which is the probability that it has not rained in the past two days given that it will rain tomorrow. Since we do not have any information about the relationship between these two events, we can assume that they are independent.
Therefore, P(B|A) = P(B) = 0.75
Now, we can use Bayes' theorem to find P(A|B):
P(A|B) = P(B|A) * P(A) / P(B)
P(A|B) = 0.75 * P(A) / 0.75
P(A|B) = P(A)
This means that the probability of rain tomorrow is the same regardless of whether it has rained in the past two days or not. Therefore, we cannot use the given information to make a prediction about the weather tomorrow.

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Answer:

119 is the value of x when y = 7

Step-by-step explanation:

Since y varies inversely with x, we can use the following equation to model this:

y = k/x, where

Step 1:  Find k by plugging in values:

Before we can find the value of x when y = k, we'll first need to find k, the constant of proportionality.  We can find k by plugging in 49 for y and 17 for x:

Plugging in the values in the inverse variation equation gives us:

49 = k/17

Solve for k by multiplying both sides by 17:

(49 = k / 17) * 17

833 = k

Thus, the constant of proportionality (k) is 833.

Step 2:  Find x when y = k by plugging in 7 for y and 833 for k in the inverse variation equation:

Plugging in the values in the inverse variation gives us:

7 = 833/x

Multiplying both sides by x gives us:

(7 = 833/x) * x

7x = 833

Dividing both sides by 7 gives us:

(7x = 833) / 7

x = 119

Thus, 119 is the value of x when y = 7.

The solution is Option A.

The translation of the center of circle is given by ( x , y ) ⟶ ( x - 15 , y + 1 )

A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle

The circumference of circle = 2πr

The area of the circle = πr²

where r is the radius of the circle

The standard form of a circle is

( x - h )² + ( y - k )² = r²,

where r is the radius of the circle and (h,k) is the center of the circle.

Given data ,

Let the equation for the circle A be represented as

( x - 7 )² + ( y - 1 )² = 16

Now , the equation is of the form ( x - h )² + ( y - k )² = r²

So , the radius of the circle is 4 and the center of the circle is ( 7 , 1 )

Let the equation for the circle A be represented as

( x + 8 )² + ( y - 2 )² = 16

Now , the equation is of the form ( x - h )² + ( y - k )² = r²

So , the radius of the circle is 4 and the center of the circle is ( -8 , 2 )

So , the translation of circle A to B is given by

( 7 , 1 ) to ( -8 , 2 )

So , the x coordinate is translated by 15 units to left and the y coordinate is translated by 1 unit up

Hence , the translation is given by ( x , y ) ⟶ ( x - 15 , y + 1 )

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To find the flow along the curve r(t) = ti + (t^2)j + k between t = 0 and t = 4 in the direction of increasing t, we need to evaluate the line integral of the velocity field F along the curve. The line integral is given by:

∫ F · dr = ∫ (3xyi + 6yj + 5k) · (dx/dt)i + (dy/dt)j + (dz/dt)k

We can calculate the differentials dx, dy, and dz by taking the derivatives of the components of r(t) with respect to t:

dx/dt = 1, dy/dt = 2t, dz/dt = 0

Substituting these values, we have:

∫ F · dr = ∫ (3xy)(1) + (6y)(2t) + (5)(0) dt

           = ∫ 3xy + 12yt dt

Since we are integrating with respect to t, we can treat x and y as constants. Integrating each term separately, we get:

∫ 3xy dt = 3xyt

∫ 12yt dt = 6yt^2

Finally, we evaluate the integral from t = 0 to t = 4:

∫ F · dr = [3xyt] from 0 to 4 + [6yt^2] from 0 to 4

           = 3xy(4) + 6y(4^2) - (3xy(0) + 6y(0^2))

           = 12xy + 96y

So, the flow along the given curve in the direction of increasing t is 12xy + 96y.

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The  inequalities that represents the possible total weights w (in pounds) of the vehicle and its contents are;

A) x ≤ 4000

B) x ≤ 60000

C) x ≤ 80000

Let the maximum weight be represented with x;

In inequality, maximum means less than or equal to i.e. ≤

(a) For 2 axles, we are given that the maximum weight is 40000.

Therefore, we can write the inequality as:

x ≤ 4000

(b) For 3 axles, we are given that the maximum weight is 60000.

