Gas cylinders are not weighed accurately. On complaint, 10 specimen cylinders were taken from a godown at random. Following are the observations (given in picture)
Find the probability that a cylinder selected at random weighs more than 30kg
Answers
Answer:
factorise completely the following polynomial 3x
3
+2x
2
−19x+6
Medium
Video Explanation
Solution To Question ID 578138
Answer
Let f(x)=3x
2
+2x
2
−19x+6
Using hit and trial method,
f(1)=3+2−19+6
=0
f(−1)=−3+2+19+6
=0
f(2)=24+8−38+6=0
∴(x−2) is a factor of f(x).
3x
2
+8x−3
Now, x−2
)3x
2
+2x
2
−19x+6
3x
2
−6x
----------------------------------
8x
2
−19x
8x
2
−16x
------------------------------------
−3x+6
−3x+6
-------------------------------------
x
--------------------------------------
To factorise 3x
2
+8x−3
=3x
2
+9x−x−3
=3x(x+3)−1(x+3)
=(3x−1)(x+3)
Hence 3x
3
+2x
3
−19x+6=(x−2)(3x−1)(x+3)
Answer verified by Toppr
Answer:
Given: Each side of an equilateral triangle is 30 cm.
⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━⠀⠀⠀
\underline{\bf{\dag} \:\mathfrak{As\;we\;know\: that\: :}}
†Asweknowthat:
⠀⠀⠀⠀
\star\:\boxed{\sf{\pink{Area \: of \: equilateral \: \triangle = \dfrac{\sqrt{3}}{\:4} (a)^2 \ cm}}}⋆
Areaofequilateral△=
4
3
(a)
2
cm
⠀⠀⠀⠀⠀⠀⠀⠀⠀
Here, a is each side of the equilateral triangle.
⠀⠀⠀⠀⠀⠀⠀
Therefore,
⠀⠀⠀⠀
\begin{gathered}:\implies\sf Area_{\:\triangle} = \dfrac{\sqrt{3}}{2} \times \Big(30 \Big)^2 \\\\\\:\implies\sf Area_{\:\triangle} = \dfrac{\sqrt{3}}{2} \times 30 \times 30 \\\\\\:\implies{\underline{\boxed{\frak{\purple{Area_{\:\triangle} = 225\sqrt{3}\:cm^2}}}}}\:\bigstar\end{gathered}
:⟹Area
△
=
2
3
×(30)
2
:⟹Area
△
=
2
3
×30×30
:⟹
Area
△
=225
3
cm
2
★
⠀⠀⠀⠀⠀⠀⠀
\therefore\:{\underline{\sf{Hence, \ Area \ of \ equilateral \ \triangle \ is \ \bf{225 \sqrt{3} \ cm^2}.}}}∴
Hence, Area of equilateral △ is 225
3
cm
2
.
⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━⠀⠀⠀⠀⠀⠀⠀⠀
\begin{gathered}\qquad\qquad\boxed{\bf{\mid{\overline{\underline{\pink{\bigstar\: Additional \: Information \: :}}}}}\mid}\\\\\end{gathered}
∣
★AdditionalInformation:
∣
Equilateral triangle is a triangle in which all the three sides have equal length.
The sum of all three angles of an equilateral triangle is equal to 180°
Altitude of equilateral triangle = \sf\dfrac{\sqrt{3}a}{2}
2
3
a
Perimeter of equilateral triangle = Sum of all sides. (a + a + a)