Light A flashes every 8 seconds.
Light B flashes every 20 seconds.
Both lights flash at the same time.
Work out how long it will take for both lights to flash at the same time
again.
ASAP

Answer:

47% or47/100

Step-by-step explanation:

A table of values that represents a proportional relationship must have a constant rate and must pass through the origin

From the question, we have the following parameters that can be used in our computation:

A table that is has proportional relation

A table of values can be represented as

x    y

a    b

c   d

......

.....

For the table of values to be proportional, the following must be true

x    y

0    0

a    b

c   d

......

.....

Also, it must have a constant ratio

i.e. b/a = d/c

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The equation of the tangent plane to f(x, y) = x^2 - 2xy + 3y^2, with slopes 2 in the positive x direction and 2 in the positive y direction, is 2x + 4y - 8 = 0.

To locate the equation of the tangent airplane to the floor described with the aid of the feature f(x, y) = \(x^2 - 2xy + 3y^2\), we need to decide the gradient vector and consider it at a given point.

The gradient vector will grant the ordinary vector to the tangent plane, and by way of the use of the slope information, we can discover the equation of the plane.

Calculate the partial derivatives of the feature with recognize to x and y:

f_x = 2x - 2y

f_y = -2x + 6y

Set up a device of equations the use of the given slope information:

f_x = 2

f_y = 2

Solve the machine of equations to discover the factor where the slopes are satisfied:

2x - 2y = 2 --> x - y = 1 --> x = y + 1

-2x + 6y = 2 --> -x + 3y = 1 --> -x = 1 - 3y --> x = 3y - 1

Setting the two expressions for x equal to every other:

y + 1 = 3y - 1

2 = 2y

y = 1

Substitute y = 1 into both expression for x:

x = 1 + 1

x = 2

Therefore, the factor the place the slopes are comfy is (2, 1).

Evaluate the gradient vector at the factor (2, 1):

grad(f) = (f_x, f_y) = (2x - 2y, -2x + 6y)

= (2(2) - 2(1), -2(2) + 6(1))

= (2, 4)

The ordinary vector to the tangent airplane is the gradient vector (2, 4).

Using the point-normal structure of the equation for a plane, the equation of the tangent airplane is:

2(x - 2) + 4(y - 1) + d = 0

To decide the price of d, alternative the coordinates of the factor (2, 1):

2(2 - 2) + 4(1 - 1) + d = 0

0 + 0 + d = 0

d = 0

The equation of the tangent airplane is:

2(x - 2) + 4(y - 1) = 0

Simplifying the equation, we have:

2x - 4 + 4y - 4 = 0

2x + 4y - 8 = 8

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Answer:

x=45

Step-by-step explanation:

90+2x=4x

2x=4x-90

2x-4x=-90

-2x=-90

x= -90/-2

x=45

If we are told that ab=0, then we can infer that either a or b (or both) must be equal to 0.

This is because when the product of two numbers is 0, at least one of the numbers must be 0 according to the zero product property.

One of the most crucial concepts for pupils to understand in maths and science is the zero product property.

The greatest educators, mathematicians, and recognized scientists in the fields of physics and chemistry have worked with Vedantu to provide their insights on the subject.

Their suggestions helped us develop materials for your understanding that would make it simple for you to put these ideas into practice.

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Angle 0 is in the 1st quadrant, its reference angle is 0 radians, and it intersects the unit circle at the point (1, 0).

Define Angle ?

In mathematics, an angle is a geometric figure formed by two rays or lines that share a common endpoint, called the vertex.

a. The angle 0 is measured from the positive x-axis in a counterclockwise direction. In the Cartesian coordinate system, the positive x-axis lies on the right side of the coordinate plane. Since the angle 0 starts from this position, it falls within the 1st quadrant. The 1st quadrant is the region where both x and y coordinates are positive.

b. The reference angle is the positive acute angle between the terminal side of an angle and the x-axis. Since the angle 0 lies entirely on the positive x-axis, the terminal side coincides with the x-axis. In this case, the reference angle for 0 radians is 0 radians itself. The reference angle is always positive and its value is less than or equal to π/2 radians (90 degrees).

c. To find the point where 0 intersects the unit circle, we consider the trigonometric functions cosine and sine. The unit circle is a circle with a radius of 1 centered at the origin (0, 0) in the Cartesian coordinate system.

For angle 0, the cosine function gives the x-coordinate on the unit circle, and the sine function gives the y-coordinate. Since 0 lies on the positive x-axis, the x-coordinate is 1 (cos(0) = 1), and the y-coordinate is 0 (sin(0) = 0). Therefore, the point of intersection with the unit circle for angle 0 is (1, 0).

In summary, angle 0 is in the 1st quadrant, its reference angle is 0 radians, and it intersects the unit circle at the point (1, 0).