Therefore, we can write the inequality as:

x ≤ 60000

(c) For 4 axles, we are told that the maximum weight is 80000.

Thus, the inequality is:

x ≤ 80000

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Answer:

35 in binary is 100011.

Step-by-step explanation:

To find decimal to binary equivalent, divide 35 successively by 2 until the quotient becomes 0.

Answer:

1.22

Step-by-step explanation:

I hope this helps!

Answer:

The value of 'g' in the equation is -1.22.

Step-by-step explanation:

Solving this problem entails of isolating the variable 'g.'  To start this process, we must use the subtraction property of equality. We will subtract 1.3 from both sides of the equation.

1.3 - 5g = 7.4

1.3 - 1.3 - 5g = 7.4 - 1.3

-5g = 6.1

You can see that we have gotten one step closer to getting the variable alone. Now we will use the division property of equality. To do this, divide both sides of the equation by negative five.

-5g = 6.1

-5g / -5 = 6.1 / -5

g = -1.22

The variable has finally been isolated. The value of 'g' is -1.22.

The area of the computer monitor display is approximately 0.103 square meters, with three significant figures.

The area of the monitor display in square meters is found by converting the measurements from inches to meters and then calculate the area.

The conversion factor from inches to meters is 0.0254 meters per inch.

Width in meters = 14.60 inches * 0.0254 meters/inch

Height in meters = 10.95 inches * 0.0254 meters/inch

Area = Width in meters * Height in meters

We calculate the area:

Width in meters = 14.60 inches * 0.0254 meters/inch = 0.37084 meters

Height in meters = 10.95 inches * 0.0254 meters/inch = 0.27813 meters

Area = 0.37084 meters * 0.27813 meters = 0.1030881672 square meters

Now, we determine the number of significant figures.

The measurements provided have four significant figures (14.60 and 10.95). However, in the final answer, we should retain the least number of significant figures from the original measurements, which is three (10.95). Therefore, the answer should have three significant figures.

Thus, the area of the monitor display in square meters is approximately 0.103 square meters, with three significant figures.

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Yes , rotating is  a congruence transformation.

What is a congruence transformation?

A transformation that changes the position of the figure while not dynamical its size or form is termed a congruity transformation.

Main body:

A congruity transformation is that the movement or locating of a form specified it produces a form that is congruent to the initial.

Translations, reflections, and rotations are the three types of congruence transformations. That is, the pre-image and the image are always congruent.

Hence ,rotating is  a congruence transformation.

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This statement is true that the In c 11 you cannot use a range-based for loop to modify the contents of an array unless you declare the range variable as a reference variable.

According to the statement

we have given that the one statement and we have to tell that the those statement is true or false after analyzing it.

So,

In C++ 11 is  a programming language which is used to write the coding. And in this language you cannot use a range-based for loop to modify the contents of an array unless you declare the range variable as a reference variable.

Because in the coding it is not possible that the you can make loop without declare the random variable in the loop.

Due to this reasons without declare the variable it is not possible.

So, This statement is true that the In c 11 you cannot use a range-based for loop to modify the contents of an array unless you declare the range variable as a reference variable.

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Answer:

179

Step-by-step explanation:

180- 2=189 this is because 2 of the students the 180 received a or b

The given question is incorrect. The correct question is:

Of the 180 students in a college course, 1/4 of the students earned an A for the course, 1/3 of the students earned a B for the course, and the rest of the students earned a C for the course. How many of the students earned a C for the course?

A. 75

B. 90

C. 105

D. 120

E. 135

The number of students who earned a C for the course can be represented by the fraction of 5/12 of the total number of students and is equal to 75. Hence, option A is the right choice.

A fraction in general means a part of. We represent a part of the whole using fractions. The total number of parts is taken as the denominator, while the parts used are taken as the numerator.

Fraction = Numerator/Denominator.

We are given that there are 180 students in a college course. 1/4 of them get an A for the course while 1/3 get a B. Rest of the students to get a C for the course.

We need to find the number of students who get a C.

Let the fraction of students getting a C be x.

We know that a whole fraction is always = 1.

∴ Fraction of students getting an A + Fraction of students getting a B + Fraction of students getting a C = Whole fraction.

or, 1/4 + 1/3 + x = 1

or, x = 1 - 1/4 - 1/3 = (12 - 3 - 4)/12 = 5/12

∴ 5/12 of the students get a C for the course.

