We are tasked to solve for the smallest angle using the law of cosines given that the three sides of the triangle are 4,5 and 6.
a=4 , b=5, c=6
Angle 1:
cosA = 5² + 6² - 4² / 2*5*6
A=41.41°
Angle 2:
cos B = 4²+6² -5² /2*4*6
B= 55.77°
Angle C:
C = 180° - 41.41° - 55.77°
C = 82.82°
The smallest angle is A which is equal to 41.41°.
The price of one senior citizen ticket is 8$ and one student ticket is 12$.
<h3>What is the equation?</h3>
The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
Let the price of one senior citizen ticket = x
And the price of one student ticket = y
Given that, on the first day of ticket sales, the school sold 13 senior citizen tickets and 13 student tickets for a total of $260
The school took in $212 on the second day by selling 13 senior citizen tickets and 9 student tickets.
13x +13y = 260
13x + 9y = 212
Subtract the equation from first
13x +13y - (13x + 9y) = 260 - 212
4y = 48
y = 48/4
y = 12
Substitute the value of y in the equation 13x + 9y = 212
13x + 9(12) = 212
13x + 108 = 212
13x = 212 - 108
13x = 104
x = 104/13
x = 8
Hence, the price of one senior citizen ticket is 8$ and one student ticket is 12$.
Learn more about the equation here:
brainly.com/question/10413253
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Answer:
A) 0.2g
Step-by-step explanation:
A.)
<span>s= 30m
u = ? ( initial velocity of the object )
a = 9.81 m/s^2 ( accn of free fall )
t = 1.5 s
s = ut + 1/2 at^2
\[u = \frac{ S - 1/2 a t^2 }{ t }\]
\[u = \frac{ 30 - ( 0.5 \times 9.81 \times 1.5^2) }{ 1.5 } \]
\[u = 12.6 m/s\]
</span>
b.)
<span>s = ut + 1/2 a t^2
u = 0 ,
s = 1/2 a t^2
\[s = \frac{ 1 }{ 2 } \times a \times t ^{2}\]
\[s = \frac{ 1 }{ 2 } \times 9.81 \times \left( \frac{ 12.6 }{ 9.81 } \right)^{2}\]
\[s = 8.0917...\]
\[therfore total distance = 8.0917 + 30 = 38.0917.. = 38.1 m \] </span>
