Answer:
The area of the shaded region is about 38.1 square centimeters.
Step-by-step explanation:
We want to find the area of the shaded region.
To do so, we can first find the area of the sector and then subtract the area of the triangle from the sector.
The given circle has a radius of 6 cm.
And the given sector has a central angle of 150°.
The area for a sector is given by the formula:
In this case, r = 6 and θ = 150°. Hence, the area of the sector is:
Now, we can find the area of the triangle. We can use an alternative formula:
Where a and b are the side lengths, and C is the angle between them.
Both side lengths of the triangle are the radii of the circle. So, both side lengths are 6.
And the angle C is 150°. Hence, the area of the triangle is:
The area of the shaded region is equivalent to the sector minus the triangle:
Therefore:
Use a calculator:
The area of the shaded region is about 38.1 square centimeters.
Answer:
the first one
Step-by-step explanation:
Well first you would start by setting up with a proportion.
In total, the girls paid $54+$22= $76
Thus 1 sister contributed $54/$76=x/100
The other sister contributed $22/$76=x/76
For each proportion, cross-multiply and simplify to get the percentage. The percentage will be the x
Answer:
The dimensions are 11 cm by 15 cm
Step-by-step explanation:
Area of a rectangle = (length)(width).
Let L represent the length and W the width.
Since L = W - 4, we have
Area of rectangle = (W - 4)W = 165 cm^2.
Thus, w^2 - 4W - 165 = 0. We can solve for W using the quadratic formula:
a = 1, b = -4 and c = -165. Thus,
-(-4) ± √ [ (-4)² - 4(1)(-165) ]
W = ---------------------------------------
2
4 ± √ [16 + 660 ]
W = ------------------------------
2
4 ± √ [ 676 ] 4 ± 26
W = ----------------------- = W = ------------- = W = 2 ± 13
2 2
Thus, W is 2 + 13 = 15. It cannot be negative, so we discard 2 - 13 = -11.
If the width, W, is 15, then the length is 4 less, or L = 11.
The dimensions are 11 cm by 15 cm
(-1.15)x3.2=
-3.68
Alright so I got -3.68 by multiplying -1.15x3.2. We get a negative number since the first number is negative.
