factor the polynomial:

2x⁵-50x³​

Answer:

  2. 26.2 m

  3. 117.2 cm

Step-by-step explanation:

You want the perimeters of two figures involving that are a composite of parts of circles and parts of rectangles.

The circumference of a circle is given by ...

  C = πd . . . . . where d is the diameter

The length of the semicircle of diameter 12.6 m will be ...

  1/2C = 1/2(π)(12.6 m) = 6.3π m ≈ 19.8 m

The two lighted sides of the rectangle have a total length of ...

  3.2 m + 3.2 m = 6.4 m

The length of the light string is the sum of these values:

  19.8 m + 6.4 m = 26.2 m

The length of the string of lights is about 26.2 meters.

The perimeter of the figure is the sum of four quarter-circles of radius 11.4 cm, and 4 straight edges of length 11.4 cm.

Four quarter-circles total one full circle in length, so we can use the formula for the circumference of a circle:

  C = 2πr

  C = 2π·(11.4 cm) = 22.8π cm ≈ 71.6 cm

The four straight sides total ...

  4 × 11.4 cm = 45.6 cm

The perimeter of the figure is the sum of the lengths of the curved sides and the straight sides:

  71.6 cm + 45.6 cm = 117.2 cm

The design has a perimeter of about 117.2 cm.

__

Additional comment

The bottom 12.6 m edge in the figure of problem 2 is part of the perimeter of the shape, but is not included in the length of the light string.

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Answer:

7 inches

Step-by-step explanation: Every 1 inch = 50 miles.  So every 50 miles of tunnel is 1 inch in a scale drawing.  350miles/50 miles=7 inches.

The scale drawing is 7 inches.

Answer:

7 inches

Step-by-step explanation:

Answer:

x equals 2 cm

Answer:

here

Step-by-step explanation:

here

Answer:

F an amazing result.

Step-by-step explanation:

I'm sure I didn't do this the way it was intended, but I think I got it right.

First of all, we have to agree that CAB is marked as a right angle. If you do not agree, leave a note.

Step One

Find the length of AC

BC = 16

AB = 10

AC^2 = BC^2 - AB^2

AC^2 = 16^2 - 10^2

AC^2 = 256 - 100

AC^2 = 156

AC = SQRT(156)

AC = SQRT(4*13 * 3)

AC = 2 SQRT(13)

Step Two

Find the height (AD)

There are two ways to find the area of the large triangle ABC

Area = 1/2 * 16 * AD          and

Area = 1/2 AC * 10            The two legs.

Since these areas must be equal, equate them. You are looking for AD

16 * AD = 2*sqrt(39) * 10   Divide by 16

AD =  20* sqrt(39)/16

AD = 5 * sqrt(39) / 4

Step 3

Find x or DB

DB^2 = 10^2 - [(5 *sqrt(39)/4]^2

DB^2 = 100 - 25*39/16

DB^2 = 100 - 60.9375

DB^2 = 39.0625

DB = SQRT(39.0625)

DB = 6 1/4

6 1/4 is the same thing as 25/6 which is F

Answer:

F. 25/4

Step-by-step explanation:

just took the quiz

Answer:

4.5 /7

Step-by-step explanation:

15/25 =x/7

Cross multiply

25×x=15×7

25x=105

Divide both sides by 25

x=4•2

Thus, we have rewritten sin (x - pi/6) in terms of sin (x) and cos (x) as: sin (x - pi/6) = (sqrt(3)/2) sin x - (1/2) cos x

To rewrite sin (x - pi/6) in terms of sin (x) and cos (x), we can use the trigonometric identity for the sine of the difference between two angles:
sin (a - b) = sin a cos b - cos a sin b
In this case, we can let a = x and b = pi/6, so we have:
sin (x - pi/6) = sin x cos (pi/6) - cos x sin (pi/6)
We know that cos (pi/6) = √(3)/2 and sin (pi/6) = 1/2, so we can substitute those values into the equation:
sin (x - pi/6) = sin x (√(3)/2) - cos x (1/2)
Thus, we have rewritten sin (x - pi/6) in terms of sin (x) and cos (x) as:
sin (x - pi/6) = (√(3)/2) sin x - (1/2) cos x

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Answer:

C

Step-by-step explanation:

lets start with the first equation

33*33^7

Since they are not in parentheses, the only one going the power of 7 is the second 33. The first 33 will just have n exponent of one, so you add those together and get 33^8

The next equation is explained like this

(33*33)^7

Since this equation is in parentheses, first you will combine the 33:

(33^2)^7

Then, you will follow power to a power rule, and multiply the 2 and 7 to get this answer:

33^14

Then, find the awnser that matches.

