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4 years ago

Can someone please explain Thales' theorem

Mathematics

1 answer:

iren2701 [21]4 years ago

7 0

Answer:

In geometry, Thales's theorem states that if A, B, and C are distinct points on a circle where the line AC is a diameter, then the angle ∠ABC is a right angle.

or in simpler words ;

angles formed in a semicircle that includes the diameter forms a 90 degree angle at the angle opposite to the diameter. since the diameter divides it into two equal halves we reffer to it as a semicircle .

IF U STILL DIDNT UNDERSTAND , THEN :

remember that when we talk about thales thorem , you should focus at some main things:

angles are constructed inside a circle.
the diameter is dividing the circle into two equal halves.(two semicircles)
the angles formed are using the diameter as a base.

so the thorem says that, in the semicircle formed by a diameter .
when an angle is made opposite the base , it makes a 90 degree angle

all angles made in a semicircle, form a 90 degree angle , opposte the diameter.

#answerwithquality #BAL

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Fernando has two equally-sized containers of clay which he is using to build a pyramid-like structure. The finished structure wi

evablogger [386]

Answer:

Fernando does not have enough clay to finish the structure since, the expressions for the volume left are not the same.

Step-by-step explanation:

Let w be the length of the longest slab. Since each slab is 2 inches less than the one beneath it, we have the width of the other 3 slabs as w - 2, w - 2 - 2 = w - 4 and w - 4 - 2 = w - 6 respectively.

Since the base of each slab is a square and has thickness 2 inches, the volume of each slab from largest to smallest is thus 2w², 2(w - 2)², 2(w - 4)² and 2(w - 6)² respectively.

We have that we have half of the container of clay left after forming the first two slabs(which are the bottom-most slabs). Let V be the volume of each clay container. Since we have half left, that is V/2, we have used 2V - V/2 = 3V/2 to make the two bottom-most slabs.

So, 3V/2 = 2w² + 2(w - 2)²

= 2w² + 2(w² - 4w + 4)

= 2w² + 2w² - 8w + 8

= 4w² - 8w + 8

= 4(w² - 2w + 2) (1)

Also we want to know if V/2 is equal to the volume of the two top-most slabs.

So, V/2 = 2(w - 4)² + 2(w - 6)²

= 2(w² - 8w + 16) + 2(w² - 12w + 36)

= 2w² - 16w + 32 + 2w² - 24w + 72

= 4w² - 40w + 104

= 4(w² - 10w + 26)

From (1) V/2 = 4(w² - 2w + 2)/3 ≠ 4(w² - 10w + 26)

Since the expressions for the remaining volume are not the same, Fernando does not have enough clay to finish the structure.

4 0

3 years ago

The value of a motorbike depreciates by 32% per year. Work out the current value of a motorbike bought 5 years ago for £3600

DaniilM [7]

$\bf \qquad \textit{Amount for Exponential Decay}
\\\\
A=P(1 - r)^t\qquad 
\begin{cases}
A=\textit{accumulated amount}\\
P=\textit{initial amount}\to &3600\\
r=rate\to 32\%\to \frac{32}{100}\to &0.32\\
t=\textit{elapsed time}\to &5\\
\end{cases}
\\\\\\
A=3600(1-0.32)^5\implies A=3600(0.68)^5\implies A\approx 523.41601$

3 0

4 years ago

What is the rate of change and initial value for the linear relation that includes the points shown in the table?

Wittaler [7]

Answer:

Initial value $12$ , rate of change: $-2$

Step-by-step explanation:

Step 1

Find the rate of change

we know that

In a linear equation the rate of change is equal to the slope

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

we have

$A(1,10)\ B(2,8)$

Substitute the values

$m=\frac{8-10}{2-1}$

$m=-2$ ----> rate of change

Step 2

Find the initial value

The equation of the line into slope-point form is equal to

$y-y1=m(x-x1)$

Substitute

$y-10=-2(x-1)$

$y=-2x+2+10$ $y=-2x+12$

The initial value is the value of y when the value of x is equal to zero (is the y-intercept)

$y=-2*0+12=12$ ----> initial value

7 0

3 years ago

Read 2 more answers

The square prism has a base length of 2 ft. Which describes the cross section of the prism that iS perpendicular to the

Anon25 [30]

Answer:

A-a rectangle with two 12-ft sides and two 2-ft sides

Step-by-step explanation:

Got it right on edge

7 0

3 years ago

PLEASE HELP!

Juliette [100K]

Answer: 135 miles

Step-by-step explanation: If you go 70 miles in ones hour, then you’ll go 140 miles in 2 hours. Then it took 6 minutes longer because of traffic, and in traffic he drove 1 mile excluding 5 because he was 5 mph slower.

6 0

3 years ago

Read 2 more answers