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The distance from the epicenter of the march 1964 earthquake to crescent city is 2600 kilometers and It took 400 seconds for the first p-wave to reach crescent city

In a seismic event like an earthquake, seismic waves propagate through the Earth at different speeds. The first type of seismic wave to reach a particular location is the primary wave, or P-wave. P-waves are compressional waves that travel faster than other seismic waves, such as S-waves or surface waves.

To calculate the time it took for the P-wave to reach Crescent City, we need to know the speed at which P-waves travel. On average, P-waves travel at a speed of about 6-7 kilometers per second in the Earth's crust. However, this speed can vary depending on the specific properties of the Earth's layers.

Using an average speed of 6.5 kilometers per second, we can calculate the time it took for the P-wave to travel a distance of 2600 kilometers:

Time = Distance / Speed = 2600 km / 6.5 km/s ≈ 400 seconds.

Therefore, it took approximately 400 seconds, or 6 minutes and 40 seconds, for the P-wave to reach Crescent City from the epicenter of the March 1964 earthquake.

It is important to note that the calculated time is an estimation based on average values, and the actual time may vary depending on the specific geological conditions along the propagation path of the P-wave.

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The modified Reynolds analogy, also known as the Chilton-Colburn analogy, is expressed mathematically as Nu = f * Re^m * Pr^n. It relates the convective heat transfer coefficient (h) to the skin friction coefficient (Cf) in fluid flow. This equation is widely used in heat transfer analysis and design applications involving forced convection.

The modified Reynolds analogy is a useful tool in heat transfer analysis, especially for situations involving forced convection. It provides a correlation between the heat transfer and fluid flow characteristics. The Nusselt number (Nu) represents the ratio of convective heat transfer to conductive heat transfer, while the Reynolds number (Re) characterizes the flow regime. The Prandtl number (Pr) relates the momentum diffusivity to the thermal diffusivity of the fluid.

The equation incorporates the friction factor (f) to account for the energy dissipation due to fluid flow. The values of the constants m and n depend on the flow conditions and geometry, and they are determined experimentally or by empirical correlations. The modified Reynolds analogy is widely used in engineering calculations and design of heat exchangers, cooling systems, and other applications involving heat transfer in fluid flow.

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Step-by-step explanation:

[(3x − 6) (4x² − 1)] – [(2x − 4) (4x² + 4x + 1)]

>[3(x-2) (2x+1)(2x-1)]-[2(x-2)(4x²+2x+2x+1)

>[3(x-2)(2x+1)(2x-1)]-[2(x-2){2x(2x+1)+1(2x+1)}]

> 3(x-2)(2x+1)(2x-1)-2(x-2)(2x+1)²

> (x-2)(2x+1) [3(2x-1)-2(2x+1)]

> (2x²-3x-2)(6x-3-4x-2)

> (2x²-3x-2)(2x-5).

hope this helps you.

The perimeter of the pool is (24 + 68 length) x 2 = 184 feet.184 feet is equal to 6.133 yards, so 6.133 yards of fencing is required to completely enclose the pool.

.

Let x = the width of the pool.

Then, the length of the pool = 2x + 20.

We can set up the equation:

2x(2x + 20) = 672

2x2 + 40x = 672

2x2 + 40x - 672 = 0

(2x - 24)(x + 28) = 0

x = 24, -28

Since x cannot be negative, x = 24.

The width of the pool is 24 feet and the length is 68 feet.

The perimeter of the pool is (24 + 68) x 2 = 184 feet.

184 feet is equal to 6.133 yards, so 6.133 yards of fencing is required to completely enclose the pool.

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Answer:

No.

Step-by-step explanation:

This only applies to solids like cubes and some prisms.

It does not apply to such solids are cylinders, pyramids, cones and triangular prisms.  It will apply to a prism whose cross-section is a rectangle.

Step-by-step explanation:

This an equation with two variables, x, and y.

The polynomial X-2 has the factor 2, the polynomial X^2-2 has the factors √2 and -√2, the polynomial X^2 + 4 has no real factors, and the polynomial X^4 - 8X^2 + 16 has the factors (X-2)^2 and (X+2)^2.

In the given table, we are provided with four polynomials: X-2, X^2-2, X^2 + 4, and X^4 - 8X^2 + 16. We need to match each polynomial with its corresponding factors.

The polynomial X-2 has a linear factor, which is 2. When we substitute 2 for X in the polynomial, we get 2-2 = 0, indicating that X-2 = 0 when X = 2. Therefore, 2 is a factor of X-2.

The polynomial X^2-2 is a quadratic polynomial. To find its factors, we set the polynomial equal to zero and solve for X. X^2-2 = 0 can be rewritten as X^2 = 2. Taking the square root of both sides, we have X = √2 and X = -√2. Thus, the factors of X^2-2 are √2 and -√2.