Answer:

The answer is B because if you take the line of y=-x (which you can look up on desmos if you don't know what y=-x looks like) and reflect over that line you can see that when the dot reflects over the line y=-x it goes to points (0,2)

Step-by-step explanation:

Answer:

114

Step-by-step explanation:

9(4)=36

9(4)=36

14(3)=42

36+36+42=114

Hope this helped!!

The Wronskian of the two solutions is constant and independent of t.

To find the Wronskian of two solutions of the given differential equation without solving the equation, we'll use the properties of the Wronskian and the formula associated with it.

Let y₁(t) and y₂(t) be the two solutions of the differential equation. The Wronskian of these solutions, denoted as W(t), is given by the determinant:

W(t) = | y₁(t) y₂(t) | | y₁'(t) y₂'(t) |

Now, differentiate the determinant with respect to t:

W'(t) = | y₁'(t) y₂'(t) | | y₁''(t) y₂''(t) |

Next, substitute the given differential equation into the second row of the Wronskian:

W'(t) = | y₁'(t) y₂'(t) | | (t-6)y₁(t) (t-6)y₂(t) |

Now, simplify the expression:

W'(t) = y₁'(t)y₂'(t) + (t-6)y₁(t)y₂(t) - (t-6)y₁(t)y₂(t) = y₁'(t)y₂'(t)

Therefore, we have W'(t) = y₁'(t)y₂'(t).

Since W(t) = W(t₀), where t₀ is any point in the interval of interest, we can conclude that:

W(t) = W(t₀) = y₁'(t₀)y₂'(t₀) = c, where c is a constant.

Therefore, the Wronskian of the two solutions is constant and independent of t.

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Answer:

x ≈ 94.4

Step-by-step explanation:

Using the tangent ratio in the right triangle

tan58° = \(\frac{LM}{KL}\) = \(\frac{x}{59}\) ( multiply both sides by 59 )

59 × tan58° = x , then

x ≈ 94.4 ( to the nearest tenth )

The required probabilities are:-

a) P(8 of the players numbers are drawn) = 1.3×10⁻⁸

b) P(7 of the players number are drawn) = 3.33×10⁻⁶

c) P(at least 6 of the players number were drawn) = 1.84×10⁻⁴

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.

Given that, In a state lottery, a player must choose 8 of the numbers from 1 to 40. The lottery commission then performs an experiment that selects 8 of these 40 numbers.

Players has 8 combinations of numbers from 1-40. The outcome S contains all the combinations of 8 out of 40

a) P(8 of the players numbers are drawn) = 1/40/8 = 1.3×10⁻⁸

b) Number of ways of drawing 78 selected numbers from 1-40 = 8×(40-7)8×32

P(7 of the players number are drawn) = 8×32/40 =3.33×10⁻⁶

c) P(at least 6 players numbers are drawn)= 32/2×(8/6) ways to draw.

P(at least 6 players numbers are drawn) = P(all 8 chosen are drawn) + P(7 players numbers drawn) + P(6 chosen are drawn) = 1+8 x32/40/8 +[8\6 ×32/2]

P(at least 6 players numbers are drawn) = 1.84×10⁻⁴

Hence, the required probabilities are:-

a) P(8 of the players numbers are drawn) = 1.3×10⁻⁸

b) P(7 of the players number are drawn) = 3.33×10⁻⁶

c) P(at least 6 of the players number were drawn) = 1.84×10⁻⁴

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Answer:

x = 15

Step-by-step explanation:

Since the triangles are similar then the ratios of corresponding sides are equal, that is

BC/DC = EC/AC , substitute values

3x×5/32 - 5x-5/56 ( cross- multiply )

56(3x - 5) = 32(5x - 5) ← distribute and simplify both sides

168x - 280 = 160x - 160 ( subtract 160x from both sides )

8x - 280 = - 160 ( add 280 to both sides )

8x = 120 ( divide both sides by 8 )

x = 15

Answer:

1⁷/15

Step-by-step explanation:

2¾(3⅜-1½)

using the rule of BODMAS

change the fractions in the bracket into improper fraction

2¾(27/8-3/2)

find LCM of the fractions in the bracket

2¾(27-12)/8

2¾(15/8)

convert the other mixed fraction to an improper fraction

11/8(15/8)= 5.15625~ 5.2

Step-by-step explanation:

this is totally simple.

the formula for the area of a circle (as you can find with any search on the internet in seconds) :

A = pi×r²

r is the radius.

and once you understand even the most basics of a circle, you know that the radius is half of the diameter.

so, in our case, r = 6/2 = 3 m

the area of the circle is therefore

pi×r² = pi×3² = pi×9 m²

Class 4 gloves, when working with voltage levels up to 20000 volts to mitigate the risk of electric shock and ensure personal safety.

These gloves provide a high level of insulation and are intended for use in situations involving high-voltage electrical work. They offer significant protection against electric shocks and are typically used by professionals who work with high-voltage equipment or in environments where there are substantial electrical hazards.

Class 4 gloves undergo rigorous testing and meet specific safety standards to ensure their effectiveness in providing insulation and protection against high voltages. It is crucial to follow proper safety protocols, receive appropriate training, and use the correct protective equipment, such as Class 4 gloves, when working with voltage levels up to 20000 volts to mitigate the risk of electric shock and ensure personal safety.

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should be roughly 8 cycles. you cnat tell exactly bc we font have how often the interest is applied

Answer:

a)  14

b)  9

c)  10

Step-by-step explanation:

Given:

⇒ Number of Button As in one bag = 126 g ÷ 9 g = 14 buttons

Given:

⇒ Number of Button Bs in one bag = 126 g ÷ 14 g = 9 buttons

Given:

Let x = number of buttons of each type.

⇒ 9x+ 14x = 230

⇒ 23x = 230

⇒ x = 10

Therefore, there are 10 of each type of button in the box.

Answer:  -2 ±√6
                    2

Step-by-step explanation:
Use the quadratic formula - its better to separate it into two parts
Δ = b²-4ac
   = 4² -4(2*-1)
   = 16 + 8

∴ Δ = 24
Then
x = (-b ± √Δ) ÷ 2a
  = (-4 ± √24) ÷ 4
  = (-4 ± 2√6) ÷ 4 (simplify the surd form)
∴ x = -2 ±√6   (simplify by crossing out the 2's)
             2

Answer:

the last answer

Step-by-step explanation:

you multiply the exponents to get 7^-4 which is equivalent to the last answer

Yes, The triangles are congruent by SSS i,e option(D)

When two corresponding sides and the angle included between them of one triangle match those of two corresponding sides and the angle included between them of another triangle, the two triangles are said to be congruent. Two triangles are said to be congruent if their three sides and three angles, in any orientation, are equal.

By applying the CPCTC (Corresponding Parts of Congruent Triangles are Congruent) theorem, the two sides of the triangle in issue are made equal, hence making the third sides equal.

Therefore, we can say the triangles are congruent by SSS i,e option(D)

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\(\\ \sf\longmapsto 2(5m-4)-3(m-5)^2\)

\(\\ \sf\longmapsto 10m-8-3(m^2-10m+5^2)\)

\(\\ \sf\longmapsto 10m-8-3(m^2-10m+25)\)

\(\\ \sf\longmapsto 10m-8-3m^2+30m-75\)

\(\\ \sf\longmapsto -3m^2+30m+10m-75-8\)

\(\\ \sf\longmapsto -3m^2+40m-83\)

Answer:

The magnitude is sqrt((-4)^2 + (-9)^2) = 9.85. The angle is atan(-9/-4) = 180 deg + 66 deg = 246 deg = -114 deg.

