Determine all solutions of the given equation. Express your answer(s) using radian measure.

2 tan²x+sec² x - 2 = 0

a. x= 1/3 + k, where k is any integer
b. x= n/6+ nk, where k is any integer
c. x = 2n/3 + nk, where k is any integer
d. x = 5/6 + mk, where k is any integer
e. none of these

Answer:

1/6

Step-by-step explanation:

there is only one side in which there is 3 out of total six sides so 1/6

The correct answer is option (c) W = 0.

Given information :F = 6xi + 6yj + 6zk; P1(4, 3, 5), P2(5, 6, 7)The formula for work done by the conservative force is given by: W = U(P2) - U(P1)Where U(P) is the potential energy at point P. The force is conservative. Hence, work done is independent of path and is equal to the difference in potential energy between points 1 and 2.To find the potential energy U at any point, we use the formula: U(x, y, z) = - ∫F.dr where F is the force, and dr is the infinitesimal displacement vector.

To find the potential difference between two points, we integrate the formula: W = - ∫F.dr over a path between those two points, P1 and P2.Now we will find the potential energy at points 1 and 2.∴U(P1) = -∫F.drbetween the limits (4,3,5) and (5,6,7)Let us take the path from P1 to P2 along the straight line. Then the position vector of the path is:r = (5 - 4) i + (6 - 3) j + (7 - 5) k = i + 3j + 2k.dr = dx i + dy j + dz k= i dx + j dy + k dz = i dt + 3j dt + 2k dt = (i + 3j + 2k) dt∴∫F.dr= ∫6x i . (i + 3j + 2k) dt + ∫6y j . (i + 3j + 2k) dt + ∫6z k . (i + 3j + 2k) dt= ∫6x dt + 3 * 6y dt + 2 * 6z dt= (6x + 18y + 12z) |_P1^P2= (6 * 5 + 18 * 6 + 12 * 7) - (6 * 4 + 18 * 3 + 12 * 5)= 30 + 108 + 84 - 24 - 54 - 60= 84Thus, U(P2) - U(P1) = 0 - 84 = -84. Hence, work done = -(-84) = 84Option (d) W = 180 is incorrect as the value of work done is 84.

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Answer:

5

Step-by-step explanation:

Answer 424

Answer:

I need more info to answer that question.

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

The X is invisible and doesn't have a value causing the answer to still be 10.

The percent of the jerseys :

6 : 800 = 0,75%

The complete proofs with all the reasons and statements; have been enumerated below

The image showing the given triangle is missing and so i have attached it.

From the attached image, we can deduce that;

Statement 1; AB * BE = CB * BD

Reason 1; Given

Statement 2; CB/BE = AB/BD

Reason 2; Property of Cross Multiplication

Statement 3; ∠ABC ≅ ∠DBE

Reason 3; Vertical Angles

Statement 4; ΔABC ~ ΔDBE

Reason 4; SAS property of similarity

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Answer:

28[tex]\sqrt{6}[/tex]

Step-by-step explanation:

Using the rule of radicals

[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex]

[tex]\sqrt{96}[/tex]

= [tex]\sqrt{16(6)}[/tex]

= [tex]\sqrt{16}[/tex] × [tex]\sqrt{6}[/tex]

= 4[tex]\sqrt{6}[/tex]

Then

7[tex]\sqrt{96}[/tex]

= 7 × 4[tex]\sqrt{6}[/tex]

= 28[tex]\sqrt{6}[/tex]

If we double the length of the pendulum, the period of the pendulum will be approximately 1.4 times longer than it was before. This relationship between the length and period of a pendulum is very important, as it allows us to calculate the length of a pendulum needed to produce a desired period. This relationship is also used in many applications, such as clocks and metronomes.

The period of a pendulum is the time it takes to swing back and forth through one complete cycle. The period of a pendulum is affected by the length of the pendulum, the acceleration due to gravity, and the amplitude of the swing. If the length of a pendulum is doubled, the period of the pendulum will also double. The reason for this is that the period of a pendulum is directly proportional to the square root of its length.

This means that if the length of the pendulum is increased by a factor of 2, the period of the pendulum will increase by a factor of sqrt(2).

Mathematically, this can be expressed as: T = 2π * sqrt(L/g).

Where T is the period of the pendulum, L is the length of the pendulum, and g is the acceleration due to gravity.

If we double the length of the pendulum (L), the equation becomes T = 2π * sqrt(2L/g).

Taking the ratio of the new period to the original period, we get: T_new/T_old = sqrt(2).

Therefore if we double the length of the pendulum, the period of the pendulum will be approximately 1.4 times longer than it was before. This relationship between the length and period of a pendulum is very important, as it allows us to calculate the length of a pendulum needed to produce a desired period. This relationship is also used in many applications, such as clocks and metronomes.

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Answer:

$36

Step-by-step explanation:

Given :

Interest rate, r = 8% = 0.08

Principal, P = 150

Time, t = 3 years

Simple interest = (principal * rate * time)

Simple interest = (150 * 0.08 * 3)

Simple interest = $36

Answer:

A

Step-by-step explanation:

the variable is how many times the two will be multiplied, so 2 times 0 equals 0, there by making the problem. -7= - 7

Answer:

that will be A. 0

Step-by-step explanation:

first, i flip the equation

2x - 7= -7

next, i add both side by 7

2x−7+7=−7+7

2x=0

and finally, you divided by 2

2x/2 = 0/2

you get x = 0

Answer:

8 people can go

Step-by-step explanation:

Answer:

It would be C since a scale factor of 2 makes the original A coordinate of (3,3) times 2 therefore the new coordinates being (6,6)

Step-by-step explanation:

The statement "W is a subspace of P2" is true, as W satisfies the conditions for being a subspace: closure under addition and scalar multiplication, and containing the zero vector.

The statement "W is a subspace of P2" is true.

To show that W is a subspace, we need to verify the three conditions for subspace:

W is closed under addition: For any two polynomials p(x) = a + 2x + bx^2 and q(x) = c + 2x + dx^2 in W, their sum p(x) + q(x) = (a + c) + 4x + (b + d)x^2 is also in W. Therefore, W is closed under addition.

W is closed under scalar multiplication: For any polynomial p(x) = a + 2x + bx^2 in W and any scalar k, the scalar multiple kp(x) = ka + 2kx + kbx^2 is also in W. Therefore, W is closed under scalar multiplication.

W contains the zero vector: The zero polynomial 0 = 0 + 0x + 0x^2 is in W since a = b = 0. Therefore, W contains the zero vector.

Since W satisfies all three conditions for subspace, it is indeed a subspace of P2.

Hence, the statement "W is a subspace of P2" is true.

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Answer:

:-):-)

Step-by-step explanation:

1) p<1000

2)p>500

3)By combining the above two, we get: 500<p<1000

Andre will agree as he thinks that the no. of paper clips in the box is less than 1000. But lin will not as she thinks that the no. of clips is more than 500.

4)This time, they both will agree as the no. of paper clips is more than 500 but less than 1000.

Answer:

5 hours and 24 minutes

Step-by-step explanation:

sorry if im wrong

Answer:

5.4 hours

Step-by-step explanation:

I'm not 100 percent sure

hope this helped ;)

Answer:Ben will roll an even number about 560 times if the number cube is rolled 1,000 times.

Step-by-step explanation:

Nia's original class average was 89%. After increasing it by 3%, she now has a 92% in her math class.

1. Let's assume Nia's original class average was X.

2. She increased her class average by 3%, which can be represented as X + (3/100)X.

3. According to the question, X + (3/100)X = 92.

4. Simplifying the equation, we have (103/100)X = 92.

5. To find X, we divide both sides of the equation by (103/100): X = (92 * 100) / 103.

6. Calculating the value, X ≈ 89.32.

7. Therefore, Nia's original class average was approximately 89.32%.

8. After increasing it by 3%, her new class average is 89.32% + (3/100) * 89.32% ≈ 92%.

Note: The values have been rounded for simplicity.

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Answer:

d = 83

Step-by-step explanation:

Answer:

d=83°

Step-by-step explanation:

the sum of the inner angles is equal to 360°

so

127+67+d+d=360

194+2d=360

2d=166

d=83°

Answer:

first is some and second is all

Step-by-step explanation:

PLEASE GIVE BRAINLIEST!!!!!!!!!!

Answer:

1. All

2. Some

Step-by-step explanation:

I belive this awnser is correct

(a) Not of exponential order.

(b) Not of exponential order.

(c) Exponential order with c = 2.

(d) Not of exponential order.

(e) Not of exponential order.

To determine if a function is of exponential order, we need to check if there exist positive constants M and c such that |y(t)| ≤ M[tex]e^{ct}[/tex] for all t ≥ t₀, where t0 is some starting point.

Let's analyze each function:

(a) y(t) = 5t² + 24 + 1

This function is not of exponential order since it contains a quadratic term (t²) and does not satisfy the exponential order condition.

(b) y(t) = sin(3t)

The sine function is periodic and oscillates between -1 and 1. It is not bounded by an exponential function. Therefore, it is not of exponential order.

(c) y(t) = 4[tex]e^{2t}[/tex]

The exponential function [tex]e^{2t}[/tex] grows exponentially as t increases. The constant multiplier 4 does not affect the exponential growth. Therefore, this function is of exponential order with c = 2.

(d) y(t) = [tex]e^{t^{2} }[/tex]

The exponent t² grows faster than any exponential function with a constant base. Therefore, this function is not of exponential order.

