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3 years ago

By definition, a round character _____.

Mathematics

1 answer:

Leya [2.2K]3 years ago

7 0

... undergoes development throughout the course of the story. They're dynamic, and change as the plot progresses.

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Select two prime numbers that have a sum of 18.

AURORKA [14]

Step-by-step explanation:

option e.5,13

.............

6 0

2 years ago

Please help! Area of part of a circle!!!

Helga [31]

The sector (shaded segment + triangle) makes up 1/3 of the circle (which is evident from the fact that the labeled arc measures 120° and a full circle measures 360°). The circle has radius 96 cm, so its total area is π (96 cm)² = 9216π cm². The area of the sector is then 1/3 • 9216π cm² = 3072π cm².

The triangle is isosceles since two of its legs coincide with the radius of the circle, and the angle between these sides measures 120°, same as the arc it subtends. If b is the length of the third side in the triangle, then by the law of cosines

b² = 2 • (96 cm)² - 2 (96 cm)² cos(120°) ⇒ b = 96√3 cm

Call b the base of this triangle.

The vertex angle is 120°, so the other two angles have measure θ such that

120° + 2θ = 180°

since the interior angles of any triangle sum to 180°. Solve for θ :

2θ = 60°

θ = 30°

Draw an altitude for the triangle that connects the vertex to the base. This cuts the triangle into two smaller right triangles. Let h be the height of all these triangles. Using some trig, we find

tan(30°) = h / (b/2) ⇒ h = 48 cm

Then the area of the triangle is

1/2 bh = 1/2 • (96√3 cm) • (48 cm) = 2304√3 cm²

and the area of the shaded segment is the difference between the area of the sector and the area of the triangle:

3072π cm² - 2304√3 cm² ≈ 5660.3 cm²

7 0

3 years ago

Help me solve this by multiplication or linar combination please

patriot [66]

X would be equal to 0 while y would be equal to -1
-20(0)+6(-1)=-6
-10(0)-4(-1)=4

4 0

4 years ago

You throw a ball up and its height h can be tracked using the equation h=2x^2-12x+20.

postnew [5]

This problem seems to be wrong because no minimum point was found and no point of landing exists

Answer:

1) There is no maximum height

2) The ball will never land

Step-by-step explanation:

Derivatives

Sometimes we need to find the maximum or minimum value of a function in a given interval. The derivative is a very handy tool for this task. We only have to compute the first derivative f' and have it equal to 0. That will give us the critical points.

Then, compute the second derivative f'' and evaluate the critical points in there. The criteria establish that

If f''(a) is positive, then x=a is a minimum

If f''(a) is negative, then x=a is a maximum

The function provided in the question is

$h(x)=2x^2-12x+20$

Let's find the first derivative

$h'(x)=4x-12$

solving h'=0:

$4x-12=0$

x=3

Computing h''

h''(x)=4

It means that no matter the value of x, the second derivative is always positive, so x=3 is a minimum. The function doesn't have a local maximum or the ball will never reach a maximum height

To find when will the ball land, we set h=0

$2x^2-12x+20=0$

Simplifying by 2

$x^2-6x+10=0$

Completing squares

$x^2-6x+9+10-9=0$

Factoring and rearranging

$(x-3)^2=-1$

There is no real value of x to solve the above equation, so the ball will never land.

This problem seems to be wrong because no minimum point was found and no point of landing exists

3 0

3 years ago

Solve for the roots in simplest form by completing the square x^2-12x+20=0

Alex17521 [72]

Answer:

x = 10 or x = 2

Step-by-step explanation:

Solve for x:

x^2 - 12 x + 20 = 0

Hint: | Solve the quadratic equation by completing the square.

Subtract 20 from both sides:

x^2 - 12 x = -20

Hint: | Take one half of the coefficient of x and square it, then add it to both sides.

Add 36 to both sides:

x^2 - 12 x + 36 = 16

Hint: | Factor the left hand side.

Write the left hand side as a square:

(x - 6)^2 = 16

Hint: | Eliminate the exponent on the left hand side.

Take the square root of both sides:

x - 6 = 4 or x - 6 = -4

Hint: | Look at the first equation: Solve for x.

Add 6 to both sides:

x = 10 or x - 6 = -4

Hint: | Look at the second equation: Solve for x.

Add 6 to both sides:

Answer: x = 10 or x = 2

5 0

3 years ago