Step-by-step explanation:

hope it help

Answer:

9.85

Step-by-step explanation:

|v|= √9²+(-4)²

=√81+16

=√97

|v|= 9.85

The length of segment RS is given as follows:

RS = 24.

The angle addition postulate states that if two or more angles share a common vertex and a common angle, forming a combination, the measure of the larger angle will be given by the sum of the measures of each of the angles.

The segment RT is the combination of segments RS and ST, hence:

RT = RS + ST.

Hence the length of segment RS is given as follows:

41 = RS + 17

RS = 24.

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The identified parameters are:

ta = 6 minutes

tθ = 11 minutes

∂a = 4 minutes

∂θ = 20 minutes

ra = 1/6 minutes^(-1)

rθ = 1/11 minutes^(-1)

ta: Mean time between calls to the center

tθ: Effective response time

∂a: Standard deviation of the time between calls to the center

∂θ: Standard deviation of the effective response time

ra: Rate of calls to the center (inverse of ta, i.e., ra = 1/ta)

rθ: Rate of effective response (inverse of tθ, i.e., rθ = 1/tθ)

Given information:

Mean time between calls to the center (ta) = 6 minutes

Standard deviation of time between calls (∂a) = 4 minutes

Effective response time (tθ) = 11 minutes

Standard deviation of effective response time (∂θ) = 20 minutes

Using this information, we can determine the values of the parameters:

ta = 6 minutes

tθ = 11 minutes

∂a = 4 minutes

∂θ = 20 minutes

ra = 1/ta = 1/6 minutes^(-1)

rθ = 1/tθ = 1/11 minutes^(-1)

So, the identified parameters are:

ta = 6 minutes

tθ = 11 minutes

∂a = 4 minutes

∂θ = 20 minutes

ra = 1/6 minutes^(-1)

rθ = 1/11 minutes^(-1)

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Answer:

420

Step-by-step explanation:

if we add 30 to each of the length of speech, we get 420 seconds

Can be a useful tool for exploring the behavior of the solution to the ODE and understanding the accuracy of the approximation. The given statement is true.

True. It is possible to set up a spreadsheet to compute the iterations of Euler's method for approximating solutions to first-order ordinary differential equations (ODEs).

Euler's method is a numerical method used to approximate solutions to first-order ODEs. It involves approximating the solution to the ODE at discrete time steps using a simple iterative formula.

To set up a spreadsheet to compute the iterations of Euler's method, we can use the following steps:

Set up the time step, h. This is the distance between the discrete time points at which we will approximate the solution. We can choose a small value for h to get more accurate approximations, but this will increase the number of iterations needed.

Set up the initial condition. This is the value of the solution at the initial time point, t_0.

Define the ODE. This is the equation that describes how the solution changes with time. For example, if we are approximating the solution to the ODE dy/dt = f(t,y), we would enter the function f(t,y) in a cell.

Set up the iterative formula. Euler's method uses the formula y_(n+1) = y_n + hf(t_n,y_n), where y_n is the approximate solution at time t_n, and y_(n+1) is the approximate solution at time t_(n+1) = t_n + h.

Fill in the spreadsheet with the initial condition and the iterative formula. We can use the copy and paste functions to quickly fill in the formula for each time step.

Finally, we can graph the approximate solution to the ODE using the spreadsheet's graphing capabilities.

In summary, it is indeed possible to set up a spreadsheet to compute the iterations of Euler's method for approximating solutions to first-order ODEs. This can be a useful tool for exploring the behavior of the solution to the ODE and understanding the accuracy of the approximation.

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Answer:

Diameter =16

Step-by-step explanation:

Chord theorem: When two chord intersect inside the circle, the product of the products of their segment are equal.

       4c * 6 = (2c +8)*4  

          24c = 2c*4 + 8*4  

           24c = 8c + 32  

Subtract 8c from both sides,

     24c - 8c = 32

             16c = 32

Divide both sides by 16,

                 c = 32 ÷ 16

                  \(\boxed{c = 2}\)

To find the horizontal diameter, add 2c +8 and 4.

   2c + 8 + 4 = 2c + 12

                    = 2*2 + 12

                   = 4 + 12

                    = 16

Diameter = 16