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3 years ago

13

Which transformation will create a similar and a congruent triangle?

1 answer:

Reptile [31]3 years ago

7 0

I believe it’s translation

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10. -0.12+0.16i

11. 1.5+1.5i

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3 years ago

A Norman window is a rectangle with a semicircle on top. Suppose that the perimeter of a particular Norman window is to be 25 fe

Varvara68 [4.7K]

Answer:

$Length =\frac{25}{4 + \pi}$ and $Width = \frac{50}{4+\pi}$

Step-by-step explanation:

This question is better understood with an attachment.

See attachment for illustration.

Given

<em>Represent Perimeter with P</em>

$P = 25ft$

Required

Determine the dimension of the rectangle that maximizes the area

First, we calculate the perimeter of the rectangular part of the window.

From the attachment, the rectangle is not closed at the top.

So, The perimeter would be the sum of the three closed sides

Where

$Width = 2x$

$Length = y$

So:

$P_{Rectangle} = y + y + 2x$

$P_{Rectangle} = 2y + 2x$

Next, we determine the circumference of the semi circle.

Circumference of a semicircle is calculated as:

$C = \frac{1}{2}\pi r$

From the attachment,

$Radius (r) = x$

So, we have:

$C = \frac{1}{2}2\pi * x$

$C = \pi x$

So, the perimeter of the window is:

$P = P_{Rectangle} + C$

$P =2y + 2x + \pi x$

Recall that: $P = 25$

So, we have:

$25 =2y + 2x +\pi x$

Make 2y the subject

$2y = 25 - 2x - \pi x$

Make y the subject:

$y = \frac{25}{2} - \frac{2x}{2} - \frac{\pi x}{2}$

$y = \frac{25}{2} - x - \frac{\pi x}{2}$

Next, we determine the area (A) of the window

A = Area of Rectangle + Area of Semicircle

$A = 2x * y + \frac{1}{2}\pi r^2$

$A = 2xy + \frac{1}{2}\pi r^2$

Recall that

$Radius (r) = x$

$A = 2xy + \frac{1}{2}\pi x^2$

Substitute $\frac{25}{2} - x - \frac{\pi x}{2}$ for y in $A = 2xy + \frac{1}{2}\pi x^2$

$A = 2x(\frac{25}{2} - x - \frac{\pi x}{2}) + \frac{1}{2}\pi x^2$

Open Bracket

$A = 2x * \frac{25}{2} - 2x * x - 2x * \frac{\pi x}{2} + \frac{1}{2}\pi x^2$

$A = 25x - 2x^2 - \pi x^2 + \frac{1}{2}\pi x^2$

$A = 25x - 2x^2 - \frac{1}{2}\pi x^2$

To maximize area, we have to determine differentiate both sides and set A' = 0

Differentiate

$A' = 25 - 4x - \pi x$

$A' = 0$

So, we have:

$0 = 25 - 4x - \pi x$

Factorize:

$0 = 25 -x(4 + \pi)$

$-25 =-x(4 + \pi)$

Solve for x

$x = \frac{-25}{-(4+\pi)}$

$x = \frac{25}{4+\pi}$

Recall that

$Width = 2x$

$Width = 2(\frac{25}{4+\pi})$

$Width = \frac{50}{4+\pi}$

Recall that:

$y = \frac{25}{2} - x - \frac{\pi x}{2}$

Substitute $\frac{25}{4+\pi}$ for x

$y = \frac{25}{2} - (\frac{25}{4+\pi}) - \frac{\pi (\frac{25}{4+\pi})}{2}$

$y = \frac{25}{2} - (\frac{25}{4+\pi}) - \frac{\frac{25\pi}{4+\pi}}{2}$

$y = \frac{25}{2} - (\frac{25}{4+\pi}) - \frac{25\pi}{4+\pi} * \frac{1}{2}$

$y = \frac{25}{2} - \frac{25}{4+\pi} - \frac{25\pi}{2(4+\pi)}$

$y = \frac{25(4+\pi) - 25 * 2 - 25\pi}{2(4 + \pi)}$

$y = \frac{100+25\pi - 50 - 25\pi}{2(4 + \pi)}$

$y = \frac{100- 50+25\pi - 25\pi}{2(4 + \pi)}$

$y = \frac{50}{2(4 + \pi)}$

$y = \frac{25}{4 + \pi}$

Recall that:

$Length = y$

So:

$Length =\frac{25}{4 + \pi}$

Hence, the dimension of the rectangle is:

<em></em> $Length =\frac{25}{4 + \pi}$ <em> and </em> $Width = \frac{50}{4+\pi}$ <em></em>

3 0

3 years ago

Find the amount and compound interest on 5000 at 6% per annum for 3 years annual

Goryan [66]

Answer:

The amount is 5,955.08

Step-by-step explanation:

Here, we want to calculate compound interest

We can find this by using the compound interest formula

A = P( 1 + r/n)^nt

A is amount

P

is the principal = 5,000

r is the interest rate = 6% = 6/100 = 0.06

n is the number of times per year in which the interest is compounded = 1

t is the number of years = 3

Substituting these values;

A = 5,000(1 + 0.06/1)^3(1)

A = 5000(1.06)^3

A = 5,955.08

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3 years ago

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const2013 [10]

Answer:

The x-intercept is 1.5

The y-intercept is -0.9

Step-by-step explanation: hope this helps!

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3 years ago

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