A cone is placed inside a cylinder as shown. The radius of the cone is half the radius of the cylinder. The height of the cone is equal to the radius of the cylinder. What is the volume of the cone in terms of the radius, r?
Answers
radius of the cone = half the radius of the cylinder
height of the cone = radius of the cylinder
Volume of the cone = π r² h/3
let x be the radius of the cylinder
V = 3.14 * (x/2)² * x/3
V = 3.14 * (x/2 * x/2) * x/3
V = 3.14 * x²/4 * x/3
V = 3.14x³ / 12
The radius of the cylinder is r.
The radius of the cone is half of the radius of the cylinder: r/2.
The height of the cone is equal to the radius of the cylinder: r.
If the volume of the cone is π r²h/3, and the radius of the cone is r/2, and the height of the cone is r, then:
V = π × r² × h / 3
V = π × (r/2)² × r / 3
V = π × r²/4 × r / 3
V = π r³/12
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2.28 kg is % of 600 g.
7.7z-2=6.7z-2 the solution is
Cindy did an experiment. She started out with 600 bacteria cells. She found that the growth rate of the bacteria cells was 4.1%. Create an equation for the situation that would work for any time, x. Pls Help thx
B x = 3
C y = 4
D y = 3
Answers
Using the point-slope formula we can substitute know values:
You could also jsut do it by inspection: since it passes through (3,4) and is horizontal it must cross at (0,4) i.e. all y=4.
Final answer:
The equation of the line parallel to the x-axis and passing through point (3,4) is 'y = 4'. Thus, the correct answer is C y=4.
Explanation:
The question asks for the equation of a line that is parallel to the x-axis and passes through the point (3,4). In the Cartesian coordinate system, a line parallel to the x-axis will have a constant y-value and an equation in the form of y = k, where k is the constant y-value. In this case, the y-coordinate of the given point is 4, which is our constant. Thus, the line parallel to the x-axis passing through the point (3,4) is y = 4. So, the correct answer is C y = 4.
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Answers
Answer:
Step-by-step explanation:
If we are given angles B and C, then all we have to do is add them together and then subtract that from 180 since all the angles of a triangle have to add up to equal 180.
62 + 48 = 110
180 - 110 = 70
Angle A = 70°
Answers
To generate a point, you plug in a number for x to get the corresponding y value.
If x = 0 for instance, then the y value is...
y = x^2 - 4
y = 0^2 - 4 ... x is replaced with 0
y = 0 - 4
y = -4
So x = 0 and y = -4 pair up to get the point (0,-4). This is the y intercept as the parabola crosses the y axis here. It turns out that this is also the vertex point as it is the lowest point on the parabola.
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If x = 1, then,
y = x^2 - 4
y = 1^2 - 4
y = 1 - 4
y = -3
meaning (x,y) = (1,-3) is another point on this line.
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Repeat for x = 2
y = x^2 - 4
y = 2^2 - 4
y = 4-4
y = 0
Since we got a y output of 0, we have found an x intercept located at (2,0). The other x intercept is (-2,0).
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The idea is to generate as many points as possible. Plot all of the points on the same xy coordinate grid. Then draw a curve through those points the best you can. You should get what you see in the diagram below. I used GeoGebra to make the graph. Desmos is another handy tool I recommend.
Note: the more points you generate, the more accurate the graph will be
Answers
Answers
let the longer piece be y and shorter piece be x
now,
according to the question,
x+y=19 .............................equation (1)
y=4+2x ...............................equation (2)
from equation 1
x+y=19
x+4+2x=19 substituting the value of y from equation 2
3x=19-4
x=(19-4)/3
x=5
now
substituting value of x in equation (2)
y=4+2(5)
y=4+10
y=14
so , the longer piece is 14 foot and the shorter piece is 5 foot
Final answer:
The shorter piece of string is 5 feet long and the longer piece is 14 feet long. These lengths were determined by setting up and solving an equation based on the given facts.
Explanation:
In this problem, we need to find the lengths of two sections of a 19-foot piece of stringthat was split such that the longer piece is 4 feet longer than twice the length of the shorter one. Let's denote the length of the shorter piece as 'x'. Thus, the longer piece of string is 2x+4 (twice the length of the shorter piece, plus an additional 4 feet).
Next, we set up an equation based on the information given: the sum of the lengths of the shorter and the longer sections of string equals 19 feet, so x + (2x+4) = 19. Simplify the equation to 3x + 4 = 19, subtract 4 from both sides to give 3x = 15, and then divide by 3 to solve for x, the length of the shorter piece, which is 5 feet. Therefore, the longer piece, by substituting x=5 in 2x+4, is 14 feet.
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Answers
Answer:
$74.75
Step-by-step explanation:
When it comes to tax, the sales tax is applied after the discount is provided by the store, as long as it is something like a direct store coupon or a discounted price. In this case, it is a discounted price by the store, so we will include sales tax after.
$79.20 after a 12% discount becomes $69.70 (or $69.696).
The state tax applies to this new price.
7.25% of $69.70 is $74.75
Final answer:
To find the total cost of the skateboard, calculate the discount and the sales tax separately. The total cost is $74.76.
Explanation:
To find the total cost of the skateboard, we need to calculate the discount and the sales tax separately.
First, calculate the discount by multiplying the original price by the discount rate:
Discount = $79.20 * 12% = $9.50
Next, subtract the discount from the original price to find the discounted price:
Discounted price = $79.20 - $9.50 = $69.70
Finally, calculate the sales tax by multiplying the discounted price by the sales tax rate:
Sales tax = $69.70 * 7.25% = $5.06
Now, add the discounted price and the sales tax to find the total cost:
Total cost = $69.70 + $5.06 = $74.76 (rounded to the nearest cent).
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