(e) y(t) = cost [tex]e^{3t}[/tex]

The exponential function [tex]e^{3t}[/tex] grows exponentially as t increases. However, the cosine function oscillates between -1 and 1, which prevents the overall function from being bounded by an exponential function. Therefore, it is not of exponential order.

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Answer:

Explanation: Realize that 4x2−25 is a difference of squares. Differences of squares, such as a2−b2 , can be factored into (a+b)(a−b) . Since 4x2=(2x)2 and 25=(5)2 , we can say that 4x2−25=(2x+5)(2x−5)

Step-by-step explanation:

Answer:

(2x + 5)(2x - 5)

Step-by-step explanation:

a² - b² = (a + b)(a - b)

4x² = 2²x²= (2x)²

25= 5* 5 = 5²

4x² - 25 = (2x)² -  5²         {a= 2x  ; b = 5}

             = (2x + 5)(2x - 5)

the derivative of y with respect to x, or dy/dx, for the given equation is y' = (y - 12x) / (1 - x).

We start by differentiating both sides of the equation with respect to x.

For the left-hand side, the derivative of y + 3 with respect to x is simply dy/dx, or y'.

For the right-hand side, we need to apply the product and chain rules.

Differentiating xy with respect to x gives us x(dy/dx) + y.

Differentiating -6x² with respect to x gives us -12x.

Putting it all together, we have y' + 0 = x(dy/dx) + y - 12x.

Rearranging the equation, we get y' = (y - 12x) / (1 - x).

Therefore, the derivative of y with respect to x, or dy/dx, for the given equation is y' = (y - 12x) / (1 - x).

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Answer:

x= 21

y= 3

z= 21

Step-by-step explanation:

Let the center be O,

=> Triangle AOD is an Isosceles triangle so AO≅DO, "21 = x"

=> Line AC is divided in two equal parts by the center so if AO= 21 then

    7y = 21, and thus "y = 3"

=> BOC is also an Isosceles triangle so CO ≅ BO, if CO = 21 (7y → 7*3) then so will be BO. Therefore "z = 21"

The projection of the region D onto the xy-plane is an ellipse centered at the origin, with a major axis length of 4 and a minor axis length of 2.

To find the projection of the region D onto the xy-plane, we need to determine the intersection curve of the two paraboloids in the xyz-space. Setting the equations of the paraboloids equal to each other, we have:

3x^2 + y^2 = 16 - x^2.

Combining like terms, we get:

4x^2 + y^2 = 16.

This equation represents an ellipse in the xy-plane. To visualize the projection, let's rewrite the equation in terms of standard form:

(x^2)/4 + (y^2)/16 = 1.

Comparing this equation to the standard equation of an ellipse, (x^2)/(a^2) + (y^2)/(b^2) = 1, we can see that the major axis of the ellipse is along the y-axis, with a length of 4, and the minor axis is along the x-axis, with a length of 2.

Therefore, the projection of the region D onto the xy-plane is an ellipse centered at the origin, with a major axis length of 4 and a minor axis length of 2. The shape of the ellipse will have its major axis along the y-axis and its minor axis along the x-axis.

In summary, the projection of the region D onto the xy-plane is an ellipse centered at the origin, with a major axis length of 4 and a minor axis length of 2.

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The t-statistic of the slope coefficient is -19 is the answer.

Suppose a regression was run between y and one x variable.

The coefficient of the x variable (slope coefficient) was -0.76.

The associated standard error of the slope coefficient was 0.04, and p value of the slope coefficient was 0.

The t stat of the slope coefficient is -19.

To find the t-statistic value, divide the slope coefficient by the standard error.

This is given as t = slope / SE.

We have the values of the slope and the SE in the problem.

Substitute these values to get the t-statistic.t = -0.76 / 0.04 = -19

From this calculation, we can see that the t-statistic of the slope coefficient is -19.

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Answer:

Step-by-step explanation:

65,115,115

Answer:

[tex]\angle ABC[/tex] and [tex]\angle ADC[/tex] will change

[tex]\angle ABC[/tex] equal [tex]\angle ADC[/tex]

Step-by-step explanation:

Given

See attachment for complete question

Required

What happens when AC changes

(a) [tex]\angle ABC[/tex] and [tex]\angle ADC[/tex] are formed from points A and C. So, a change in AC will result to a change in the measures of [tex]\angle ABC[/tex] and [tex]\angle ADC[/tex].

(b) [tex]\angle ABC[/tex] and [tex]\angle ADC[/tex] are in the same segment, meaning that they will always have the same measure

Answer:

The value of X is 6.

Step-by-step explanation:

5 + 3 + 7 + 9 = 24

30 - 24 = 6

X = 6

The difference is 6.