Answer:
The other side was decreased to approximately .89 times its original size, meaning it was reduced by approximately 11%
Step-by-step explanation:
We can start with the basic equation for the area of a rectangle:
l × w = a
And now express the changes described above as an equation, using "p" as the amount that the width is changed:
(l × 1.1) × (w × p) = a × .98
Now let's rearrange both of those equations to solve for a / l. Starting with the first and easiest:
w = a/l
now the second one:
1.1l × wp = 0.98a
wp = 0.98a / 1.1l
1.1 wp / 0.98 = a/l
Now with both of those equalling a/l, we can equate them:
1.1 wp / 0.98 = w
We can then divide both sides by w, eliminating it
1.1wp / 0.98w = w/w
1.1p / 0.98 = 1
And solve for p
1.1p = 0.98
p = 0.98 / 1.1
p ≈ 0.89
So the width is scaled by approximately 89%
We can double check that too. Let's multiply that by the scaled length and see if we get the two percent decrease:
.89 × 1.1 = 0.979
That should be 0.98, and we're close enough. That difference of 1/1000 is due to rounding the 0.98 / 1.1 to .89. The actual result of that fraction is 0.89090909... if we multiply that by 1.1, we get exactly .98.
Since the perimeter is the sum of the length of all sides we multiply width and length by 2 and then add them together
Answer:
X=9 or x=-9
Step-by-step explanation:
X^2=81
Can be written as
x^2-81=0
Factorize by the property:
a^2-b^2=(a-b)(a+b)
So the expression becomes:
(x-9)(x+9)=0
Therefore, either x-9=0or x+9=0
Then the solutions are x=9 or x=-9
The question in English
<span>1 Determine the length and area of a circle whose measures are:
a) radius 11cm b) radius 4.2 cm c) diameter 42.3 cm
2 considering that a large traditional pizza is 36 cm in radius and a small traditional pizza has 26 cm.Determine the difference between the area of the two pizzas
3.a worker spends 3 hours to clear a circular terrain of 6 meters radius. If the terrain was 12 meters radius, how much time would the worker spend to clean such terrain ???
4, transform the following arcs into radians
a) 27 ° b) 81 ° c) 144 ° d) 225 ° d) 315 °
Part 1)
we know that
length of a circle is equal to the circumference
circumference=2*pi*r
area of the circle=pi*r²
part a ) radius 11 cm
</span><span>circumference=2*pi*11-----> 69.08 cm
area of the circle=pi*11²----> 379.94 cm²
</span>
<span><span>part b) radius 4.2 cm
</span><span>circumference=2*pi*4.2-----> 26.38 cm
area of the circle=pi*4.2²----> 55.39 cm²
</span></span>
<span><span>part c ) diameter 42.3 cm
radius r=42.3/2=21.15 cm
</span><span>circumference=2*pi*21.15-----> 132.82 cm
area of the circle=pi*21.15²----> 1404.59 cm²
Part 2)
</span></span>
<span>area large traditional pizza
r=36 cm
area=pi*36²----> 4069.44 cm²
area </span><span>small traditional pizza
r=26 cm
area=pi*26²-----> 2122.64 cm²
</span><span>difference between the area of the two pizzas
=4069.44-2122.64
difference </span><span>between the area of the two pizzas=1946.80 cm²
Part 3)
Area of the </span><span>circular terrain of 6 meters radius
area=pi*6²-----> 113.04 m²
</span><span>Area of the <span>circular terrain of 12 meters radius
area=pi*12²-----> 452.16 m²
</span></span>
if a <span>worker spends 3 hours to clear a circular terrain of--------> 113.04 m²
x hours---------------------------> 452.16 m²
x=452.16*3/113.04-----> x=12 hours
Part 4) </span><span>transform the following arcs into radians
a) 27°
pi radians------> 180°
x radians-----> 27°
x=27*pi/180-----> x=0.15*pi radians------> 0.47 radians
</span><span>b) 81°
pi radians------> 180°
x radians-----> 81°
x=81*pi/180-----> x=0.45*pi radians------> 1.41 radians
</span>
<span>c) 144°
pi radians------> 180°
x radians-----> 144°
x=144*pi/180-----> x=0.80*pi radians------> 2.51 radians
</span>
<span>d) 225°
pi radians------> 180°
x radians-----> 225°
x=225*pi/180-----> x=1.25*pi radians------> 3.93 radians
</span>
<span>e) 315°
pi radians------> 180°
x radians-----> 315°
x=315*pi/180-----> x=1.75*pi radians------> 5.50 radians
</span><span>
the answer in Portuguese
</span>
<span>Parte 1)
</span>
<span>nós sabemos isso
</span><span>comprimento de um círculo é igual à circunferência
</span><span>circunferência=2*pi*r
</span>área do círculo<span>=pi*r²
parte a )
</span>raio<span> 11 cm
</span><span>circunferência=2*pi*11-----> 69.08 cm
</span><span><span>área do círculo=pi*11²----> 379.94 cm²
</span>
<span>parte b) raio 4.2 cm
</span></span><span>circunferência=2*pi*4.2-----> 26.38 cm
</span><span><span>área do círculo=pi*4.2²----> 55.39 cm²
</span>
<span>parte c )
</span></span>diâmetro<span> 42.3 cm
</span><span>raio r=42.3/2=21.15 cm
</span><span>circunferência=2*pi*21.15-----> 132.82 cm
</span><span><span>área do círculo=pi*21.15²----> 1404.59 cm²
Parte 2)
</span>
</span>
área grande pizza tradicional<span>r=36 cm
</span><span>área=pi*36²----> 4069.44 cm²
</span>
<span>área pequena pizza tradicional<span>
r=26 cm
</span></span><span>área=pi*26²-----> 2122.64 cm²
</span>diferença entre a área das duas pizzas<span> =4069.44-2122.64
</span>diferença entre a área das duas pizzas<span>=1946.80 cm²
Parte 3)
</span><span><span>
Área do terreno circular de 6 metros de raio</span>
</span><span>área=pi*6²-----> 113.04 m²
</span>
<span>Área do terreno circular de 12 metros de raio
</span><span><span>área=pi*12²-----> 452.16 m²
</span>
</span>se um trabalhador gastar 3 horas para limpar um terreno <span>-----> 113.04 m²
x hours---------------------------> 452.16 m²
x=452.16*3/113.04-----> x=12 horas
Parte 4) </span><span><span>transformar os seguintes arcos em radianos
a) 27°
pi radianos------> 180°
x radianos-----> 27°
x=27*pi/180-----> x=0.15*pi radianos------> 0.47 radianos
</span><span>b) 81°
pi radianos------> 180°
x radianos-----> 81°
x=81*pi/180-----> x=0.45*pi radianos------> 1.41 radianos
</span>
<span>c) 144°
pi radianos------> 180°
x radianos-----> 144°
x=144*pi/180-----> x=0.80*pi radianos------> 2.51 radianos
</span>
<span>d) 225°
pi radianos------> 180°
x radianos-----> 225°
x=225*pi/180-----> x=1.25*pi radianos------> 3.93 radianos
</span>
<span>e) 315°
pi radianos------> 180°
x radianos-----> 315°
x=315*pi/180-----> x=1.75*pi radianos------> 5.50 radianos</span></span>
