Answer:
The value of f(x) - g(x) is:
f(x) - g(x) = 2x² + 6x - 4
Step-by-step explanation:
Given
f(x) = 3x² + x - 3
g(x) = x² - 5x + 1
To determine
f(x) - g(x)
Using the formula
f(x) - g(x) = 3x² + x - 3 - ( x² - 5x + 1)
= 3x² + x - 3 - x² + 5x - 1
= 2x² + 6x - 4
Therefore, the value of f(x) - g(x) is:
f(x) - g(x) = 2x² + 6x - 4
Perpendicular lines refers to a pair of straight lines that intercept each other. The slopes of this lines are opposite reciprocal, meaning that it's multiplication is -1.
On this case they give you the equation of a line and a point, and is asked to find the equation of a line that is perpendicular to the given one, and that passes through this point.
-2x+3y=-6 Add 2x in both sides
3y=2x-6 Divide by 3 in both sides to isolate y
y=2/3x-6/3
The slope of the given line is 2/3, which means that the slope of a line perpendicular to this one, needs to be -3/2. Now you need to find the value of b or the y-intercept by substituting the given point into the formula y=mx+b, where letter m represents the slope.
y=mx+b Substitute the given point and the previous slope found
-2=(-3/2)(6)+b Combine like terms
-2=-9+b Add 9 in both sides to isolate b
7=b
The equation that represents the line perpendicular to -2x+3y=-6 and that passes through the point (6,-2), is y=-3/2x+7.
Answer:
(n + 1)(3n + 7)
Step-by-step explanation:
3n² + 10n + 7
Consider the factors of the product of the n² term and the constant term which sum to give the coefficient of the n- term.
product = 3 × 7 = 21 and sum = + 10
The factors are + 3 and + 7
Use these factors to split the n- term
3n² + 3n + 7n + 7 ( factor the first/second and third/fourth terms )
3n(n + 1) + 7(n + 1) ← factor out (n + 1) from each term
= (n + 1)(3n + 7) ← in factored form
Answer:
-15e+14f-30
Step-by-step explanation:
First using distributive property to expand the first term:
-21e+14f-28+6e-2
Combining like terms:
-15e+14f-30
Answer:
The rate of change of the tracking angle is 0.05599 rad/sec
Step-by-step explanation:
Here the ship is traveling at 15 mi/hr north east and
Port to Radar station = 2 miles
Distance traveled by the ship in 30 minutes = 0.5 * 15 = 7.5 miles
Therefore the ship, port and radar makes a triangle with sides
2, 7.5 and x
The value of x is gotten from cosine rule as follows
x² = 2² + 7.5² - 2*2*7.5*cos(45) = 39.04
x = 6.25 miles
By sine rule we have
Therefore,
α = Angle between radar and ship α
∴ α = 58.052
Where we put
to get
and differentiate to get
= 3.208 degrees/second = 0.05599 rad/sec.
