The number π is a mathematical constant, the ratio of a circle's circumference to its diameter, commonly approximated as 3.14159. It has been represented by the Greek letter "π" since the mid-18th century, though it is also sometimes spelled out as "pi" (/paɪ/
Answer:
-5
Step-by-step explanation:
Moving all terms of the quadratic to one side, we have
.
A quadratic has one real solution when the discriminant is equal to 0. In a quadratic 
, the discriminant is 
.
(The discriminant is more commonly known as 
, but I changed the variable since we already have a 
in the quadratic given.)
In the quadratic above, we have 
, 
, and 
. Plugging this into the formula for the discriminant, we have
.
Using the distributive property to expand and simplifying, the expression becomes
Setting the discriminant equal to 0 gives
.
We can then solve the equation as usual: first, divide by 2 on both sides:
.
Squaring both sides gives
,
and subtracting 5 from both sides, we have
Answer:
10
Step-by-step explanation:
5/6 =0.8333
12x0.8333 = 10
Suggest you use some punctuation here: "The h<span>eight of window is 0.6 feet less than 2.5 times it width. The height of window is 4.9 feet. Find the width of the window."
height of window = 4.9 feet = 2.5(width) - 0.6 feet.
simplify this equation by adding 0.6 feet to both sides of the equation:
4.9 feet + 0.6 feet = 2.5 (width); find width:
5.5 feet = 2.5 (width)
Dividing both sides of this equation by 2.5 will result in an equation for the width of the window, in feet.</span>
Answer: Area of the shaded region is 6.867 square cm
Step-by-step explanation:
The shaded area corresponds to the difference of the area of the rectangle and the area of the semicircle.
Area of the rectangle = 4 times 8 = 32 cm^2
Area of the semicircle = 0.5 * pi * r^2 (where r is the radius, i.e., half of the diameters, i.e., 4 cm). So Area = 0.5*pi*4^2 = 25.133 cm^2
The difference: 32 - 25.133 = 6.867 cm^2 (area of the shaded region)
