Answer:
Domain and Range of g(f(x)) are 'All real numbers' and {y | y>6 } respectively
Step-by-step explanation:
We have the functions, f(x) = eˣ and g(x) = x+6
So, their composition will be g(f(x)).
Then, g(f(x)) = g(eˣ) = eˣ+6
Thus, g(f(x)) = eˣ+6.
Since the domain and range of f(x) = eˣ are all real numbers and positive real numbers respectively.
Moreover, the function g(f(x)) = eˣ+6 is the function f(x) translated up by 6 units.
Hence, the domain and range of g(f(x)) are 'All real numbers' and {y | y>6 } respectively.
Answer:
<em>2 7/24</em>
Step-by-step explanation:
<em>First we have to add the gallons of two cow of each owner:</em>
<em>Hank's cows: </em><em>4 3/4 + 4 1/8</em>
<em>Add the whole numbers:</em>
<em>4 + 4 = 8</em>
<em>Now for 3/4 and 1/8 </em>
<em>Find common</em>
<em>6/8 + 1/8</em>
<em>= 7/8</em>
<em>Put together :</em>
<em>8 7/8</em>
<em>Debra's cows: </em><em>5 1/2 + 5 2/3</em>
<em>Add the whole number</em>
<em>5 + 5 = 10</em>
<em>Now for 1/2 and 2/3</em>
<em>3/6 + 4/6</em>
<em>1 1/6</em>
<em>10 + 1 1/6 </em>
<em>= 11 1/6</em>
<u><em>Since now we know that:</em></u>
<u><em>Hank - </em></u><em>8 7/8</em>
<u><em>Debra - </em></u><em>11 1/6</em>
<em>we can solve the question:</em>
<em>How many more gallons of milk did Debra's two cows produce on that compared to Hank's two cows?</em>
<em>Solution:</em>
<em>11 1/6 - 8 7/8</em>
<em>Subtract whole number</em>
<em>11 - 8 = 3</em>
<em>Now for 1/6 and 7/8</em>
<em>4/24 - 21/24</em>
<em>4-21/24</em>
<em>-17/24</em>
<em>2 7/24</em>
<em />
<u>~lenvy~</u>
F(x) = 18-x^2 is a parabola having vertex at (0, 18) and opening downwards.
g(x) = 2x^2-9 is a parabola having vertex at (0, -9) and opening upwards.
By symmetry, let the x-coordinates of the vertices of rectangle be x and -x => its width is 2x.
Height of the rectangle is y1 + y2, where y1 is the y-coordinate of the vertex on the parabola f and y2 is that of g.
=> Area, A
= 2x (y1 - y2)
= 2x (18 - x^2 - 2x^2 + 9)
= 2x (27 - 3x^2)
= 54x - 6x^3
For area to be maximum, dA/dx = 0 and d²A/dx² < 0
=> 54 - 18x^2 = 0
=> x = √3 (note: x = - √3 gives the x-coordinate of vertex in second and third quadrants)
d²A/dx² = - 36x < 0 for x = √3
=> maximum area
= 54(√3) - 6(√3)^3
= 54√3 - 18√3
= 36√3.
This question is essentially asking you to find the surface area of the box.
The formula for SA on a rectangular prism is: 2(L*W+L*H+W*H)
L=Length W=Width H=Height
Lets input the information we know:
2(20*8+20*30+8*30)
Follow BEDMAS
2(160+600+240)
2(760+240)
2(1000)
2*1000
=2000
The box will need 2000 centimeters squared of material.
Hope this helps!
-Benjamin
Answer:
15 units.
Step-by-step explanation:
The distance between the points (x1, y1) and (x2, y2) is
√(x1-y1)^2 + (y1-y2)^2))
So here it is:
√(10- -2)^2 + (6- -3)^2)
= √(144+81)
= √225
= 15.
