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3 years ago

Explain how the sign of a in the equation y=a(x-h)^2 + k tells you whether the parabola has a minimum or maximum value.

Mathematics

1 answer:

Svet_ta [14]3 years ago

8 0

In short, for a vertical parabola, namely one whose independent variable is on the x-axis, usually is x², if the leading term coefficient is negative, the parabola opens downward, and its peak or vertex is at a maximum, check the picture below at the left-hand-side.

and when the leading term coefficient is positive, the parabola opens upwards, with a minimum, check the picture below at the right-hand-side.

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Scoateti factori de sub radical, apoi calculati: v3 + 2v27 - v75

Temka [501]

I’m not sure if your asking help to factor the equation. Here is the answer to the equation that I factored. -v^3(v^72-2v^24 + 1) Hope that helps you.

5 0

3 years ago

A home gardener estimates that 24 apple trees will have an average yield of 104 apples per tree. But because of the size of the

d1i1m1o1n [39]

Answer:

The farmer should plant 14 additional trees, for maximum yield.

Step-by-step explanation:

Given

$Trees = 24$

$Yield = 104$

$x \to additional\ trees$

So, we have:

$Trees = 24 + x$

$Yield = 104 - 2x$

Required

The additional trees to be planted for maximum yield

The function is:

$f(x) = Trees * Yield$

$f(x) = (24 + x) * (104 - 2x)$

Open bracket

$f(x) = 24 * 104 + 104x - 24 * 2x - x * 2x$

$f(x) = 2796 + 104x - 48x - 2x^2$

$f(x) = 2796 + 56x - 2x^2$

Rewrite as:

$f(x) = - 2x^2 + 56x + 2796$

Differentiate

$f'(x) = -4x + 56$

Equate $f'(x) = -4x + 56$ to 0 and solve for x to get the maximum of x

$-4x + 56 = 0$

$-4x =- 56$

Divide by -4

$x =14$

The farmer should plant 14 additional trees, for maximum yield.

5 0

3 years ago

Solve the following system of equations graphically on the set of axes below.

Montano1993 [528]

You need to plot each line and see where they intersect.

Line 1: y = x+2

Plot the y-intercept (0,2) because of the +2 in the equation.

From (0,2), count "up 1, right 1" to get a second point, because the slope is 1.

From that new point, repeat the "up 1, right 1" to plot a third point.

Connect the dots to make your line.

Line 2: y = -1/3 x - 2

Repeat the same process, using the the y-intercept and slope for this line.

Then identify where they intersect.

5 0

3 years ago

Si 4x= 5/6y entonces 5y=

Hunter-Best [27]

Answer:

$5y=24x$

Step-by-step explanation:

The question in English is

If 4x= 5/6y then 5y=

we have

$4x=\frac{5}{6}y$

Solve for 5y

Multiply both sides by 6

$6*4x=(6)*\frac{5}{6}y$

Simplify

$24x=5y$

Rewrite

$5y=24x$

8 0

3 years ago

A student throws a rock into the sky from the top of the Webster build- ing with an angle α = π 4 from the horizontal line and t

lord [1]

Answer:

r(0) = <0, 100> . . . . . . . .meters
r'(0) = <7.071, 7.071> . . . . meters per second

Step-by-step explanation:

Initial Position

The problem statement tells us we're measuring position from the ground at the base of the building where the projectile was launched. The initial horizontal position is presumed to be zero. The initial vertical position is said to be 100 meters from the ground, so (in meters) ...

r(0) = <0, 100>

Initial Velocity

The velocity vector resolves into components in the horizontal direction and the vertical direction. For angle α from the horizontal, the horizontal component of velocity is v₁·cos(α), and the vertical component is v₁·sin(α). For v₁ = 10 m/s and α = π/4, the initial velocity vector (in m/s) is ...

r'(0) = <10·cos(π/4), 10·sin(π/4)>

r'(0) ≈ <7.071, 7.071>

7 0

3 years ago