A metronome uses an inverted pendulum rod to control tempo. A weight can be slid up the pendulum rod to decrease tempo, or down the pendulum rod to increase tempo. A second fixed weight is hidden inside the metronome at the base of the pendulum. The longer the distance between the two weights, the slower the tempo. This equation is used to calculate the frequency of the metronome pendulum:
[tex]f = \frac{ \sqrt{ \frac{g}{l} } }{2\pi} [/tex]
Each time the metronome's pendulum completes one back and forth cycle, it produces two ticks or beats. To calibrate the metronome for beats per minute (bpm) the manufacturer needs to know the length of the pendulum for various tempos. Solve
[tex]f = \frac{ \sqrt{ \frac{g}{l} } }{2\pi} [/tex]
for L.​

Answer:

1/125

Step-by-step explanation:

Answer:

8.1

Step-by-step explanation:

The length of the missing side is 8.1 inches. You apply the pythagorean theorem to 5,b,10 and get 5sqrt3. Next, you apply the pythagorean theorem to 3, b, 5sqrt3 to get the square root of 66, which is 8.1, rounded to the nearest tenth.

Answer:

[tex]\displaystyle 8,1[/tex]

Step-by-step explanation:

Use the Pythagorean Theorem twise [first time for the reflexive edge and the second time for the longer leg of the other triangle]:

[tex]\displaystyle a^2 + b^2 = c^2 \\ \\ a^2 + 5^2 = 10^2 \hookrightarrow 100 = 25 + a^2 \hookrightarrow \sqrt{75} = \sqrt{x^2}; 5\sqrt{3}\:[or\:8,6602540378...] = a \\ \\ \\ \\ a^2 + b^2 = c^2 \\ \\ x^2 + 3^2 = 5\sqrt{3}^2 \hookrightarrow 75 = 9 + x^2 \hookrightarrow \sqrt{66} = \sqrt{x^2}; \sqrt{66}\:[or\:8,1240384046...] = x \\ \\ \boxed{\boxed{8,1 \approx x}}[/tex]

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Answer:

10.) b. not a function

11.) a. function

Step-by-step explanation:

hope it helps. good luck :)

Answer:

a is the answer

Step-by-step explanation:

The equation of P(E1 ∪ E2) that represents the condition that the mutually exclusive events is one of the events occurs, or both occur which is correct option(A).

Mutually Exclusive events is defined as in probability the particular addition rule is applicable when two occurrences are incompatible with one another. It claims that the probability of either event is equal to the probability of each event separately.

If E₁ and E₂ are said to be mutually exclusive events then the probability of an event E₁ occurring or the probability of event E₂ occurring is given as P(E₁) + P(E₂) :

P(E₁ ∪ E₂) = P(E₁) + P(E₂)

Hence, the equation of P(E1 ∪ E2) that represents the condition that the mutually exclusive events is one of the events occurs, or both occur.

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Answer:

6 hours

Step-by-step explanation:

356-56

=300

300/50

=6

Answer:

4x+6y³

Step-by-step explanation:

give me thanks, please;)

Answer:

NOTHING

Step-by-step explanation:

Answer:

[tex]\left \{ {{x=-2} \atop {y=1}} \right.[/tex]

Step-by-step explanation:

[tex]\left \{ {{y=-2x-3} \atop {y=2x+5}} \right.[/tex]

Substitute into one of the equations
[tex]-2x-3=2x+5[/tex]

Rearrange variables to the left side of the equation
[tex]-2x-2x=5+3[/tex]

Combine like terms
[tex]-4x=5+3[/tex]

Calculate the sum or difference
[tex]-4x=8[/tex]

Divide both sides of the equation by the coefficient of variable
[tex]x=-\frac{8}{4}[/tex]

Cross out the common factor
[tex]x=-2[/tex]

Substitute into one of the equations
[tex]y=-2\times\left(-2\right)-3[/tex]

Calculate
[tex]y=1[/tex]

The solution of the system is
[tex]\left \{ {{x=-2} \atop {y=1}} \right.[/tex]

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:)

Answer:

[tex]\displaystyle [-2, 1][/tex]

Step-by-step explanation:

Use the Elimination method sinse both coefficients in the system are OPPOCITES:

[tex]\displaystyle \left \{{{y = -2x - 3} \atop {y = 2x + 5}} \right.[/tex]

2y = 2; 1 = y [Plug this y-coordinate back into the system to get the x-coordinate of −2 (−2 = x).]

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Answer:

Step-by-step explanation:

h(t) = 32 = -16t^2 + 50t + 5

-16t^2 + 50t - 27 = 0

Drawing a graph gives time = 0.7 seconds.

The ball is 32 feet above the ground after 2.9 seconds

We have,

To determine the time at which the ball is 32 feet above the ground, we can set the height function h(t) equal to 32 and solve for t:

h(t) = 32

-16t² + 50t + 5 = 32

-16t² + 50t + 5 - 32 = 0

-16t² + 50t - 27 = 0

We can solve this quadratic equation using various methods, such as factoring, completing the square, or the quadratic formula.

Let's use the quadratic formula:

t = (-b ± √(² - 4ac)) / (2a)

Plugging in the values a = -16, b = 50, and c = -27, we have:

t = (-50 ± √(50² - 4(-16)(-27))) / (2(-16))

Simplifying further:

t = (-50 ± √(2500 - 1728)) / (-32)

t = (-50 ± √(772)) / (-32)

Now, we can calculate the two possible solutions:

t ≈ (-50 + √772) / (-32) ≈ 2.85 seconds (rounded to the nearest tenth)

t ≈ (-50 - √772) / (-32) ≈ 0.18 seconds (rounded to the nearest tenth)

Based on the graph of the function, the ball is 32 feet above the ground after approximately 2.9 seconds (rounded to the nearest tenth).

Thus,

The ball is 32 feet above the ground after 2.9 seconds

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Answer:

edge ⬇️  

If   invested at the rate of 2.5% for one year. The amount that tyrell pay in additional interest each month is: c. $1,000.

First step

Amount for one year=Simple interest amount/Interest rate

Amount for one year=$300/0.025

Amount for one year=$12,000

Second step

Additional interest each month=$12,000/12 months

Additional interest each month=$1,000

Therefore the amount that tyrell pay in additional interest each month is: c. $1,000.

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Answer:

A. x>2

Step-by-step explanation:

11x>22

x>22/11

x>2

Answer:8.9

Step-by-step explanation: y=2.2 +3.5 =6.7 +0.18

y= 8.9

good luck

Answer:

Length = 18 cm

Width = 12 cm

Area = 216 cm^2

Step-by-step explanation:

The perimeter of a rectangle is twice it's length(l) plus twice it's width(w):

Perimeter = 2l + 2w

We are told that (l/w) = (3/2) [ratio of its length to its width is 3:2]

Therefore:

60cm = 2l + 2w

---

(l/w) = (3/2)

We can rewrite this as:  l = (3/2)w

----

Now substitute this expression into the perimeter equation:

60 cm = 2l + 2w

60 cm = 2((3/2)w) + 2w

60 cm = 3w + 2w

60cm = 5w

w = 12 cm

l = (3/2)w

l = (3/2)*12

l = 18 cm

Area = 1*w

Area = (12cm)(18cm) = 216 cm^2

Answer:

x = 22-3y/5-y

y=-22-5x/x-3

Step-by-step explanation:

Solve for x:

1)  Subtract 3y from both sides.

5x - xy = 22 - 3y

2) Factor out the common term x.

x(5 - y) = 22 - 3y

3) Divide both sides by 5 - y.

x = 22-3y/5-y

Solve for y:

1) Subtract 5x from both sides.

=xy + 3y = 22 - 5x

2) Factor out the common term y.

- y=(x-3)=22-5x

3) Divide both sides by x-3.

-y=22-5x/x-3

4) Multiply both sides by -1.

y=-22-5x/x-3

Answer:

x= 9.3 but im not to sure this is right

Step-by-step explanation:

Answer:

9*3.14=28.26

Step-by-step explanation:

Hope this Helps!

Answer:

[tex]C\approx28.27ft[/tex]

Step-by-step explanation:

[tex]C=\pi d\\C=\pi(9)\\C=9\pi\\C\approx28.27[/tex]

Thus, your circumference is about 28.27 ft

Answer:

-40

Step-by-step explanation:

Answer:

-13

Step-by-step explanation:

Answer:

2feet

Step-by-step explanation:

There brother is 2 feet and 6 inches

Formula: 12 inches = 1 foot

4'2 + 10 inches = 5 foot

Half of 5 foot would be 2'6 since there are 12 inches in a foot.

Answer:

10x+2

Step-by-step explanation:

2×(2x+1+3x)

4x+2+6x

10x+2

Answer:

10x + 2

Step-by-step explanation:

The perimeter is the sum of the 4 sides of the rectangle, where opposite sides are equal in measure, thus

perimeter = 3x + 3x + 2x + 1 + 2x + 1 = 10x + 2

Answer:

24 Ohms

Step-by-step explanation:

Resistance is a function of amperes. For each amp, there is one and only one value for resistance.

It works the other way, too.