The polynomial X^2 + 4 is also a quadratic polynomial. However, it has no real factors. This can be determined by observing that the discriminant, which is the expression under the square root in the quadratic formula, is negative. Therefore, X^2 + 4 has no real factors.

The polynomial X^4 - 8X^2 + 16 is a quartic polynomial. We can factor it by recognizing that it is a perfect square trinomial. The expression (X-2)^2 yields X^4 - 4X^2 + 4 as its expansion, and (X+2)^2 yields X^4 + 4X^2 + 4 as its expansion. Thus, the factors of X^4 - 8X^2 + 16 are (X-2)^2 and (X+2)^2.

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Answer:The solution is in the attached file

Step-by-step explanation:

Answer:

\(2.630007\) × \(10^{11}\)

Step-by-step explanation:

263,000,700,000 ÷ 10^11 = 2.630007

we have only one outcome that is neither positive nor negative, then the statement is false.

What is square root?

A value known as the square root of a number is one that, when multiplied by itself, yields the original number. An alternative to square rooting a number is to use it. Therefore, the concepts of squares and square roots are connected. The original number is equal to the square root of any integer, which is equivalent to a number.

Let's assume that m is an integer that is positive, such that (m.m) = (m2) = m.

This seems to be true because:

-2*-2 = 2*2 = 4

So √4 = 2 and -2

But particularly the square root of zero is:

√0 = 0

So here we have only one outcome that is neither positive nor negative, then the statement is false.

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The given equation is:\(3y" + 18y' + 102y = f(t)\)where f(t) is the applied force.

Let's solve the given differential equation: Solve for\($y(t) = \frac{10}{123} [1 - e^{-3t} \cos \sqrt{11}t]$b) For y(0) = 0,$y(t) = \frac{10}{123} [1 - e^{-3t} \cos \sqrt{11}t]$For y(0) = 10,Let $y'(0) = v_0$We know that,$y'(t) = -3y(t) - 6y'(t) - 34y''(t) + \frac{1}{3}f(t)$By initial conditions,$y'(0) = -3y(0) - 6y'(0)$i.e.,$v_0 = -18$$\) homogenous part: We know that:\($m^2 + 6m + 34 = 0$\)is the characteristic equation of the given differential equation.

The roots of the characteristic equation are $m = -3 ± i \sqrt{11}$

Therefore the homogenous solution is\(:$y_h(t) = e^{-3t} (c_1 \cos \sqrt{11}t + c_2 \sin \sqrt{11}t)$\)

\(Solve for the particular part: Now, let's solve for the particular part, for \($t≥ 0$ and $f(t) = 10$.Therefore, $y_p(t) = A$.So, we can write the equation as:$$3A + 18A + 102A = 10$$$$\Rightarrow 123A = 10$$$$\Rightarrow A = \frac{10}{123}$$\)\pi\)

Therefore the particular solution is:$y_p(t) = \frac{10}{123}$Complete solution:Therefore the complete solution \(is\(:$y(t) = y_h(t) + y_p(t)$$$\\)Rightarrow\(y(t) = e^{-3t} (c_1 \cos \sqrt{11}t + c_2 \sin \sqrt{11}t) + \frac{10}{123}$$For y(0) = y'(0) = 0, c1 = $\frac{10}{123}$ and c2 = 0.a)\) Now the solution becomes,$y(t) = \frac{10}{123} [1 - e^{-3t} \cos \sqrt{11}t]$b) For y(0) = 0,$y(t) = \frac{10}{123} [1 - e^{-3t} \cos \sqrt{11}t]$For y(0) = 10,Let $y'(0) = v_0$\)We know that,$y'(t) = -3y(t) - 6y'(t) - 34y''(t) + \frac{1}{3}f(t)$By initial conditions,$y'(0) = -3y(0) - 6y'(0)$i.e.,$v_0 = -18$$\Rightarrow y(t) = \frac{10}{123} [1 - e^{-3t} \cos \sqrt{11}t] - \frac{6}{\sqrt{11}} e^{-3t} \sin \sqrt{11}t + \frac{18}{\sqrt{11}} e^{-3t} \cos \sqrt{11}t$

\(know that,$y'(t) = -3y(t) - 6y'(t) - 34y''(t) + \frac{1}{3}f(t)$By initial conditions,$y'(0) = -3y(0) - 6y'(0)$i.e.,$v_0 = -18$$\Rightarrow y(t) = \frac{10}{123} [1 - e^{-3t} \cos \sqrt{11}t] - \frac{6}{\sqrt{11}} e^{-3t} \sin \sqrt{11}t + \frac{18}{\sqrt{11}} e^{-3t} \cos \sqrt{11}t$\)

The plot of y(t) for all cases are as follows: (a) The plot of y(t) for y(0) = y'(0) = 0 is as follows: (b) The plot of y(t) for y(0) = 0 and y(0) = 10 is as follows: The nonzero initial velocity causes a phase shift in the graphs, which means that the graph has moved horizontally. Therefore, there is a change in the starting point of the curve.

