Solve for x. 6 + |4x - 1| > 10 Graph the solution on the number line.

The angular velocity of link CD when angle BAD = 60° is 21.16 rad/s.

The given values are:

AD = 150 mm

AB = 40 mm

CD = 80 mm

The crank AB rotates at 120 r.p.m. clockwise.

BC and AD are of equal length.

To find:

The angular velocity of link CD when angle BAD = 60°.

From the given data, we have to first find the value of angle BCD.

Angle BCD can be calculated as follows:

AB = 40 mm

BC = AD

= 150 mm

In ΔABC,

By using Cosine rule;

AC² = AB² + BC² - 2 × AB × BC × Cos ∠ABC∴ AC² = (40)² + (150)² - 2 × 40 × 150 × Cos 180°

∴ AC = 160.6 mm

In ΔBCD,

By using Cosine rule;

BD² = BC² + CD² - 2 × BC × CD × Cos ∠BCD

∴ BD² = (150)² + (80)² - 2 × 150 × 80 × Cos ∠BCD

In ΔABD,By using Cosine rule;

BD² = AB² + AD² - 2 × AB × AD × Cos ∠BAD

∴ BD² = (40)² + (150)² - 2 × 40 × 150 × Cos 60°

∴ BD = 184.06 mm

In ΔABD,By using Sine rule;

AB / Sin ∠BAD = BD / Sin ∠ABD

∴ Sin ∠ABD = BD × Sin ∠BAD / AB

∴ ∠ABD = Sin⁻¹ [BD × Sin ∠BAD / AB]

∴ ∠ABD = Sin⁻¹ [184.06 × Sin 60° / 40]

∴ ∠ABD = 87.2°∠ACD = ∠ABD - ∠ACB

∴ ∠ACD = 87.2° - 180°

∴ ∠ACD = - 92.8°∠BCD

= 180° - ∠ACD

∴ ∠BCD = 180° - (- 92.8°)

∴ ∠BCD = 272.8°

As we know that for four-bar mechanism, we have a formula for finding the angular velocity of link CD.

ωCD / Sin ∠BCD = ωAB / Sin ∠BADωCD / Sin 272.8°

= ωAB / Sin 60°

Substituting the values, ωCD / Sin 272.8° = ωAB / Sin 60°ωCD

= ωAB × Sin 272.8° / Sin 60°

But, ωAB = 2 × π × N / 60

= 2 × π × 120 / 60

= 4 × π rad/s

∴ ωCD = 4 × π × Sin 272.8° / Sin 60°ωCD

= 21.16 rad/s

Therefore, the angular velocity of link CD when angle BAD = 60° is 21.16 rad/s.

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Setting k = 3, the three-period moving average forecast for week 6 is 24 (option A)

A moving average method is a time series average that moves through the series by replacing the last term of the previous averaged group and adding the next term in each consecutive average.

A moving average of an order n, k = n,  is calculated as:

(x₁ + x₂ + ... + xₙ) / n

The given data is:

Week      Number of units sold

1                15

2               20

3               25

4               30

5               17

Using k = 3 means the order of the moving average is 3, hence

forecast for week 6 = (25 + 30 + 17) / 3 = 24 (option A)

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Answer:

$2.90 %Step-by-step explanation:

because if you round it it would be close to 90 and if you mutiply 2 x 2 =4 x 89

Answer:

1600 years

Step-by-step explanation:

Let A = age of ancient artifact

Let B = age of antique book

The artifact is 4 times the age of the book, so:

A = 4B

In 200 years it will be 3 times the age of the book:

A + 200 = 3(B + 200)

⇒  A = 3B + 400

Equate equations for A:

A = A

4B = 3B +400

B = 400 years

Substitute value found for B into A = 4B and solve for A:

A = 4 x 400 = 1600 years

Answer:

maybe its 32 or maybe its just HeLl in real life :)

Step-by-step explanation:

Answer:

\(Area = 4 \pi \ cm^2\)

Step-by-step explanation:

\(Area = \pi r^2 = \pi \times 2^2 = 4 \pi \ cm^2\)

Answer:

A = 4 cm squaree

this us because u multiply π r and square it. sorry if it's confusing

Answer:0.375

Step-by-step explanation:

3/4=0.75

0.75/2=0.375

(3/4)/2=0.375

Answer:

163.3m²

Step-by-step explanation:

area = Pi(r²)

r = d / 2

r = 12

12² = 144

144 x 3.14 = 452.16

diameter of bigger circle = 24 + 4 (2 on each side)

28 / 2 = 14

14² = 196

196 x 3.14 = 615.44

sidewalk = bigger - smaller

sidewalk = 615.44 - 452.16

sidewalk = 163.3

The rate of return on the bond is approximately 11.67%.

To calculate the rate of return on a bond, we can use the formula:

Rate of return = (Coupon payment + (Sale price - Purchase price)) / Purchase price

Given:

Coupon payment = $55

Purchase price = $900

Sale price = $950

Substituting the values into the formula, we get:

Rate of return = (55 + (950 - 900)) / 900

= (55 + 50) / 900

= 105 / 900

To express the rate of return as a percentage, we divide by 900 and multiply by 100:

Rate of return = (105 / 900) * 100

≈ 11.67%

Therefore, the rate of return on the bond is approximately 11.67%.

