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Galina-37 [17]
3 years ago
13

The sum of the internal angles of a convex polygon is 1080º. Calculate the number of diagonals of this polygon.

Mathematics
1 answer:
vlabodo [156]3 years ago
7 0

Answer:

b

Step-by-step explanation:

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The breadth of a rectangular garden is 2/3 of its legth. If its perimeter is 40cm, find its dimensions.
Arisa [49]

Answer:

12; 8

Step-by-step explanation:

length-x

breadth-2/3x

2(x+2/3 x)=40

2×5/3x=40

10/3x=40

x=40÷10/3

x=40×3/10

x=12 (cm) length

2/3×12=8 (cm) breadth

6 0
3 years ago
Need help with this im confused
Jet001 [13]

Answer:

-\frac34 -\frac14 i

Step-by-step explanation:

Let's start with distributing: \frac1{4i}-\frac{3i}{4i} Simplify i with i in the second term, and rearrange.-\frac34 +\frac1{4i}. Since i in the denominator looks ugly, let's multiply top and bottom by i. -\frac34 +\frac i{4i^2} = -\frac34 +\frac i{4(-1)} =-\frac34 -\frac14 i. The middle passage is based on the fact that, by definition, i^2=-1

6 0
3 years ago
Calc 3 iiiiiiiiiiiiiiiiiiiiiiiiiiii
Lilit [14]

Take the Laplace transform of both sides:

L[y'' - 4y' + 8y] = L[δ(t - 1)]

I'll denote the Laplace transform of y = y(t) by Y = Y(s). Solve for Y :

(s²Y - s y(0) - y'(0)) - 4 (sY - y(0)) + 8Y = exp(-s) L[δ(t)]

s²Y - 4sY + 8Y = exp(-s)

(s² - 4s + 8) Y = exp(-s)

Y = exp(-s) / (s² - 4s + 8)

and complete the square in the denominator,

Y = exp(-s) / ((s - 2)^2 + 4)

Recall that

L⁻¹[F(s - c)] = exp(ct) f(t)

In order to apply this property, we multiply Y by exp(2)/exp(2), so that

Y = exp(-2) • exp(-s) exp(2) / ((s - 2)² + 4)

Y = exp(-2) • exp(-s + 2) / ((s - 2)² + 4)

Y = exp(-2) • exp(-(s - 2)) / ((s - 2)² + 4)

Then taking the inverse transform, we have

L⁻¹[Y] = exp(-2) L⁻¹[exp(-(s - 2)) / ((s - 2)² + 4)]

L⁻¹[Y] = exp(-2) exp(2t) L⁻¹[exp(-s) / (s² + 4)]

L⁻¹[Y] = exp(2t - 2) L⁻¹[exp(-s) / (s² + 4)]

Next, we recall another property,

L⁻¹[exp(-cs) F(s)] = u(t - c) f(t - c)

where F is the Laplace transform of f, and u(t) is the unit step function

u(t) = \begin{cases}1 & \text{if }t \ge 0 \\ 0 & \text{if }t < 0\end{cases}

To apply this property, we first identify c = 1 and F(s) = 1/(s² + 4), whose inverse transform is

L⁻¹[F(s)] = 1/2 L⁻¹[2/(s² + 2²)] = 1/2 sin(2t)

Then we find

L⁻¹[Y] = exp(2t - 2) u(t - 1) • 1/2 sin(2 (t - 1))

and so we end up with

y = 1/2 exp(2t - 2) u(t - 1) sin(2t - 2)

7 0
2 years ago
The area of a circle is 153.86 square meters. What is the diameter of the circle? Use 3.14 for π.
iren2701 [21]

Answer:

14m

Step-by-step explanation:

The area of a circle is given by

A = pi r^2

153.86 = 3.14 r^2

Divide each side by  3.14

153.86 /3.14 = r^2

49 = r^2

Take the square root of each side

sqrt(49) = sqrt(r^2)

7 = r

We want the diameter which is twice the radius

d = 2r

d =2*7

d =14

5 0
2 years ago
Xavier is buying bottled water for his basketball team. If he has $20 to spend on water, and each bottle of water
SSSSS [86.1K]

Answer:

Step-by-step explanation:

1.5 * 13 = 19.5 dollars

0.50 = 20 - 1.5x   where 0.50 is the amount of money he has left and x is the number of bottles of water  he buys

4 0
3 years ago
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