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2 years ago

A regular polygon has a perimeter of 40 cm and a apothem of 6 cm. find the polygons area

Mathematics

1 answer:

Anestetic [448]2 years ago

3 0

Answer:

a = 120 cm²

Step-by-step explanation:

n = number of sides

edge length

40/n

divide the polygon into n congruent triangles

a = (1/2)(edge * apothem) * number of triangles

a = (1/2)(40/n)(6) * n

n cancels out

a = (1/2)(40)(6)

a = 120 cm²

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I got:
-2(2f-3g)

explanation:
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3 years ago

What is the range of the equation

a_sh-v [17]

The range of the equation is $y>2$

Explanation:

The given equation is $y=2(4)^{x+3}+2$

We need to determine the range of the equation.

<u>Range:</u>

The range of the function is the set of all dependent y - values for which the function is well defined.

Let us simplify the equation.

Thus, we have;

$y=2 \cdot 4^{x+3}+2$

This can be written as $y=2^{1+2(x+3)}+2$

Now, we shall determine the range.

Let us interchange the variables x and y.

Thus, we have;

$x=2^{1+2(y+3)}+2$

Solving for y, we get;

$x-2=2^{1+2(y+3)}$

Applying the log rule, if f(x) = g(x) then $\ln (f(x))=\ln (g(x))$ , then, we get;

$\ln \left(2^{1+2(y+3)}\right)=\ln (x-2)$

Simplifying, we get;

$(1+2(y+3)) \ln (2)=\ln (x-2)$

Dividing both sides by $\ln (2)$ , we have;

$2 y+7=\frac{\ln (x-2)}{\ln (2)}$

Subtracting 7 from both sides of the equation, we have;

$2 y=\frac{\ln (x-2)}{\ln (2)}-7$

Dividing both sides by 2, we get;

$y=\frac{\ln (x-2)-7 \ln (2)}{2 \ln (2)}$

Let us find the positive values for logs.

Thus, we have,;

$x-2>0$

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7 0

3 years ago

Segment CD has point E located on it such that CE:ED = 3:5. If the endpoints are located at C(5, -6) and D(11,18) then what are

wlad13 [49]

Answer:

E(29/4,3)

Step-by-step explanation:

Given that,

Segment CD has point E located on it such that CE:ED = 3:5

The coordinates of C and D are (5, -6) and (11,18) respectively.

We need to find the coordinates of E. Let the coordinates are (x,y). Using section formula to find it as follows :

$(x,y)=(\dfrac{m_1x_2+m_2x_1}{m_1+m_2},\dfrac{m_1y_2+m_2y_1}{m_1+m_2})\\\\(x,y)=(\dfrac{3(11)+5(5)}{3+5},\dfrac{3(18)+5(-6)}{3+5})\\\\=\dfrac{29}{4},3$

So, the coordinates of E are (29/4,3).

4 0

3 years ago

Simplify the algebraic expression: 4x + 8y + 7x² + 5x – 2y.

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Answer:

7x² + 9x + 6y

Step-by-step explanation:

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5 0

3 years ago

If an object is projected upward from ground level with an initial velocity of 128 ft per sec, then it's height in feet after t

antoniya [11.8K]

Answer: t= 4 seconds

Maximum height = 256 feet

Step-by-step explanation:

The height of the object projected upwards after t seconds is given by

s(t)=-16t^2+128t.

The expression is a quadratic equation. When this equation is plotted on a graph, height against time, it takes the shape of a parabola whose vertex represents the maximum height attained by the object.

To get the value of t at the maximum height,

t = -b/2a

From the equation,

a = -16

b = 128

t = -128/-2×-16

= -128 /- 32= 4

it will take 4 seconds to reach its maximum height

To find maximum height attained, put t= 4 in the equation

s(t)=-16t^2+128t

S = -16× 4^2 + 128×4

S = -256+512

S = 256 feet

3 0

3 years ago