Number of Students who get a C for the course = 5/12 of 180 = 5*15 = 75.

∴ The number of students who earned a C for the course can be represented by the fraction of 5/12 of the total number of students and is equal to 75. Hence, option A is the right choice.

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Answer:

False

Step-by-step explanation:

4/8 equals to 1/2 but 6/10 equals to 3/5. Correct would be if it was 5/10

The derivative of the first equation with respect to x is: y' = (4\(x^3\) - 1) * \(32x/(16x^2 - 9)^2 + 12x^2 * In(16x^2 - 9)\)

The derivative of the second equation with respect to x is: \(y' = -6x^3 * CSc(x^3 + 1)\)

To find the derivative of the first equation:

For the first equation, using the product rule and the chain rule, we get:
\(y' = [(4x^3 - 1) * d/dx(In(16x^2 - 9))] + [(In(16x^2 - 9)) * d/dx(4x^3 - 1)]\)
\(y' = [(4x^3 - 1) * 1/(16x^2 - 9) * d/dx(16x^2 - 9)] + [(In(16x^2 - 9)) * 12x^2]\)
\(y' = [(4x^3 - 1) * 32x/(16x^2 - 9)^2] + [12x^2 * In(16x^2 - 9)]\)
Therefore, the derivative of the first equation with respect to x is:
\(y' = (4x^3 - 1) * 32x/(16x^2 - 9)^2 + 12x^2 * In(16x^2 - 9)\)

To find the derivative of the second  equation:
For the second equation, using the chain rule, we get:
\(y' = d/dx(1 - CSc(x^3 + 1)) * d/dx(1 + x^2)\)

\(y' = [-CSc(x^3 + 1) * d/dx(x^3 + 1)] * 2x\)
\(y' = [-CSc(x^3 + 1) * 3x^2] * 2x\)
\(y' = -6x^3 * CSc(x^3 + 1)\)
Therefore, the derivative of the second equation with respect to x is:
y' = -6x^3 * CSc(\(x^3\) + 1)

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Answer:

i dont think u can on a chrome book

Newton's method, the left-hand zero is approximately -6.905, and the right-hand zero is approximately x2 = 3.923.

Newton's method to estimate the two zeros of the function \(3x - x^2 + 8\), starting with x0 = 1 for the left-hand zero and

x0 = 3 for the right-hand zero.

Newton's method formula is: x_n+1 = x_n - f(x_n) / f'(x_n)

First, we need to find the derivative of the function:

\(f(x) = 3x - x^2 + 8\)

f'(x) = 3 - 2x

Now, let's find x1 and x2 for the left-hand zero (starting with x0 = 1):

x1 = x0 - f(x0) / f'(x0) = 1 - (3(1) -\(1^2\) + 8) / (3 - 2(1)) = 1 - 10 / 1 = -9

x2 = x1 - f(x1) / f'(x1) = -9 - (3(-9) - \((-9)^2\) + 8) / (3 - 2(-9)) = -9 - (-44) / 21 = -9 + 44/21 = -9 + 2.095 = -6.905

For the left-hand zero, x2 = -6.905.

Now, let's find x1 and x2 for the right-hand zero (starting with x0 = 3):

x1 = x0 - f(x0) / f'(x0) = 3 - (3(3) - \(3^2\) + 8) / (3 - 2(3)) = 3 - 2 / -3 = 3 + 2/3 = 3.667

x2 = x1 - f(x1) / f'(x1) = 3.667 - (3(3.667) - \((3.667)^2\) + 8) / (3 - 2(3.667)) = 3.667 - 1.111 / -4.333 = 3.667 + 0.256 = 3.923

For the right-hand zero, x2 = 3.923.

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We can use the radical rules to simplify the product 3(4x2). To start, we simplify 4 to its square root, which equals 2. Next, we employ the power property of radicals, which asserts that (a,m) = (a(m/2)), to simplify the cube root (x2) by using it. In this instance, (x2) = x.

