The square (call it 
) has one vertex at the origin (0, 0, 0) and one edge on the y-axis, which tells us another vertex is (0, 3, 0). The normal vector to the plane is 
, which is enough information to figure out the equation of the plane containing :
We can parameterize this surface by
for 
and 
. Then the flux of 
, assumed to be
,
is
I'm going to separate this into sections so it makes more sense for you to read. For the problems with π where you have to round, ask your teacher where to round, unless your textbook specifies it:
A – 100 cm^2
To calculate area of squares, you multiply l • w. It's a square, so all sides are equal, and since we know that one side = 10 cm, the area is 10 • 10 = 100
B – πr^2 (not sure if the r shows up very well, so I'm retyping it in words - pi • radius squared)
C – 25π cm^2 or an approximate round like 78.54 cm^2 (ask your teacher about this – it could be to the nearest tenth, hundredth, etc.)
To find the area of a circle, you must follow the formula πr^2. In this case, the diameter is 10. The radius is half the diameter, so to substitute the values you must find 10 ÷ 2 = 5. So the radius is 5 cm. From there you can substitute r for 5, ending up with π • 5^2. 5^2 = 25, so the area is 25π, or about 78.54, depending on where the question wants you to round.
D – An approximate round (to the nearest hundredth it is 21.46 cm^2)
To find the area of the shaded region, just subtract the circle's area from the square's area, or 100 – 25π ≈ 21.46. Again, though, ask your teacher about where to round, unless your textbook specifies it.
E – dπ (diameter • pi)
F – 10π cm^2 or an approximate round like 31.42 cm^2
The diameter is 10. 10π ≈ 31.42
Hope this helps!
Answer:
19.5 ounces of spices
Step-by-step explanation:
Raheem made 14 ounces of curry sauce which contained (among other things), 3.25 ounces of spices. He wants to make a larger batch for a family dinner and decides he will need a total of 84 ounces of sauce altogether. How many ounces of spices will he need to complete his recipe?
The question above is calculated as:
14 ounces of sauce = 3.25 ounces of spices
84 ounces of sauce = x ounces of spices
Cross Multiply
14x = 84 × 3.25
x = 84 × 3.25/14
x = 19.5 ounces of spices
Hence, for 84 ounces of curry sauce he would need 19.5 ounces of spices
Answer:
Match the vocabulary words to the proper definition.
1. a decimal that ends
2
repeating decimal
2. a decimal whose digits to the right of the decimal point repeat indefinitely
1
terminating decimal
3. a set of three dots at the end of a number used to indicate that the number will infinitely continue in the same pattern
4
irrational number
4. a horizontal bar used in mathematical notation; in fractions, it is the bar that separates the numerator from the denominator; in repeating decimals, it indicates a group of repeating numbers
6
vinculum
5. a number that can be written as a ratio in fraction form
3
ellipsis
6. a number that, when in decimal form, does not terminate or repeat
5
rational number
Step-by-step explanation:
