Answer:
32.59 (nearest hundredth)
Step-by-step explanation:
<u />
<u>Geometric sequence</u>
General form of a geometric sequence: 
(where a is the first term and r is the common ratio)
Given:
Therefore:
<u>Sum of the first n terms of a geometric series</u>:
To find the sum of the first 20 terms, substitute the found values of a and r, together with n = 20, into the formula:
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
R(0,0)
A=((0+2a)/2,(0+2b)/2)=(a,b)
S(2a,2b)
B=((2a+2c)/2,(2b+2d)/2)=(a+c,b+d)
T(2c,2d)
C=((2c+2c)/2,(2d+0)/2)=(2c,d)
V(2c,0)
D=((2c+0)/2,(0+0)/2)=(c,0)
R(0,0)
slope of AB=(b+d-b)/(a+c-a)=d/c
slope of DC=(d-0)/(2c-c)=d/c
slope of AD=(0-b)/(c-a)=-b/(c-a)
slope of BC=(d-b-d)/(2c-a-c)=-b/(c-a)
Answer:
Volume of a cup
The shape of the cup is a cylinder. The volume of a cylinder is:
\text{Volume of a cylinder}=\pi \times (radius)^2\times heightVolume of a cylinder=π×(radius)
2
×height
The diameter fo the cup is half the diameter: 2in/2 = 1in.
Substitute radius = 1 in, and height = 4 in in the formula for the volume of a cylinder:
\text{Volume of the cup}=\pi \times (1in)^2\times 4in\approx 12.57in^3Volume of the cup=π×(1in)
2
×4in≈12.57in
3
2. Volume of the sink:
The volume of the sink is 1072in³ (note the units is in³ and not in).
3. Divide the volume of the sink by the volume of the cup.
This gives the number of cups that contain a volume equal to the volume of the sink:
\dfrac{1072in^3}{12.57in^3}=85.3cups\approx 85cups
12.57in
3
Step-by-step explanation:
Answer:
The equation is y= 0,65 x
If x is the price of the ticket without the coupon, and the theater offers a discount if you have a coupon, then having a coupon means that the price a person ultimately pays (y) is the original price (x) minus a 35% of this price: y= x -0.35 x . By association: y= (1-0.35) x and then y= 0.65 x.
The line should be in the first quadrant because the first quadrant allows you to represent a situation in which the dependent variable (y) and the independent variable (x) are both positive. This is the case in this exercise, because both prices, the one without discount (x) and the one with discount (y) are necessary positive (you can not pay a negative price!).
Step-by-step explanation:
- The price without discount (or without the coupon) is x.
- The price with discount (or with coupon) is y.
- y and x are both related: y is a percentage of x, specifically, y is 35% smaller than x. This means that y =0.65 x.
