Answer:
The volume of the silo is about 142.3 cubic meters. Try It! The volume of a sphere is twice the volume of a cone that has the same circular base and height. The formula for the volume of a sphere with radius r is V= r3.
Step-by-step explanation:
Notice that if a cone and a sphere have equal radius, and if the cone has a height equal to its radius, then the cone will fill the sphere exactly four times. This means that the volume of the sphere is $4 times the volume of the cone.
Answer:
1. numbers 2. numbers 3. numbers 4. numbers 5. numbers 6. numbers 7. numbers 8. numbers 9. numbers 10. numbers 11. numbers 12. numbers
Step-by-step explanation:
Answer:
B.70
Step-by-step explanation:
For one or two angles are complementary angle(s), they have to equal 90°.
So, we need to find the larger angle, but what about the other?
Let x be the other angle and y be the angle we are looking for
x + y = 90
Lets look for x first, since one angle is ten less than four times the angle we are looking for or visa versa, we must:
y = 4x - 10
For an exchange, lets take out the y variable for another x variable:
So now we should have x + 4x - 10 = 90
Combine like terms and do cross equation :
x + 4x -10 = 90
5x - 10 = 90
Add 10 to both sides:
5x = 100
100/5 = 20
So <u><em>x=20</em></u>
<u><em></em></u>
Now for y which is what we are looking for,
y = 4x - 10
Since x is 20, plug it in
y = 80 - 10
y=70 is our larger angle
#1) A
#2) B
#3) C
#5) A
#7) D
#10) D
#11) D
#14) A
#15) D
#16) A
#19) D
Explanation
#1) If the data set is linear, the slope will be constant throughout the entire data set. For data set A, the slope between the first two points is:
m = (y₂-y₁)/(x₂-x₁) = (1--2)/(3-1) = 3/2
Between the second two points,
m=(4-1)/(5-3) = 3/2
Between the third pairs of points,
m=(7-4)/(7-5) = 3/2
The slope is constant throughout the entire set. The set is also increasing; as x increases, y increases as well.
#2) Substituting 4 for y and 1 for x,
y = (x+1)²
4 = (1+1)² = 2²
9 = (1+2)² = 3²
16 = (1+3)² = 4²
This works for each point, so this is the solution.
#3) Since he runs 10 laps per hour t, this is 10t. Adding the first lap to this, we get y=10t+1.
#5) If a sequence is arithmetic, each term is found by adding a constant (called the common difference) to the previous term. If the common difference is 2, this means that 2 was added each time. This only works for choice A.
#7) For x to vary directly as y, this means that y/x = k; in other words, the quotient of y and x is constant for every point.
#10) The formula for slope is:
m=(y₂-y₁)/(x₂-x₁)
Using the information we're given, we have
3=(d-5)/(4-2)
3=(d-5)/2
Multiply both sides by 2:
3*2 = ((d-5)/2)*2
6 = d-5
Add 5 to both sides:
6+5 = d-5+5
11 = d
#11) Using point slope form,
y-y₁ = m(x-x₁)
y-1 = 3(x--2)
y-1 = 3(x+2)
Using the distributive property,
y-1 = 3*x + 3*2
y-1 = 3x + 6
Add 1 to both sides:
y-1+1 = 3x+6+1
y=3x+7
#14) If two lines are parallel, they have the same slope. The slope of the given equation is 4; the only one with a slope of 4 is A.
#15) If two lines are perpendicular, they have slopes that are negative reciprocals (opposite signs and flipped). The slope of the given equation is 2; this means the slope of the perpendicular line would be -1/2. The only one with this slope is D.
#16) The two equations are not the same, so there are not infinitely many solutions. The variables do not both cancel, so there is at least one solution. This only leaves one solution as the answer.
#19) Using 1 for 7 and 4 for x, we check each equation. The only one that comes out correct is D.
