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2 years ago

Please help me with this question

Mathematics

1 answer:

Trava [24]2 years ago

4 0

Applying the formula for the area of a sector and length of an arc, the value of k is calculated as: 27.

<h3>What is the Area of a Sector?</h3>

Area of a sector of a circle = ∅/360 × πr²

<h3>What is the Length of an Arc?</h3>

Length of arc = ∅/360 × 2πr

Given the following:

Radius (r) = 9 cm
Length of arc = 6π cm
Area of sector = kπ cm²

Find ∅ of the sector using the formula for length of acr:

∅/360 × 2πr = 6π

Plug in the value of r

∅/360 × 2π(9) = 6π

∅/360 × 18π = 6π

Divide both sides by 18π

∅/360 = 6π/18π

∅/360 = 1/3

Multiply both sides by 360

∅ = 1/3 × 360

∅ = 120°

Find the area of the sector:

Area = ∅/360 × πr² = 120/360 × π(9²)

Area = 1/3 × π81

Area = 27π

Therefore, the value of k is 27.

Learn more about area of sector on:

brainly.com/question/22972014

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Softa [21]

The important formula to this problem is $distance=rate(time)$ or $d=rt$

Now, the speed of the car is 70 km/h, and the speed of the truck is 50 km/h. It will take the two vehicles the same amount of time to meet since they both left at the same time. So, since distance equals rate times time, and t = time:

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Because they both left in opposite directions, and the towns are 420 kilometers apart, the equation for this would be

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We now solve the equation.

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So, the car and the truck will pass each other at 1:30 PM.

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3 years ago

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Nataly [62]

<h2>Answer:</h2>

$\boxed{y=-3}$

<h2>Step-by-step explanation:</h2>

The graph of this parabola is shown below. From this graph we know that:

VERTEX:

$(h,k)=(0,0)$

DIRECTIX:

Since the vertex lies on the origin and the parabola opens upward, then the standard form of this parabola is:

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So:

$y=\frac{1}{12}x^2 \\ \\ \therefore 12y=x^2 \ or \ x^2=12y \\ \\ \\ Then: \\ \\ 4p=12 \therefore p=3$

Then the directrix is:

$y=k-p \\ \\ \therefore y=0-3 \therefore \boxed{y=-3}$

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$\text{Hey there!}$

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