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stiks02 [169]
3 years ago
12

The graph of f(x)=ax^2 is narrower than the graph of g(x)=dx^2 when a<d

Mathematics
1 answer:
Lynna [10]3 years ago
4 0

Answer:

Step-by-step explanation:

as given in question that a > 0 so

if we put a=1

we get g(x) = f(x)

now put a =2

we get

g(x) = 2 f(x)

here we can see that g(x) would always be greater than or equals to f(x)

so we can say that the graph of g(x) will never be narrower than graph of g(x)

You might be interested in
The vertex of a parabola is at (-4,-3). If one x-intercept is at -11, what is the other x intercept?
Reil [10]
The equation of the parabola could be written as y-k = a(x-h)^2, where (h,k) is the vertex.  Thus, y-(-3) = a(x+4)^2, or y+3 = a(x+4)^2.

The coordinates of one x-intercept are (-11,0).  Thus, y+3 = a(x+4)^2 becomes 
0+3 = a(-11+4)^2, so that 3 = a(-7)^2, or 3 = 49a.  Therefore, a = 3/49, and the equation of the parabola becomes

y+3 = (3/49)(x+4)^2.

To find the other x-intercept, let y = 0 and solve the resulting equation for x:

0+3 = (3/49)(x+4)^2, or (49/3)*2 = (x+4)^2

Taking the sqrt of both sides, plus or minus 49/3 = x+4.

plus 49/3 = x+4 results in 37/3 = x, whereas

minus 49/3 = x+4 results in x = -61/3.  Unfortunatelyi, this disagrees with what we are told:  that one x-intercept is x= -11, or (-11,0).


Trying again, using the quadratic equation y=ax^2 + bx + c,
we substitute the coordinates of the points (-4,-3) and (-11,0) and solve for {a, b, c}:

-3 = a(-4)^2 + b(-4) + c, or -3 = 16a - 4b + c

 0 = a(-11)^2 - 11b + c, or 0 = 121a - 11b + c

If the vertex is at (-4,-3), then, because x= -b/(2a) also represents the x-coordinate of the vertex,                       -4 = b / (2a), or  -8a = b, or 
0 = 8a + b

Now we have 3 equations in 3 unknowns:

0  =  8a +  1b
-3 = 16a - 4b + c
0 = 121a - 11b + c

This system of 3 linear equations can be solved in various ways.  I've used matrices, finding that a, b and c are all zero.  This is wrong.


So, let's try again.  Recall that x = -b / (2a) is the axis of symmetry, which in this case is x = -4.  If one zero is at -11, this point is 7 units to the left of x = -4.  The other zero is 7 units to the right of x = -4, that is, at x = 3.

Now we have 3 points on the parabola:  (-11,0), (-4,-3) and (3,0).

This is sufficient info for us to determine {a,b,c} in y=ax^2+bx+c.
One by one we take these 3 points and subst. their coordinates into 
y=ax^2+bx+c, obtaining 3 linear equations:

0=a(-11)^2 + b(-11) + 1c   =>  0 = 121a - 11b + 1c
-3 = a(-4)^2 +b(-4)  + 1c   =>  -3 = 16a   - 4b  +  1c
0 = a(3)^2   +b(3)    + c     =>   0 = 9a     +3b   + 1c

Solving this system using matrices, I obtained a= 3/49, b= 24/49 and c= -99/49.

Then the equation of this parabola, based upon y = ax^2 + bx + c, is

y = (1/49)(3x^2 + 24x - 99)               (answer)

Check:  If x = -11, does y = 0?

(1/49)(3(-11)^2 + 24(-11) - 99 = (1/49)(3(121) - 11(24) - 99
                                                = (1/49)(363 - 264 - 99)  =  (1/49)(0)   YES!

y = (1/49)(3x^2 + 24x - 99)               (answer)
6 0
3 years ago
This is why brainly is lame
Pachacha [2.7K]

Answer:lol so true

Step-by-step explanation:

7 0
2 years ago
Write an equation of the line that passes through (6,-10) and is perpendicular To the line that passes through 4,-6) and (3,-4)
iVinArrow [24]

Answer:

all work is shown and pictured

7 0
3 years ago
Differential cos^2x dy/dx =e^y-tanx​
gulaghasi [49]

Answer:

y=t−1+ce

−t

where t=tanx.

Given, cos

2

x

dx

dy

+y=tanx

⇒

dx

dy

+ysec

2

x=tanxsec

2

x ....(1)

Here P=sec

2

x⇒∫PdP=∫sec

2

xdx=tanx

∴I.F.=e

tanx

Multiplying (1) by I.F. we get

e

tanx

dx

dy

+e

tanx

ysec

2

x=e

tanx

tanxsec

2

x

Integrating both sides, we get

ye

tanx

=∫e

tanx

.tanxsec

2

xdx

Put tanx=t⇒sec

2

xdx=dt

∴ye

t

=∫te

t

dt=e

t

(t−1)+c

⇒y=t−1+ce

−t

where t=tanx

8 0
2 years ago
Please help!!<br> I’m so confused <br> And please don’t use the link joke
bagirrra123 [75]

Answer:

15u + 141 = 420

Step-by-step explanation:

So basically we are modelling how much the coach is spending. Each player is given a uniform and a basketball

We can use 'u' as the cost of a single uniform

We can use 'b' as the cost of a single basketball

Since there is 15 players we must give a ball and uniform to each so

15u + 15b = 420

The problem gives us the cost of each basketball: 9.40

so now 15u + 15(9.4) = 420

15u + 141 = 420

8 0
3 years ago
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