The age of ben and david is 24 and 38 years.
According to the statement
we have to find the age of the Ben now.
So,For this purpose, we know that the
One application of linear equations is what are termed age word problems. When solving age problems, generally the age of two different people (or objects) both now and in the future (or past) are compared.
From the given information:
The sum of Ben's and David's ages is 62 yrs now
And
Five years from now David will be twice as old as Ben.
Let the ben age is x
and the david age is y.
So, from given information:
x+y = 62 -(1)
5 years from now,
y = 2x -(2)
put (2) in the (1) then
x+y = 62 -5
x+2x = 57
3x = 57
x = 19.
And the age of davud become
y = 2(19)
y = 38 years
So, five years from now the age of ben is 19 and david is 38 years.
And now the age of the ben and age of david is
Age of ben now = 19+5
Age of ben now = 24.
Age of david now = 62 -24
Age of david = 38.
So, The age of ben and david is 24 and 38 years.
Learn more about age word problems here
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Problem 1
1a) Jon created a torus while Nadia created a cone. A torus is basically a donut shaped 3D object. You can think of it as a 3D inflatable pool ring (lifeguard pool ring), or one of the rings from the game of ring toss.
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1b) Each plane of symmetry that Nadia points out is a plane that runs through points B and C. In a similar manner, Jon has the same plane of symmetry. Both have infinitely many planes of symmetry of this nature.
For Jon, his torus or donut shaped object can be cut in half along the horizontal axis. Imagine cutting a bagel so you can apply cream cheese or butter or whatever item you like. Each half of the bagel would be congruent to one another. This is the "plus 1" Jon is talking about.
This horizontal cut cannot be applied to Nadia's cone. If she were to cut her cone anywhere along a horizontal plane then she'd have a frustum at the bottom and a smaller cone up top (instead of two congruent smaller cones)
note: to be fair, infinity+1 is the same as infinity. They both describe the idea of listing numbers forever. We can add any number to infinity to get infinity.
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Problem 2
2a) To reflect over the xz plane, we keep the x and z coordinates the same. Only the y coordinate flips from positive to negative (or vice versa). For instance, the point P(0,5,4) becomes P'(0,-5,4) after such a reflection.
The algebraic way to write the rule is
(x,y,z) ---> (x,-y,z)
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2b) After applying the reflection rule, you should get the following
P(0,5,4) ---> P ' (0,-5,4)
Y(-2,7,4) ---> Y ' (-2,-7,4)
R(0,7,4) ---> Y ' (0,-7,4)
A(0,7,6) ---> Y ' (0,-7,6)
Once again, only the y value is changing. The sign of the y value specifically.
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2c) It's not entirely clear what your teacher means by "back", "left" and "up". Why is that? Because there are at least 2 different ways to orient the xyz axis.
One such way is to have the z axis sticking up and have the xy axis as the "floor" so to speak. Another way is to have the z axis come out of the board and have the y axis sticking up (so the xy axis is flat against the wall).
Concepts of "left", "right", "up", "down", etc are all relative to your frame of reference. One person's "up" is another person's "down". Unfortunately I don't think there's enough info to solve here. It would have been much more ideal if your teacher said something like "3 units along the x axis" rather than "3 units back".
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2d) See part C above. There isn't enough info (at least, in my opinion anyway).
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Problem 3
3a) A cylinder forms. The rectangle RECT is basically a revolving door. When you spin the revolving door really fast, it leads to the illusion of a 3D cylindrical block. You can also picture a propeller fan to visualize the same basic idea. This cylinder has a height of TC = 3 units. The radius is EC = 5 units.
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3b)
From part A, r = radius = 5, h = height = 3
SA = 2*pi*r^2 + 2*pi*r*h
SA = 2*pi*5^2 + 2*pi*5*3
SA = 50*pi + 30*pi
SA = 80*pi <--- exact surface area
SA = 251.3274 <--- approx surface area
surface area is in square units
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3c)
Use the same dimensions (r = 5, h = 3) from part B
V = pi*r^2*h
V = pi*5^2*3
V = pi*25*3
V = pi*75
V = 75*pi <--- exact volume
V = 235.6194 <--- approx volume
volume is in cubic units
Answer:
21
Step-by-step explanation:
Given the following expressions
f(x) = x³-2x
g(x) =-x-2
We are to find (fog)(-5)
fog = f(g(x))
f(g(x)) = f(-x-2)
Replace x with -x-2 in f(x)
f(-x-2) = (-x-2)³-2(-x-2)
f(-x-2) = (-x-2)³+2x+4
fog = (-x-2)³+2x+4
Substitute x = -5 into the result
fog(-5) = (-x-2)³+2x+4
fog(-5) = (-(-5)-2)³+2(-5)+4
fog(-5) = (5-2)³-10+4
fog(-5) = 3³-6
fog(-5) = 27-6
fog(-5) = 21
Hence the required result of the composite function is 21
Answer:
Opposites are basically the negative and positive of a number. I cannot think of something for a real world situation though.
Step-by-step explanation:
