Answer:
The volume of the space outside the pyramid but inside the prism is 225 cubic centimeters.
Step-by-step explanation:
To find this, you subtract the volume of the pyramid from the volume of the rectangular prism.
The prism and pyramid's bases is 25 cm²
The pyramid's height is 12÷2 or 6 cm
The volume formula for a prism is l×w×h
The volume formula for a pyramid is 
×b×h
The area of the prism is 5×5×12 or 300 cm³
The area of the pyramid is 
or 75 cm³
300 cm³-75 cm³=225 cm³
The volume outside the pyramid but inside the prism is 225 cm³.
If
<em>f(x)</em> = <em>ax</em> ³ + <em>bx</em> ² - 5<em>x</em> + 9
then
<em>f '(x)</em> = 3<em>ax </em>² + 2<em>bx</em> - 5
Given that <em>f</em> (-1) = 12 and <em>f</em> '(-1) = 3, we get the system of equations
-<em>a</em> + <em>b</em> + 5 + 9 = 12
3<em>a</em> - 2<em>b</em> - 5 = 3
or
-<em>a</em> + <em>b</em> = -2
3<em>a</em> - 2<em>b</em> = 8
Multiply through the first equation by 2 and add it to the second one to eliminate <em>b</em> and solve for <em>a</em> :
2(-<em>a</em> + <em>b</em>) + (3<em>a</em> - 2<em>b</em>) = 2(-2) + 8
-2<em>a</em> + 2<em>b</em> + 3<em>a</em> - 2<em>b</em> = -4 + 8
<em>a</em> = 4
Substitute this into the first equation above to solve for <em>b</em> :
-4 + <em>b</em> = -2
<em>b</em> = 2
Answer:
148 tickets
Step-by-step explanation:
444 ÷ 3 = 148
Answer:
A. Building A, it is around 100.69 feet taller than building B.
Step-by-step explanation:
Since building A is 120 feet away at and elevation of 
, then:
Tan = 
Where x is the height of the building at the horizontal plane.
x = Tan × 120
= 100.692 feet
For building B at the same elevation,
Tan = 
x = Tan × 60
= 50.346 feet
Since the angle of elevation are the same, building A is around 100.69 feet taller than building B.
Answer:
22.2
Step-by-step explanation:
The missing side is x
- cos19° = 21/x switch x and cos19°
- x = 21/cos 19°
x = 22.21≈ 22.2