E=IR (well-known relationship). If IR=12, R=12/I

R=E* (1/I)

When the current is 0.5 amp, R=12/0.5 - 24 ohms

Answer:

Step-by-step explanation:

[tex]\begin{bmatrix}2 & -3\\ 1 & 2\end{bmatrix}^{-1}\times \begin{bmatrix}2 & -3\\ 1 & 2\end{bmatrix}\times \begin{bmatrix}x\\y \end{bmatrix}=\frac{1}{7} \begin{bmatrix}2 & 3 \\ -1 & 2\end{bmatrix}\times \begin{bmatrix}19\\ -1\end{bmatrix}[/tex]  

Since, [tex]\begin{bmatrix}2 & -3\\ 1 & 2\end{bmatrix}^{-1}=\frac{1}{7}\begin{bmatrix}2 & 3\\ -1 & 2\end{bmatrix}[/tex]

And [tex]A^{-1}A=I[/tex]

[tex]\begin{bmatrix}x\\y \end{bmatrix}=\frac{1}{7}\begin{bmatrix}2 & 3\\ -1 & 2\end{bmatrix}\times \begin{bmatrix}19\\-1 \end{bmatrix}[/tex]

[tex]\begin{bmatrix}x\\y \end{bmatrix}=\frac{1}{7}\begin{bmatrix}35\\ -21\end{bmatrix}[/tex]

[tex]\begin{bmatrix}x\\y \end{bmatrix}=\begin{bmatrix}5\\ -3\end{bmatrix}[/tex]                

Therefore, x = 5 and y = -3 will be the value of variables.

Answer:

16/100 or simplified is 4/25

Step-by-step explanation:

The domain and range of the linear function described are given as follows:

The domain is all real values from 0 to 8.5 and the range is all real values from 0 to 425.

A linear function is modeled by:

[tex]y = mx + b[/tex]

In which:

In this problem, the car travels 425 miles at a speed of 50 miles per hour, hence for the amount of miles left for the car to travel after t hours is given by a linear function with m = -50 and b = 425, that is:

d(t) = 425 - 50t.

The domain is the set of all possible values of the input, which considering that the car travels while the distance is greater than 0, is given by:

d(t) > 0 -> 425 - 50t > 0 -> t < 8.5.

The range is the set of all possible values of the input, which is the distance remaining, assuming real values from 0 to 425.

Hence, the correct option is:

The domain is all real values from 0 to 8.5 and the range is all real values from 0 to 425.

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Answer:

the sale price will be 130% off

Step-by-step explanation:

h(x) = x^2 - 2

h(-3) = (-3)^2 - 2

= 9-2

= 7

Both solutions are valid, so the solutions to the quadratic function [tex]f(x) = 4x^2 - 9[/tex] are x = -3/2 and x = 3/2.

To solve the quadratic function [tex]f(x) = 4x^2 - 9[/tex] by factoring, we set the expression equal to zero and then try to factor it.

Step 1: Set f(x) equal to zero:

[tex]4x^2 - 9 = 0[/tex]

Step 2: Factor the quadratic expression:

The expression [tex]4x^2 - 9[/tex] is in the form of a difference of squares, which can be factored as follows:

[tex]a^2 - b^2 = (a + b)(a - b)[/tex]

In our case, a = 2x and b = 3:

[tex]4x^2 - 9 = (2x + 3)(2x - 3)[/tex]

Step 3: Set each factor equal to zero and solve for x:

First factor: 2x + 3 = 0

Subtract 3 from both sides:

2x = -3

Divide both sides by 2:

x = -3/2

Second factor: 2x - 3 = 0

Add 3 to both sides:

2x = 3

Divide both sides by 2:

x = 3/2

Step 4: Check the solutions:

Plug the values of x back into the original equation to verify:

For x = -3/2:

[tex]f(-3/2) = 4(-3/2)^2 - 9\\f(-3/2) = 4(9/4) - 9\\f(-3/2) = 9 - 9\\f(-3/2) = 0\\For x = 3/2:\\f(3/2) = 4(3/2)^2 - 9\\f(3/2) = 4(9/4) - 9\\f(3/2) = 9 - 9\\f(3/2) = 0[/tex]

Both solutions are valid, so the solutions to the quadratic function f(x) = [tex]4x^2 - 9[/tex] are x = -3/2 and x = 3/2.

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Answer:

5 x - 6 y - 8 = 0

Step-by-step explanation:

Answer:

it looks like c

Step-by-step explanation:

its not quite 50 but its extreemly close so its got to be c

[tex]12 {}^{2} = 9 {}^{2} + 8 {}^{2} - 2(9)(8)(cosx)[/tex]

[tex]144 = 81 + 64 - 2(72)(cosx)[/tex]

[tex]144 = 145 - 144(cosx)[/tex]

[tex] - 144(cosx) = 144 - 145[/tex]

[tex](cosx) = \frac{ - 1}{ - 144} [/tex]

[tex]arccos( \frac{1}{144} ) = > a = 89.6[/tex]