Answer:
<em>h = 8.54 units</em>
Step-by-step explanation:
<u>The Law of Cosines
</u>
It relates the length of the sides of a triangle with one of its internal angles.
Let a,b, and c be the length of the sides of a given triangle, and x the included angle between sides a and b, then the following relation applies:
Since we know the values of all three side lengths, we solve the equation for x:
For the triangle ABC in the image, a=10, b=15, c=13, thus:
Thus, A = 58.67°
For the right triangle of height h and hypotenuse 10, we use the sine ratio:
Solving for h:
h = 8.54 units
Answer:
<em>x = 49°</em>
Step-by-step explanation:
<u>Angles in a Triangle</u>
The sum of the internal angles in any triangle adds up to 180°.
The figure shows a triangle that includes two angles with the same tick mark. This means they are congruent, i.e. they measure the same.
The larger triangle has three defined angles: 43°, 39°, and 2x. Since the sum of them is 180°:
43° + 39° + 2x = 180°
Operating:
82° + 2x = 180°
Subtracting 82°:
2x = 180° - 82° = 98°
x = 98°/2 = 49°
x = 49°
The ticket price which will maximize the student's council is: C. $3.10.
<h3>What is price?</h3>
Price can be defined as an amount of money which is primarily set by the seller of a product, and it must be paid by a buyer to the seller, so as to enable the acquisition of this product.
Based on the information provided about Valley High School student council, we can logically deduce the following data:
- Total number of students = 420 students.
- Lowest ticket price = $2.00.
- Increase in ticket price = $0.20.
- Attendance = 20 fewer students
<h3>How to determine the ticket price?</h3>
Mathematically, the equation which model the profit is given by:
Profit = price × number of tickets sold
P(x) = (2 + 0.2x)(420 - 20x)
P(x) = 840 + 84x - 40x - 4x²
P(x) = -4x² + 44x + 840.
For any quadratic equation with a parabolic curve, the axis of symmetry is given by:
Xmax = -b/2a
Xmax = -44/2(-4)
Xmax = -44/-8.
Xmax = 5.5
Ticket price for maximum profit is given by:
Ticket price = 2 + 0.2x
Ticket price = 2 + 0.2(5.5)
Ticket price = $3.10.
Read more on maximized profit here: brainly.com/question/13800671
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Answer
The expression is equivalent to sin^{2}x
The first step is to multiply the two expressions between parentheses :
(II)
There is a trigonometric identity that states :
Working with this expression :
⇒
(I)
Using the equation (I) in (II) :
⇒
Read more on Brainly.com -
brainly.com/question/3907632#readmore
The solid that has five faces , four lateral faces, one base, five vertices, and eight edges would be :
Square pyramid
Hope this helps
