9514 1404 393
Answer:
B. 49/2 units squared
Step-by-step explanation:
The area is that of a triangle 7 units wide and 7 units high. Its area is given by the formula ...
A = 1/2bh
A = (1/2)(7 units)(7 units) = 49/2 units squared
Combine like terms by adding their FACES (Coefficients)
1) 4c² - 4
2) 20m^4 + 6m
3) -6a³ - 19a² + 8a - 10
4) -10a² - 2b + 3ab³ + 4a²b² -5b^4 - 9a²b² - 12a³b + 15ab³ = -10a² - 2b + 18ab³ - 5a²b² - 12a³b - 5b^4
5) 5a³ - 5a²
Answer:
( About ) 1,099 pounds
Step-by-step explanation:
The force required to keep this truck from rolling down the hill is opposed by the force of friction, comparative to the 2600 pounds of force against this friction. It should be that this opposing force is at work more towards the bottom of this hill, and thus the question asks the magnitude of latter force to keep this truck idle -
|| F || = sin( 25 ) * ( Fg ) = sin( 25 ) * ( 2600 lb ) = ( About ) 1098.80748 pounds
<u><em>This can be rounded to a solution of 1099 pounds</em></u>
<span>The two points that are most distant from (-1,0) are
exactly (1/3, 4sqrt(2)/3) and (1/3, -4sqrt(2)/3)
approximately (0.3333333, 1.885618) and (0.3333333, -1.885618)
Rewriting to express Y as a function of X, we get
4x^2 + y^2 = 4
y^2 = 4 - 4x^2
y = +/- sqrt(4 - 4x^2)
So that indicates that the range of values for X is -1 to 1.
Also the range of values for Y is from -2 to 2.
Additionally, the ellipse is centered upon the origin and is symmetrical to both the X and Y axis.
So let's just look at the positive Y values and upon finding the maximum distance, simply reflect that point across the X axis. So
y = sqrt(4-4x^2)
distance is
sqrt((x + 1)^2 + sqrt(4-4x^2)^2)
=sqrt(x^2 + 2x + 1 + 4 - 4x^2)
=sqrt(-3x^2 + 2x + 5)
And to simplify things, the maximum distance will also have the maximum squared distance, so square the equation, giving
-3x^2 + 2x + 5
Now the maximum will happen where the first derivative is equal to 0, so calculate the first derivative.
d = -3x^2 + 2x + 5
d' = -6x + 2
And set d' to 0 and solve for x, so
0 = -6x + 2
-2 = -6x
1/3 = x
So the furthest point will be where X = 1/3. Calculate those points using (1) above.
y = +/- sqrt(4 - 4x^2)
y = +/- sqrt(4 - 4(1/3)^2)
y = +/- sqrt(4 - 4(1/9))
y = +/- sqrt(4 - 4/9)
y = +/- sqrt(3 5/9)
y = +/- sqrt(32)/sqrt(9)
y = +/- 4sqrt(2)/3
y is approximately +/- 1.885618</span>
Answer:
Step-by-step explanation:Graph the parabola using the direction, vertex, focus, and axis of symmetry.
Direction: Opens Up
Vertex:
(
1
,
−
2
)
Focus:
(
1
,
−
7
4
)
Axis of Symmetry:
x
=
1
Directrix:
y
=
−
9
4
x
y
−
1
2
0
−
1
1
−
2
2
−
1
3
2
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