We now get 3 * 2 * x, which simplifies to 6x when the simpler terms are combined.The result is that the product 3(4x2) has the simplest form (6x).We can dissect the constituent parts and use the radical-simulation principles to simplify the product 3(4x2).In the beginning, we may reduce the square root of 4 to 2: 3(2x2).Then, since it contains a square (2) and a cube root (), we can reduce them as follows:

3 * 2 * x^(²/³)Taking the square root before the cube root is shown by the exponent 2/3. We may calculate the exponent by reducing it to: 3 * 2 * x(2/3)The terms are then combined when we multiply the coefficients: 6 * x(2/3)As a result, 6x(2/3) is the product of 3(4x2) in its simplest form.

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Answer:

D

Step-by-step explanation:

In 2 hours they wash 8 cars total so...

8

16

24

The extra time is 15 mins for 2 cars

Answer:  The middle school has 652 students.

Step-by-step explanation:  Divide the number of student in the high school by 4.5

\(\frac{2934}{4.5}\) = 652

Answer:

576

Step-by-step explanation:

5 + 3 = 8

5 - 2 = 3

8 x 3 = 24

24 to the second power is 576

Answer:

27x+5

Step-by-step explanation:

5+3x(5-2)^2

5+3x(3)^2

5+3x*9

5+27x

27x+5

The equations of the tangent plane and the normal line to the surface defined by 2(x - 3)^2 + (y - 9)^2 + (z - 7)^2 = 10 at the point (4, 11, 9) are:

a) The equation of the tangent plane is 4(x - 3) + 2(y - 9) + 2(z - 7) = 0.

b) The equation of the normal line is x(t) = 4 + 2t, y(t) = 11 - t, and z(t) = 9 + t.

To find the equation of the tangent plane at the given point, we first need to take the partial derivatives of the surface equation with respect to x, y, and z.

∂/∂x(2(x - 3)^2 + (y - 9)^2 + (z - 7)^2) = 4(x - 3)

∂/∂y(2(x - 3)^2 + (y - 9)^2 + (z - 7)^2) = 2(y - 9)

∂/∂z(2(x - 3)^2 + (y - 9)^2 + (z - 7)^2) = 2(z - 7)

Then, we evaluate these partial derivatives at the point (4, 11, 9):

∂/∂x(2(x - 3)^2 + (y - 9)^2 + (z - 7)^2)|(4,11,9) = 4(4 - 3) = 4

∂/∂y(2(x - 3)^2 + (y - 9)^2 + (z - 7)^2)|(4,11,9) = 2(11 - 9) = 2

∂/∂z(2(x - 3)^2 + (y - 9)^2 + (z - 7)^2)|_(4,11,9) = 2(9 - 7) = 4

Using these values, we can write the equation of the tangent plane in point-normal form:

4(x - 4) + 2(y - 11) + 4(z - 9) = 0

Simplifying, we get:

4(x - 3) + 2(y - 9) + 2(z - 7) = 0

To find the equation of the normal line, we use the fact that the direction of the normal vector to the surface is given by the gradient of the surface equation at the point of interest. So, the direction vector of the normal line is:

∇f(4, 11, 9) = ⟨4, 2, 4⟩

We can use this vector and the point (4, 11, 9) to write the equation of the normal line in vector form:

r(t) = ⟨4, 11, 9⟩ + t⟨4, 2, 4⟩

Expanding this, we get:

x(t) = 4 + 4t

y(t) = 11 + 2t

z(t) = 9 + 4t

Alternatively, we can write the equation of the normal line in parametric form:

x(t) = 4 + 2t

y(t) = 11 - t

z(t) = 9 + t

Both of these forms give the same line, but the parametric form is simpler and easier.

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Answer:

20÷8=2,5 12÷2,5=4,8 8÷2,5=3,2 10÷2,5=4 5÷2,5=2 therefore 4,8+3,2+4+2=14

Answer:

The place value of 4 in 12.47 is the tenths place.

Step-by-step explanation:

One place to the right of the decimal point is the tenths place. Two places to the right of the decimal is the hundredths place. Hope this helps.

The place value of the 4 in the decimal number 12.47 will be the tenth place.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

In a decimal number, if we move from right to left before the decimal, then the places of the number are given as,

Ones, Tens, Hundreds, and so on.

In a decimal number, if we move from left to right after the decimal, then the places of the number are given as,

Tenths, Hundredths, and so on.

The place value of the 4 in the decimal number 12.47 will be the tenth place.

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