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Answer:

just a few feet (within 1 to 10)

Step-by-step explanation:

You cannot enter zero, since the city could be inundated with water, so include something between 1 or at most 10 feet.

Answer:

556 ft²

Step-by-step explanation:

The given information is,

→ Length (l) = 11 ft

→ Breadth (b) = 10 ft

→ Height (h) = 8 ft

Formula we use,

→ 2(lb + bh + lh)

The surface area of cuboid will be,

→ 2(lb + bh + lh)

→ 2{(11 × 10) + (10 × 8) + (11 × 8)}

→ 2(110 + 80 + 88)

→ 2 × 278

→ [ 556 ft² ]

Therefore, the TSA is 556 ft².

Answer:

3x^2 + x - 6 = 0

Step-by-step explanation:

x - 6 = -3x^2

step 1: add 3x^2 to both sides

x - 6 + 3x^2 = 0

step 2: put the terms in order from greatest degree (exponent) to least.

3x^2 + x - 6 = 0

done! :)

Choice D is not the correct answer. Point L is equally distant from J and K. In other words, JL = LK. If two friends lived at points J and K, then point L would be a good meeting spot as they would travel the same distance. Point N has the same properties as point L does (with regard to being equally distant from J and K). It is not correct to say that LJ = JN.

The answer is actually choice C. Segments JL and KL need to be constructed using a straightedge.

Otherwise, these segments are not going to be shown and you cannot use them. A segment is simply a straight line between two endpoints. Two triangles form (triangle JNL and KNL) to help with the proof, so it's very beneficial to draw in these segments. It might help to use a different color pen, or lightly draw the segment using a faint pencil mark to erase later.

Answer:

y = 18 + 12x

Step-by-step explanation:

To find the total cost Mr. Montenegro pays in dollars when x shirts are ordered, we can use the equation y = 18 + 12x, where y is the total cost in dollars and x is the number of shirts ordered. This equation takes into account the delivery fee of $18 and the cost of each shirt, which is $12. Therefore, we can use the equation y = 18 + 12x to find the total cost Mr. Montenegro pays when he orders x shirts.

Answer:

B 39$

Step-by-step explanation:

Answer:

neither

Step-by-step explanation:

Answer:

error= 0.1/2, 0.05

4.8 + 0.05 = 4.85

6.3 + 0.05 = 6.35

4.85 x 6.35 = 30.7975 cm (when rounded, gives 30.80 cm).

Step-by-step explanation:

We have been given a circle. We are asked to find the measure of arc MN.

We know that the measure of all arcs in a circle is equal to 360 degrees. SO we can set an equation as:

\(\widehat{MN}+\widehat{NO}+\widehat{OL}+\widehat{LM}=360^{\circ}\)

Upon substituting our given values, we will get:

\(\widehat{MN}+110^{\circ}+130^{\circ}+54^{\circ}=360^{\circ}\)

\(\widehat{MN}+294^{\circ}=360^{\circ}\)

\(\widehat{MN}+294^{\circ}-294^{\circ}=360^{\circ}-294^{\circ}\)

\(\widehat{MN}=66^{\circ}\)

Therefore, measure of arc MN is 66 degrees and option 'c' is the correct choice.

Answer:

Step-by-step explanation:

Answer:

13.41

Step-by-step explanation:

Hope it helps!

Answer:

6\(\sqrt{5}\)

Step-by-step explanation:

Using the rule of radicals

\(\sqrt{a}\) × \(\sqrt{b}\) ⇔ \(\sqrt{ab}\)

Simplifying the radicals

\(\sqrt{20}\)

= \(\sqrt{4(5)}\)

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

\(\sqrt{80}\)

= \(\sqrt{16(5)}\)

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

Then

\(\sqrt{20}\) + \(\sqrt{80}\)

= 2\(\sqrt{5}\) + 4\(\sqrt{5}\)

= 6\(\sqrt{5}\)

Answer:

24%

Step-by-step explanation:

25 - 19 = 6

25 = 100%

2.5 = 10%

1.25 = 5%

0.25 = 1%

5 = 20%

1 = 4%

6 = 24%

Hope this helps :)

Answer:

24% Decrease

Step-by-step explanation:

Start by looking at the formula for percent change.

\(\frac{(V^{2} -V^{1})}{V^{1} }\) x 100 = ?

Plug in the numbers, V1 being 25 and V2 being 19.

\(\frac{19-25}{25}\) x 100 = ?

19 - 25 = -6

Put -6 as the new numerator.

\(\frac{-6}{25}\) x 100 = ?

Divide and get the decimal version of the fraction.

-0.24 x 100 = ?

Multiply and get your final answer of 24% decrease.