Hey, can anyone solve this real quick? (It's pretty easy but my brain has melted today.)
2 answers:
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Hey there!
<h3>Question 1</h3>Let's use 3.14 for pi during this. It'll make it a lot easier.
The volume for a cone is .
The diameter of this cone is 17.6 inches. Since the radius is half the diameter, we can find the radius by dividing this amount by 2.
17.6 ÷ 2 = 8.8
The height of this cone is 23.4 inches.
Plug the values into the equation.
Next, square 6.8 and divide 23.4 by 3. Also, replace the pi symbol with 3.14.
Multiply the numbers together.
<u>The volume of this cone is approximately 1896.66 cubic inches.</u>
<h3>Question 2</h3>Finding the volume of a trapezoidal prism can be done by finding the are of the trapezoidal face and multiplying it by the depth.
Formula for finding the area of a trapezoid is
The two bases are 10 and 34, and the height is 24.7 feet. Put these values into the equation.
Add 10 and 34, then multiply it by 24.7 and 1/2.
a = 543.4
Multiply that value by 19, which is the depth of the figure.
<u>The volume of the prism is 10324.6 cubic feet.</u>
<h3>Question 3</h3>The formula for volume of a triangular pyramid is v = 1/3ah, with a the area of the base and h the height.
The formula for the area of an equilateral triangle, which is the base, is
The length of the side is 12, so we can square that to get 144.
Now multiply that by to get the area of the base.
The area of the base is about 62.35 square meters.
The height of the pyramid is 20 meters. Plug that and the area of the base into the equation.
v = 1/3 x 62.35 x 20
Multiply the numbers together to get the volume.
<u>The volume of the pyramid is approximately 415.67 cubic meters.</u>
Hope this helps!
Answer:
(i) The name of the part of the circle, OQ is a radius
(ii) The radius of the sector QOR is 21 cm
Step-by-step explanation:
The given figure is a sector of the circle O
∵ Any sector of a circle formed from 2 radii and an arc
∴ OQ is a radius
(i) The name of the part of the circle, OQ is a radius
The rule of the length of an arc of a circle is L = × 2 π r, where
- α is the angle of the sector
- r is the radius of the circle
∵ The length of the arc QR is 22 cm
∴ L = 22
∵ The measure of the angle of the arc is 60°
∴ α = 60°
∵ π =
→ Substitute them in the rule above
∵ 22 = × 2 ×
× r
∴ 22 = r
→ Divide both sides by
∴ 21 = r
(ii) The radius of the sector QOR is 21 cm
Answer:
No; Because g'(0) ≠ g'(1), i.e. 0≠2, then this function is not differentiable for g:[0,1]→R
Step-by-step explanation:
Assuming: the function is in [0,1]
And rewriting it for the sake of clarity:
Does there exist a differentiable function g : [0, 1] →R such that g'(x) = f(x) for all g(x)=x² ∈ [0, 1]? Justify your answer
1) A function is considered to be differentiable if, and only if both derivatives (right and left ones) do exist and have the same value. In this case, for the Domain [0,1]:
2) Examining it, the Domain for this set is smaller than the Real Set, since it is [0,1]
The limit to the left
g'(x)=f(x) then g'(0)=f(0) and g'(1)=f(1)
3) Since g'(0) ≠ g'(1), i.e. 0≠2, then this function is not differentiable for g:[0,1]→R
Because this is the same as to calculate the limit from the left and right side, of g(x).
This is what the Bilateral Theorem says: