Answer:
To make given quadratic equation a whole number , we have to add 6 in the equation.. (3 x - 4 )²
Step-by-step explanation:
The given quadratic equation is
9 x² - 24 x + 10 = 0
(3 x )² - 24 x + 10 = 0
(3 x )² - ( 2 × 3 x × 4 ) + 10 = 0
Now if we add 6 to the equation , it will become whole square as (a + b)²
I.e (3 x )² - ( 2 × 3 x × 4 ) + 10 + 6 = 0
Or, (3 x )² - ( 2 × 3 x × 4 )+ 16 = 0
Or, 9 x² - 24 x + 16 = 0
Or, (3 x - 4 )² = 0
Hence to make given quadratic equation a whole number , we have to add 6 in the equation.. Answer
Answer:
,
Step-by-step explanation:
One is asked to find the root of the following equation:
Manipulate the equation such that it conforms to the standard form of a quadratic equation. The standard quadratic equation in the general format is as follows:
Change the given equation using inverse operations,
The quadratic formula is a method that can be used to find the roots of a quadratic equation. Graphically speaking, the roots of a quadratic equation are where the graph of the quadratic equation intersects the x-axis. The quadratic formula uses the coefficients of the terms in the quadratic equation to find the values at which the graph of the equation intersects the x-axis. The quadratic formula, in the general format, is as follows:
Please note that the terms used in the general equation of the quadratic formula correspond to the coefficients of the terms in the general format of the quadratic equation. Substitute the coefficients of the terms in the given problem into the quadratic formula,
Simplify,
Rewrite,
,
Answer:
A) X=pi/2 or X=-pi/2
B) X=pi/6 or X=-pi/6
C) X=pi/4 , 3pi/4, 5pi/4 and 7pi/4
D) X= 1-cos^2(x/2)
E) X= pi/3 +2pi N, 5pi/3+2pi N
Step-by-step explanation:
Don't even bother asking. :)
Answer:
2sin((1)x + 135)-3
Step-by-step explanation:
Asin(Bx+C)+D
A = amplitude = distance from top to bottom divided by 2
y value of top = -1
y value of bottom = -5
distance from top to bottom = -1 - (-5) = 4
divide by 2 to get 4/2 = 2 as our amplitude
2π/B = period
in this case, we're working in degrees for our x axis - 2π = 360°
thus, 360°/B = period
period = time it takes to get from one high to the next (alternatively, one low to the next etc.) = 360 degrees in this case
thus, 360°/B = 360°
divide both sides by 360° and multiply both sides by B to isolate B
360/360 = B = 1
phase shift = -C/B
phase shift refers to how much the graph is shifted to the left/right. normally, the middle of a sin wave is at 0, with a peak being to the right of it. now, the middle of the sin wave (which has a peak to the right of it) is at x = -135 degrees to the right of a regular sine wave
thus,
-135 degrees = -C/B
B = 1
-135 degrees = -C
C = 135 degrees
D = vertical shift
the center is now at y = -3. normally, the center is at y = 0. thus, D = -3
our formula is thus
2sin((1)x + 135)-3
Answer:
1436.03 mm³
Step-by-step explanation:
I believe the 7mm should be the radius?
The volume of a sphere is πr³
π * 343
since pi is rounded to 3.14, we get
1436.026 mm³