Answer:
-34 -7a
Step-by-step explanation:
–34–23a+16a
Combine like terms
-34 -7a
The congruence theorem that can be used is: B. ASA
<h3>What is the ASA Congruence Theorem?</h3>
If we have two triangles that have two pairs of corresponding congruent angles (e.g. ∠LGH ≅ ∠HKJ and ∠LHG ≅ ∠KHJ), and a pair of corresponding congruent sides (e.g. GH ≅ HK), the triangles are said to be congruent triangles by the ASA congruence theorem.
Therefore, triangles GHL and KHL in the image given are congruent triangles by the ASA congruence theorem.
Learn more about the ASA congruence theorem on:
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Part A
Everything looks good but line 4. You need to put all of the "2h" in parenthesis so the teacher will know you are squaring all of 2h. As you have it right now, you are saying "only square the h, not the 2". Be careful as silly mistakes like this will often cost you points.
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Part B
It looks like you have the right answer. Though you'll need to use parenthesis to ensure that all of "75t/(2pi)" is under the cube root. I'm assuming you made a typo or forgot to put the parenthesis.
dh/dt = (25)/(2pi*h^2)
2pi*h^2*dh = 25*dt
int[ 2pi*h^2*dh ] = int[ 25*dt ] ... applying integral to both sides
(2/3)pi*h^3 = 25t + C
2pi*h^3 = 3(25t + C)
h^3 = (3(25t + C))/(2pi)
h^3 = (75t + 3C)/(2pi)
h^3 = (75t + C)/(2pi)
h = [ (75t + C)/(2pi) ]^(1/3)
Plug in the initial conditions. If the volume is V = 0 then the height is h = 0 at time t = 0
0 = [ (75(0) + C)/(2pi) ]^(1/3)
0 = [ (0 + C)/(2pi) ]^(1/3)
0 = [ (C)/(2pi) ]^(1/3)
0^3 = (C)/(2pi)
0 = C/(2pi)
C/(2pi) = 0
C = 0*2pi
C = 0
Therefore the h(t) function is...
h(t) = [ (75t + C)/(2pi) ]^(1/3)
h(t) = [ (75t + 0)/(2pi) ]^(1/3)
h(t) = [ (75t)/(2pi) ]^(1/3)
Answer:
h(t) = [ (75t)/(2pi) ]^(1/3)
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Part C
Your answer is correct.
Below is an alternative way to find the same answer
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Plug in the given height; solve for t
h(t) = [ (75t)/(2pi) ]^(1/3)
8 = [ (75t)/(2pi) ]^(1/3)
8^3 = (75t)/(2pi)
512 = (75t)/(2pi)
(75t)/(2pi) = 512
75t = 512*2pi
75t = 1024pi
t = 1024pi/75
At this time value, the height of the water is 8 feet
Set up the radius r(t) function
r = 2*h
r = 2*h(t)
r = 2*[ (75t)/(2pi) ]^(1/3) .... using the answer from part B
Differentiate that r(t) function with respect to t
r = 2*[ (75t)/(2pi) ]^(1/3)
dr/dt = 2*(1/3)*[ (75t)/(2pi) ]^(1/3-1)*d/dt[(75t)/(2pi)]
dr/dt = (2/3)*[ (75t)/(2pi) ]^(-2/3)*(75/(2pi))
dr/dt = (2/3)*(75/(2pi))*[ (75t)/(2pi) ]^(-2/3)
dr/dt = (25/pi)*[ (75t)/(2pi) ]^(-2/3)
Plug in t = 1024pi/75 found earlier above
dr/dt = (25/pi)*[ (75t)/(2pi) ]^(-2/3)
dr/dt = (25/pi)*[ (75(1024pi/75))/(2pi) ]^(-2/3)
dr/dt = (25/pi)*[ (1024pi)/(2pi) ]^(-2/3)
dr/dt = (25/pi)*(1/64)
dr/dt = 25/(64pi)
getting the same answer as before
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Thinking back as I finish up, your method is definitely shorter and more efficient. So I prefer your method, which is effectively this:
r = 2h, dr/dh = 2
dh/dt = (25)/(2pi*h^2) ... from part A
dr/dt = dr/dh*dh/dt ... chain rule
dr/dt = 2*((25)/(2pi*h^2))
dr/dt = ((25)/(pi*h^2))
dr/dt = ((25)/(pi*8^2)) ... plugging in h = 8
dr/dt = (25)/(64pi)
which is what you stated in your screenshot (though I added on the line dr/dt = dr/dh*dh/dt to show the chain rule in action)
The scale model of a building 3 inches tall if the building is 90 feet tall is 2:5
<h3>Scaling of measurement</h3>
Scaling is the way of enlarging or reducing the image of an object.
Given scale model of a building is 3 inches, if the building is 90feet tall, to write the scale;
Convert both measures to same units
Since 1 feet. = 12 in
90 feet = 90/12 in = 7.5 in
Take the ratio
3 : 7.5 = 30: 75
Reduce to lowest term
30: 75 = 2 : 5
Hence the scale model of a building 3 inches tall if the building is 90 feet tall is 2:5
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Answer:
790 units^2
Step-by-step explanation:
Take the area of each side and add them all up. Remember each side is there twice.
Formula: SA = 2(15*5 + 15*16 + 5*16)
SA = 2(75 + 240 + 80)
SA = 2(395)
SA = 790
