Which statements are true? Select all that apply.


A. m∠WZX = 34°
B. m∠WXY = 123°
C. m∠XYZ = 46°
D. m∠WPZ = 90°

To find this solution, we first use the method of undetermined coefficients to find two particular solutions, y1, and y2. Then, we add these two particular solutions to get the general solution.

The general solutions to the three differential equations you gave me:

i. y" + 6y' + 13y = e-3x sin(2x)

The general solution to this equation is:

y = C1e-3x cos(2x) + C2e-3x sin(2x) - 2x e-3x sin(2x)

where C1 and C2 are arbitrary constants.

To find y1, we guess that the solution is of the form Ae-3x cos(2x). We then substitute this into the differential equation and solve for A. We get A = 1. To find y2, we guess that the solution is of the form Be-3x sin(2x). We then substitute this into the differential equation and solve for B. We get B = -2.Finally, we add y1 and y2 to get the general solution:

y = C1e-3x cos(2x) + C2e-3x sin(2x) - 2x e-3x sin(2x)

ii. y(x2y" + y) = (xy')2

The general solution to this equation is:

y = (C1 + C2x) e-x/2

where C1 and C2 are arbitrary constants.

To find this solution, we first use the method of separation of variables to separate the variables in the equation. This gives us:

y(dy/dx) = x2y" + y

We can then integrate both sides of the equation:

y^2/2 = x^2y' + y^2/2 + C

We can then solve for y:

y = (C1 + C2x) e-x/2

iii. xy' + 2y = -x3y2 cos x

The general solution to this equation is:

y = C1 e-x/2 (1 + x^2)

where C1 is an arbitrary constant.

To find this solution, we first use the method of separation of variables to separate the variables in the equation. This gives us:

y(dy/dx) = -x^3y^2 cos x

We can then integrate both sides of the equation:

y^2/2 = -x^3y^3/3 + C

We can then solve for y:

y = C1 e-x/2 (1 + x^2)

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Answer:

9/2 -9/2

Step-by-step explanation:

Hope this helps! ;-)

Im pretty sure its $32.4

Step-by-step explanation:

An example of a geometric formula that contains pi(π) is the formula for the circumference of a circle, which is

C = 2πr. This formula is used to calculate the distance around a circle.

A geometric formula is a mathematical equation that describes a relationship between geometric figures or their properties.

Geometric formulas are used to calculate the area, perimeter, volume, surface area, and other properties of shapes such as circles, triangles, rectangles, spheres, cubes, and cylinders. For example, the formula for the area of a triangle is

A = 1/2 b×h, where b is the base of the triangle and h is its height.

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Step-by-step explanation:

please mark me as a brainlist...

Equation f(x) = ax² + bx + c reveals its extreme value without needing to be altered.

The extreme value of this equation has a minimum or maximum at the point (h, k).

Explanation: The extreme value of a quadratic function is also known as the vertex of the parabola. The vertex is the highest or lowest point on the parabola, depending on the coefficient of the x² term. For a quadratic function of the form f(x) = ax² + bx + c, the vertex can be found using the formula: h = -b/2a and k = f(h) = a(h²) + b(h) + c. The value of h represents the x-coordinate of the vertex, while the value of k represents the y-coordinate of the vertex. The sign of the coefficient of the x² term determines whether the vertex is a minimum or maximum. If a > 0, the parabola opens upwards and the vertex is a minimum. If a < 0, the parabola opens downwards and the vertex is a maximum. Therefore, equation f(x) = ax² + bx + c reveals its extreme value without needing to be altered. The extreme value of this equation has a minimum or maximum at the point (h, k).

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Answer:

D

Step-by-step explanation:

Answer:

D

Bro this is the answer!

First, we see that 6 represents tenths. If it represents 1/10 it must be 6 divided by 10. Doing so, 6 must represent now the hundredths of the three last numbers. The answers must be C,D and E.

Increasing the confidence level would increase the margin of error of a confidence interval, all other things remaining the same. This is because a higher confidence level corresponds to a wider interval so larger range of possible values.

In order to maintain the same level of precision, a wider interval requires a larger margin of error to account for the increased variability in the data.  For example, a 95% confidence interval would have a smaller interval width than a 99% confidence interval, as the latter requires a larger range of possible values to be included in the interval.

As a result, increasing the confidence level would increase the precision and accuracy of the estimate but at the cost of a larger margin of error.

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Answer:

When A is positive there is a minimum vertex.

Step-by-step explanation:

When a parabola is positive the opening goes upwards. When a parabola is negative it goes downwards. The negative sign on the A coefficient means that you reflect your equation across the x-axis

Answer:

The first one.

