the local maximum is at x = -2.2 and has a value of 72.576
The opposite angles of a parallelogram are equal.
Therefore
m∠A = m∠C, so that
5y - 3 = 3y + 27
Subtract 3y from each side.
5y - 3y - 3 = 3y - 3y + 27
2y - 3 = 27
Add 3 to each side.
2y - 3 + 3 = 27 + 3
2y = 30
y = 30/2 = 15
Therefore
m∠A = 5*15 - 3 = 72°
m∠C = 72°
Let x = m∠B
Then x = , m∠B = m∠C
Because the sum of the angles in the parallelogram is 360°, therefore
x + x + 72 + 72 = 360
2x = 360-144 = 216
x = 216/2 = 108
Answer:
m∠A = 72°
m∠B = 108°
To solve these type of problems you need to use the pythagoras theorem ⇨ Hypotenuse² = Base² + Altitude².
Here,
- Altitude = 1.6 cm.
- Base = 1.2 cm
- Hypotenuse = x
Now, let's solve for x.
Hypotenuse² = Base² + Altitude²
x² = (1.2)² + (1.6)²
x² = 1.44 + 2.56
x² = 4
x = √4
x = <em><u>2</u></em><em><u>.</u></em>
- So, the value of x is <em><u>2</u><u> </u><u>cm.</u></em>
<h3>
<u>NOTE</u><u> </u><u>:</u><u>-</u></h3>
- Pythagoras theorem can be used only in the cases of right-angled triangles. Here, it's given that the triangle is right angled so we can use this theorem.
- To solve the squares if decimals, take them as whole numbers & then just add the decimal points. For example, ⇨ for (1.2)², take it as 12² , then multiply 12 by 12, you'll get 144. Now, add the decimal place accordingly ⇨ 1.44 . So, (1.2)² = 1.44.