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2 years ago

A soccer ball, which has a circumference of 70.0 cm, rolls 14.0 yards in 3.30 s .

1 answer:

7 0

14 yards = 1280.16 cm

1280.6cm/70cm/rot=18.288 rotations 

3.55s/18.288 rots =.428 s/rot 

2pi/.428 s/rot = angular speed = 14.68 rad/s

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Find the length of side AB Give answer to 3 significant figures

Rina8888 [55]

Answer:

AB = 8.857 cm

Step-by-step explanation:

Here, we are given a right angle $\triangle ABC$ in which we have the following things:

$\angle A = 90 ^\circ\\\angle C = 41 ^\circ\\\text{Side }BC = 13.5 cm$

Side BC is the hypotenuse here.

We have to find the side AB.

Trigonometric functions can be helpful to find the value of Side AB here.

Calculating $\angle B$ :

Sum of all the angles in $\triangle ABC$ is $180^\circ$ .

$\Rightarrow \angle A + \angle B + \angle C = 180^\circ\\\Rightarrow 90^\circ + \angle B + 41^\circ = 180^\circ\\\Rightarrow \angle B = 49^\circ$

We know that cosine of an angle is:

$cos \theta = \dfrac{\text{Base}}{\text{Hypotenuse}}\\\Rightarrow cos B = \dfrac{AB}{BC}\\\Rightarrow cos 49^\circ = \dfrac{AB}{13.5}\\\Rightarrow AB = 13.5 \times 0.656\\\Rightarrow AB = 8.857 cm$

So, side AB = 8.857 cm .

6 0

2 years ago

If x and y satisfy both 9x+2y=8 and 7x+2y=4, then y=?

Alex

Answer:

The value of y is -5

Step-by-step explanation:

we have

$9x+2y=8$ ------> equation A

$7x+2y=4$ ------> equation B

we know that

If x and y satisfy both equations, then (x,y) is the solution of the system of equations

Using a graphing tool

Remember that

The solution of the systems of equations is the intersection point both graphs

The intersection point is (2,-5)

therefore

The solution of the system of equations is the point (2,-5)

The value of y is -5

7 0

2 years ago

Accident rate data y1, ...., y12 were collected over 12 consecutive years t=1,2,...12. At over 12 consecutive years t = 1,2,...,

e-lub [12.9K]

Answer:

The correct option is;

The accident rate is a linear model function of t. After t = 7, the slope changes, with the two lines intersecting at t = 7

Step-by-step explanation:

The given parameters are;

Accident rate data = y₁, y₂, y₃, y₄, y₅, y₆, y₇, y₈, y₉, y₁₀, y₁₁, y₁₂

Time at which data was recorded = t₁, t₂, t₃, t₄, t₅, t₆, t₇, t₈, t₉, t₁₀, t₁₁, t₁₂

Accident rate equation is a linear model given as follows;

y = X·B + E

Where:

y = Accident rate

X = Slope of linear model

B = Year

E = y intercept of model

At the end of the 6th year, a change in a regulation that affects safety, hence accident rate occurred given as follows;

Before the change in safety regulations occurred for year t < 7 y₁ = X₁B + E₁

After the change in safety regulations occurred for year t < 7 y₂ = X₂B + E₂

Therefore the slope changes from X₁ to X₂ after t = 7 with the second linear model starting from the end of the first linear model making the two lines intersect at t = 7 (the beginning of year 7)

Hence the correct option is that "The accident rate is a linear model function of t. After t = 7, the slope changes, with the two lines intersecting at t = 7."

4 0

2 years ago

Daisy measured the heights of 20 plants.

sergiy2304 [10]

Answer: