Answer:
A real number which can be expressed in the form of a/b where b≠0 is called rational number.
A real number which cannot be expressed in the form of a/b where b≠0 is called irrational number.
1. = 14 = 14/1 ..... rational number
2. = ..... irrational number
3. = 4 = 4/1 ........ rational number
4. = 3.142857...... ....... irrational number
5. = ..... irrational number
6. ............. rational number (a/b form)
The y-coordinate of B' after the translation is -6
<h3>How to determine the y-coordinate of B'?</h3>
From the graph, the coordinate of B is given as:
B = (1,2)
The translation 
means:
(x,y) ⇒ (x - 3, y - 8)
So, we have:
B' = (1 - 3, 2 - 8)
Evaluate the difference
B' = (-2, -6)
Remove the x-coordinate
B' = -6
Hence, the y-coordinate of B' is -6
Read more about translation at:
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Option B) Determine the volume of the cake V= πr²h and divide that amount by 18
<u>Step-by-step explanation:</u>
- It is given that, the birthday cake is in the shape of the cylinder.
- Therefore, to find the entire volume of the cake, the volume of the cylinder formula is used.
<u>The volume of the cylinder is given by,</u>
Volume of the birthday cake = πr²h
After that, it was asked to find the volume of each piece of the cake.
In this case, the birthday cake is cut into 18 pieces.
We already know the total volume of the birthday cake which is πr²h.
In order to find the volume of each piece of cut cake, the total volume must be divided by the number of parts it has been cut into pieces.
Here, the whole part of the cake is 1.
The number of parts it has been divided after it is made into pieces = 18 parts.
Therefore, the volume of the birthday cake must be divided by 18 to get the volume of each piece of cake.
Option B) Determine the volume of the cake V= πr²h and divide that amount by 18 is correct.
Using Laplace transform we have:L(x')+7L(x) = 5L(cos(2t))sL(x)-x(0) + 7L(x) = 5s/(s^2+4)(s+7)L(x)- 4 = 5s/(s^2+4)(s+7)L(x) = (5s - 4s^2 -16)/(s^2+4)
=> L(x) = -(4s^2 - 5s +16)/(s^2+4)(s+7)
now the boring part, using partial fractions we separate 1/(s^2+4)(s+7) that is:(7-s)/[53(s^2+4)] + 1/53(s+7). So:
L(x)= (1/53)[(-28s^2+4s^3-4s^2+35s-5s^2+5s)/(s^2+4) + (-4s^2+5s-16)/(s+7)]L(x)= (1/53)[(4s^3 -37s^2 +40s)/(s^2+4) + (-4s^2+5s-16)/(s+7)]
denoting T:= L^(-1)and x= (4/53) T(s^3/(s^2+4)) - (37/53)T(s^2/(s^2+4)) +(40/53) T(s^2+4)-(4/53) T(s^2/s+7) +(5/53)T(s/s+7) - (16/53) T(1/s+7)
Answer:
228.4cm²
Step-by-step explanation:
Find the diagram attached
Total surface area of the prism = Ph + 2B
P is the perimeter of the base (triangle)
h is the height of the prism
B is Base area
P = 5cm + 5cm + 4cm
P = 14cm
h = 15cm
B = 1/2 * base * height
B = 1/2 * 4.6 * 4
B = 4.6 * 2
B = 9.2cm²
Substitute the values into the formula;
Total surface area of the prism = Ph + 2B
Total surface area of the prism = 14(15)+2(9.2)
Total surface area of the prism = 210 + 18.4
Total surface area of the prism = 228.4cm²
Hence the total surface area of the triangular prism is 228.4cm²
