Using cosine rule, the length of the required side = sqrt(32^2 + 35^2 - 2 x 32 x 35cos 120)
= sqrt(1024 + 1225 - (-1120))
= sqrt(2249 + 1120)
= sqrt(3369)
= 58.04
We know that
angle (3x) and angle (9x) are supplementary angles
so
3x+9x=180°------> 12x=180°------> x=180°/12-----> x=15°
angle (9x) and angle (1) are supplementary angles
so
9x+∡1=180---------> 9*15+∡1=180
∡1=180-9*15---------> ∡1=180-135------> ∡1=45°
the answer is
∡1 is 45°
alternative method
angle 1 = angle 3x----------> vertical angles
∡1=3x-----> 3*15-----> 45°
the area A of the cross section of the column is
.
<u>Step-by-step explanation:</u>
Here we have , building engineer analyzes a concrete column with a circular cross section. The circumference of the column is 18π, pi meters. We need to find What is the area A of the cross section of the column .Let's find out:
We know that , Circumference of circle = 
⇒ 
⇒ 
⇒ 
⇒ 
⇒ 
We know that area of circle = 
⇒ 
⇒ 
⇒ 
Therefore , the area A of the cross section of the column is
.
Answer:
P( At least one of the two cards was a heart)=7/16
Step-by-step explanation:
The solution to this question can be found in two ways.
First way: Since total number of heart in a deck are four,
Probability that neither of two cards had a heart is that at both times the card drawn was not a heart, since it is an independent event, thus probability both were not heart=
×
=
Thus, Probability that at least one of the two cards was a heart= 1- P( Neither of two cards had a heart= 1- 
=
Second way:
Probability that first card drawn is a heart and the second one is not a heart=
×
=
Probability that the first card drawn is not a heart and the second one is a heart=
×
=
Probability that both cards drawn are hearts=
×
=
Adding all these probabilities, we have the probability that at least one of the card drawn was heart= 