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Answer:

0

Step-by-step explanation:

Answer:

80 teaspoons

Step-by-step explanation:

According to the scenario, computation of the given data are as follows,

Teaspoon capacity = 0.015 L

Total quantity = 1.2L

So, we can calculate the number of teaspoons in 1.2L oil by using following formula,

Number of teaspoons = Total quantity ÷ Teaspoon capacity

By putting the value of following, we get

Number of teaspoons = 1.2 ÷ 0.015

= 80 teaspoons

Hence, there are 80 teaspoons of oil in 1.2L.

The roots of the quadratic equation are:  5 and -6.5

A quadratic equation is an algebraic expression of the form ax^2 + bx + c = 0, where a, b, and c are real numbers.

In algebra, a quadratic equation (from Latin quadratus 'square') is any equation that can be rearranged in standard form ax²+bx+c=0\,,} where x represents an unknown value, and a, b, and c represent known numbers, where a ≠ 0.

the given equation is 2x²+3x=65

Using the quadratic formula we have

(-b±√b²-4ac)/2a

x = (-3±√3²-4*2*-65)/2*2

x = -3±√9+520)/4

x= (-3±√529)/4

x = (-3±23)/4

⇒(-3+23)/4 or( -3-23)/4

⇒20/4  or -26/4

x = 5 or x = -6.5

Therefore the possible values pf x are 5 and -6.5

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Answer:

\(\sqrt[3]{27}\)

Step-by-step explanation:

Let's split the cube root of 27 to make this easier:

\(\sqrt[3]{27}=\sqrt[3]{3\cdot9}=\sqrt[3]{3\cdot3\cdot3}\\\text{Now, let's put }3\cdot3\cdot3 \text{ in exponential form. We would have:}\\\sqrt[3]{3^3}\\\text{Now, the 3 and 3 and the square root symbol would cancel out, and we }\\\text{ would be left with 3. And since three is an integer, we know that} } \sqrt{27} \text{ is perfect }\)

Answer:

C. p -> q

Step-by-step explanation:

Just did this on Edge2020. Hope this helps :)

Answer:

-3 1

Step-by-step explanation:

2+1 =3

-3-2=--=+5 answer

Step-by-step explanation:

We can use trigonometry to solve this problem. Let's draw a diagram:

```

A - observer (1.5 m above ground)

B - base of the clock tower

C - top of the clock tower

D - intersection of AB and the horizontal ground

E - point on the ground directly below C

C

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B

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A

```

We want to find the height of the clock tower, which is CE. We have the angle of elevation ACD, which is 19 degrees, and the distance AB, which is 100 m. We can use tangent to find CE:

tan(ACD) = CE / AB

tan(19) = CE / 100

CE = 100 * tan(19)

CE ≈ 34.5 m (rounded to 1 decimal place)

Therefore, the height of the clock tower is approximately 34.5 m.

Answer:

The answer is 7.5 tax rate

Step-by-step explanation:

I used a calculator to get the answer and it is correct.

Answer: $66.20; close

Step-by-step explanation:

The down arrow indicates the stock price has decreased from yesterday’s price of $ 66.20  at the  close  of the market day.

Answer:

C

Step-by-step explanation:

Hey There so the first step of this problem is to find the formula for circumference

\(C=2\pi r\)

given some of the values we can form an equation to solve for the radius (r)

\(31.4=3.14(2)r\\3.14(2)=6.28\\31.4=6.28r\\\frac{31.4}{6.28} =5\)

so we can conclude that the radius is equal to 5

Answer:

C) 5 ft

Step-by-step explanation:

Equation used: C=2πr

This isn't a hard question once you understand the basics of it. The radius squared by 2 equals the diameter, and other way around. Your going to divide the circumference by the pie (π).

31.4 ÷ 3.14 = 10

Now you'll do 10/2 to equal 5.

Answer:

27.5 miles

Step-by-step explanation:

55 divided by 2 is 27.5

Answer:

27.5 miles

always half it when it is half a mile

Answer:

Convert from degrees to radians using the ratio

π

180.001989675

radians

Answer:

Quadrant  II

Step-by-step explanation:

Sin is positive in Quad I and II

Cos is negative in  Quad II and II

Therefor ∅ is in Quadrant  II

Using proportional relationships, we can say that They will walk 12 laps and run 20 laps for a total of 32 miles.

In a direct proportional relationship, the output variable is found by the multiplication of the input variable and the constant of proportionality k, as follows:

y = kx.

Given that we know this, they walk 3/8 of the 8 miles that make up the complete distance. Run 5/8 of the route.

The following are the proportional relationships for the distances:

For a total distance of 32 miles, the distances walked and run are given:

therefore, They will walk 12 laps and run 20 laps for a total of 32 miles as per the proportional relation.

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Answer:

Mark me as brainlist

Step-by-step explanation:

The rate of change of one quantity in a system often causes other quantities to change. By knowing the relationship between the different quantities, we may be able to find the relationship between their rates of change.

59/150

How?

w= 59/150

59/150 and -2/3 have to have the same denominators.

So, what I did was, -2/3×50= -100/150.

(Process of a new equation)

59/150-(-100/150)

[The two - signs cross each other out, making it a + ]

59/150+100/150 <- New Equation

__________________________________

59/150+100/150= 159/150

159/150= 1 9/150

9÷150=0.06

1+0.06= 1.06

(PROOF ABOVE)

Answer

add 1.06 = 1 3/50  = 1 3/50 + (-2/3) =  59/150

Step-by-step explanation:

Answer:

Step-by-step explanation:

1/6 ÷ 8

1/6 × 1/8

1/48

for each batch