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3 years ago

What is the area of a semicircle with a diameter of 21.5

Mathematics

1 answer:

denis-greek [22]3 years ago

7 0

Area of a circle = PI x R^2

r = 1/2 diameter

r = 21.5/2

r = 10.75

Area of circle = 3.14 x 10.75^2 = 3.14 x 115.5625 = 362.86625 square units.

A semicircle is half a circle:

Area of semicircle = 362.86625 / 2 = 181.433125 square units (round the answer as needed).

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If ln(4x+y)=2x-3,then dy/dx=

Viktor [21]

$\ln(4x+y)=2x-3$

Differentiate both sides wrt $x$ :

$\dfrac{\mathrm d(\ln(4x+y))}{\mathrm dx}=\dfrac{\mathrm d(2x-3)}{\mathrm dx}$

By the chain rule, we get

$\dfrac1{4x+y}\dfrac{\mathrm d(4x+y)}{\mathrm dx}=2$

$\dfrac{4+\frac{\mathrm dy}{\mathrm dx}}{4x+y}=2$

Solve for $\frac{\mathrm dy}{\mathrm dx}$ :

$4+\dfrac{\mathrm dy}{\mathrm dx}=8x+2y$

$\boxed{\dfrac{\mathrm dy}{\mathrm dx}=8x+2y-4}$

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3 years ago

Simplify (3x – 5) + (5x + 1)

Archy [21]

Answer:

8x-4

Step-by-step explanation:

(3x-5)+(5x+1)

=3x-5+5x+1

=8x-4

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3 years ago

Jim used his debit card to withdraw $35 from the ATM. Then, he wrote a check for $8.00. Which equation represents the total amou

ryzh [129]

$x = 35 + 8$
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4 years ago

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3 years ago

What is the equation of the parabola in vertex form with vertex (2,-4) and directrix y=-6

Pachacha [2.7K]

Answer:

$y=\dfrac{1}{8}(x-2)^2-4$

Step-by-step explanation:

The directrix y=-6 is parallel to the x axes, so parabola has equation of the form

$(x-x_0)^2=2px(y-y_0),$

where $(x_0,y_0)$ is the vertex of parabola and p is parabola's parameter.

By the definition, $\frac{p}{2}$ is the distance from the vertex to the directrix, so

$\dfrac{p}{2}=2\Rightarrow p=4$

Hence, the equation of parabola is

$(x-2)^2=8(y+4)$

See attached diagram for the graph of parabola and its directrix.

In vertex form this equation is

$y=\dfrac{1}{8}(x-2)^2-4$

8 0

3 years ago