Step-by-step explanation:

Answer:

right i can't see the puestion

Step-by-step explanation:

Answer:

bro ik

Step-by-step explanation:

Answer:

30

Step-by-step explanation:

the street and the diameter of the bike are not measured in the same units. We have to convert them to the same units

1 feet = 12 inches

157 x 12 = 1884

circumference of a circle = 2nr

2 x 3.14 x 10 = 62.8 in

Number of revolutions = 1884/62.8 = 30

We evaluate the integral using the Fundamental theorem of Calculus, by using and antiderivative of the funtion in the integrand;

An antiderivative of x^3 - 2 x is = 1/4 x^4 - x^2

So we evaluate this antiderivative at the two limits of integration:

At x = 1 the antiderivative becomes: 1/4 (1) - 1 = - 3/4

At x = - 1/2 the antiderivative becomes: 1/4 (-1/2)^4 - (-1/2)^2 = - 15/64

Now we subtract the evaluation at the upper limit minus the evaluation at the lower limit:

- 3/4 - (-15/64) = - 33/64

Allow me to show you the actual area we have calculated in a graph for the integration:

The curve in blue is the original function you provided : f(x) = x^3 - 2x

You can see that there is an area above the x axis that has been integrated and that gives as a result a positive number.

The area below the x axis is the part of the integral that provides the negative part which as you see is dominant in this calculation, therefore resulting in a negative final result.

Please, make sure you type -33/64 in the box provided.

Answer:

  3x -y = -6

Step-by-step explanation:

You want the equation of the line with intercepts (0, 6) and (-2, 0).

The equation of the line with x-intercept 'a' and y-intercept 'b' is ...

  x/a +y/b = 1

For the given intercepts, the equation is ...

  x/(-2) +y/6 = 1

In standard form, we want the leading coefficient positive and the integer coefficients mutually prime. We can get there by multiplying by -6:

  3x -y = -6

__

Additional comment

You can get slope-intercept form by solving for y, or you can recognize that ...

  slope = rise/run = -(y-intercept)/(x-intercept) = -6/-2 = 3

Since you already know the y-intercept, you can write the slope-intercept equation as ...

  y = 3x +6

There are perhaps a dozen or more forms of the equation for a line. The "intercept form" equation is one of the more useful ones.

To estimate the number of subscribers as a single digit times an integer power of 10, we can round the given number to the nearest power of 10.

The given number of subscribers is 77,000.

Rounding 77,000 to the nearest power of 10 (which is 10^4 or 10,000), we get:

77,000 ≈ 8 × 10,000

So, an estimate for the number of subscribers as a single digit times an integer power of 10 would be 80,000.

Answer:

x = 0.6

Step-by-step explanation:

We use tangent because the given numbers are opposite and adjacent from x

So, tangent (x) = opposite/adjacent

tan(x) = 8.78/12

\(tan^{-1}(\frac{8.78}{12}) = x\)

x = 0.631664

Round to nearest tenth:

x ~ 0.6

The particular solution of the differential equation y'' + 2y' + y = 5e^(-t) using the method of variation of parameters is \(y_p(t) = -e^{(-t)} + 5te^{(-t).\)

To find the particular solution, we first find the complementary solution by solving the characteristic equation r² + 2r + 1 = 0, which has a double root of -1. Therefore, the complementary solution is \(y_c(t) = c_1e^{(-t)} + c_2te^{(-t)\).

Next, we use the method of variation of parameters to find a particular solution of the form \(y_p(t) = u_1(t)e^{(-t)} + u_2(t)te^{(-t)\). We then substitute this particular solution into the differential equation and solve for the coefficients u1(t) and u2(t).

After simplifying, we get u1'(t) = 0 and u2'(t) = 5e^(-t). Integrating u2'(t) gives \(u_2(t) = -5e^{(-t)} + C\), where C is a constant of integration.

To determine the value of C, we substitute \(y_p(t)\) into the differential equation and simplify, which gives C = 0.

Therefore, the particular solution is\(y_p(t) = -e^{(-t)} + 5te^{(-t)\).

The general solution is \(y(t) = y_c(t) + y_p(t) = c_1e^{(-t)} + c_2te^{(-t)} - e^{(-t)} + 5te^{(-t).\)

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The area of the acute triangle can be found by the formula: area of acute triangle = (1/2) × b × h.

According to Pythagoras theorem the triangle is termed as acutely angled if the square of its longest side is less than the sum of the squares of two other smaller sides. Let a, b, and c are the length of sides of a triangle, where side "a" is the longest, then the given triangle is acutely angled if and only if a^2 < b^2 + c^2.

The area of the acute triangle can be calculated by the formula:

         area of acute triangle = (1/2) × b × h

         b = base, and

         h = height

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If the raft travels the distance between ports a and b after 30 hours and the motorboat travels the distance in 6 hours. After the departure the two boats will after 5 hours 4 minutes.

Given that,

After leaving the port,

Raft travels the distance between a and b ports = 30 hours

Motorboats travels the distance between a and b ports = 6 hours

The triangle formed by their tracks and the line joining their current positions in a right angled triangle.

According to the Pythagoras Theorem,

    a² + b² = c²

⇒ (30)²+ (6)² = c²

⇒ 900 + 36 = c²

⇒ 936 = c²

⇒ c = √936

⇒ c = 30.59

Rounding up 30.59 in 30.6.

Therefore, the boats will the two meet by 30 hours and 6 minutes after they leave the port.

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The fuction f(x) = x², as represented in the graph. we now need to fond the equation of function G(x) which is same as function f(x) but slightly displaced to the left side of x - axis.

As we know, when the displacement is along negative x - axis (let it be c), the function changes as :

\(\qquad\displaystyle \tt \dashrightarrow \: g(x) = f(x + c)\)

\(\qquad\displaystyle \tt \dashrightarrow \: g(x) = (x + c) {}^{2} \)

Now, lets check it out to fond the value of c ~

put value of x and y from any point on the graph of g(x)

[ let it be (-3, 0) ]

\(\qquad\displaystyle \tt \dashrightarrow \: 0 =( - 3 + c) {}^{2} \)

\(\qquad\displaystyle \tt \dashrightarrow \: 0 = ( - 3 + {c}^{} )\)

\(\qquad\displaystyle \tt \dashrightarrow \: c = 0 + 3\)

\(\qquad\displaystyle \tt \dashrightarrow \: c = 3\)

now, plug in the value of of c in the required equation and its done ~

\(\qquad\displaystyle \tt \dashrightarrow \: g(x) = (x + 3) {}^{2} \)

Answer: 2 + 3/8 is 2 3/8, 19/8, or 2.375

Step-by-step explanation:

Answer:

184 square inches

Step-by-step explanation:

Bases: 4 in × 5 in × 2 bases = 40 in²

Smaller pair of lateral faces: 4 in × 8 in × 2 faces = 64 in²

Larger pair of lateral faces: 5 in × 8 in × 2 faces = 80 in²

40+64+80=184 in²

The surface area of the box is 184 in² or 184 square inches.

Answer: B) 184 Square Inches

Step-by-step explanation:

To find the surface area of the box we have to use the formula, the formula is  A = 2wl + 2lh + 2hw....

To find the front and the back we have to multiply the width and the length...

8 * 5 = 40 + 40 = 80

To find the right and the left we have to multiply the length and the height...

8 * 4 = 32 + 32 = 64

To find the bottom and the top we have to multiply the height and the width...

4 * 5 = 20 + 20 = 40

40 + 64 + 80 = 184

The surface is 184 square inches, I hope this helps!

Answer:

5/3

Step-by-step explanation:

\(slope = \frac{change \: in \: y}{change \: in \: x} \)

A survey found that individuals that use a lot of illegal drugs are also much more likely to take a lot of multivitamins. These findings demonstrate that there is a positive correlation between the use of illegal drugs and the consumption of multivitamins.

The statement indicates that there is a positive correlation between the use of illegal drugs and the consumption of multivitamins based on the findings of a survey. A positive correlation means that as the use of illegal drugs increases, the consumption of multivitamins also tends to increase. There could be several reasons for this observed correlation:

Health-conscious behavior: Individuals who are concerned about their health and well-being may take multivitamins to compensate for any potential nutrient deficiencies caused by drug use.

Lifestyle factors: People who engage in risky behaviors, such as using illegal drugs, might also adopt other behaviors like taking multivitamins to counterbalance the negative effects of their lifestyle choices.

Awareness and information: It is possible that individuals who use illegal drugs are more aware of the importance of taking care of their health and are actively seeking ways to mitigate potential health risks associated with drug use, leading them to consume multivitamins.

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Answer:

scalene right

Step-by-step explanation:

because all sides are not equal to another so its scalene and it has a right angle

The logical equivalence (p ∨ ~q) ∧ (~p ∨ ~q) ≡ ~q.

1. Start with the given expression: (p ∨ ~q) ∧ (~p ∨ ~q).
2. Apply the distributive law: (p ∧ ~p) ∨ (~q ∧ ~q).
3. Apply the law of contradiction: False ∨ (~q ∧ ~q).
4. Simplify: ~q ∧ ~q.
5. Apply the law of idempotence: ~q.

In this derivation, we used the distributive law to expand the expression and then applied the law of contradiction to simplify it further. Finally, we used the law of idempotence to arrive at the final expression ~q, which proves the logical equivalence.

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