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3 years ago

Identify the vertical shift, maximum and minimum values of each function

Mathematics

1 answer:

Delicious77 [7]3 years ago

5 0

ANSWER

Vertical shift: 6 units up

Maximum value: 9

Minimum value: 3

EXPLANATION

The given since function is

$y = 3(2 - \sin(x))$

Expand and rewrite to obtain,

$y = 6 - 3 \sin(x)$

$y =- 3 \sin(x) + 6$

The vertical shift is 6 units up.

The maximum value is 6+3=9.

The minimum value is -3+6=3

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Find the equation of the parabola with vertex (1,3) and focus (1/2,3).

daser333 [38]

Answer:

A (y-3)^2 = -2(x-1) is the correct choice :)

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3 years ago

What is the value of x?

uranmaximum [27]

x = 41 cm

Here is why:

For this question we have to use the pythagorean theorem, which is used for right triangles. The hypotenuse will always be the last in this theorem.

$a^2+b^2=c^2$

Plug in.

$9^2+40^2=c^2$

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Add together.

$1,681=c^2$

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3 years ago

The difference between the roots of the quadratic equation x^2−14x+q=0 is 6. Find q.

pychu [463]

Answer :

The value of q for, the given quadratic equation is 40

Step-by-step explanation :

Given quadratic equation as :

x² - 14 x + q = 0

And , Difference between the roots of equation is 6

Let A , B be the roots of the equation

So, A - B = 6

The roots of the quadratic equation ax² + bx + c = 0 as can be find as :

x = $\frac{-b\pm \sqrt{b^{2}-4\times a\times c}}{2\times a}$

x = $\frac{14\pm \sqrt{(-14)^{2}-4\times 1\times q}}{2\times 1}$

or, x = $\frac{-14\pm \sqrt{196-4 q}}{2}$

Or, x = $\frac{-14\pm \sqrt{196-4 q}}{2}$

So , The roots are

A = $-7 + \frac{\sqrt{196-4q}}{2}$

And B = $-7 - \frac{\sqrt{196-4q}}{2}$

∵ The difference between the roots is 6

So, A - B = 6

Or, ( $-7 + \frac{\sqrt{196-4q}}{2}$ ) - ( $-7 - \frac{\sqrt{196-4q}}{2}$ ) = 6

Or, ( - 7 + 7 ) + 2 ( $\sqrt{196-4q}$ = 6

Or, 0 + 2 ( $\sqrt{196-4q}$ = 6

∴ 196 - 4 q = 36

or, 4 q = 196 - 36

or 4 q = 160

∴ q = $\frac{160}{4}$

I.e q = 40

S0, The value of q = 40

Hence The value of q for, the given quadratic equation is 40 . Answer

8 0

3 years ago

Question 9 OT 10

lbvjy [14]

Answer:

(3/2)

Step-by-step explanation:

A perpendicular line has a slope that has the negative inverse of the reference line. The green line's slope of -(2/3) becomes (3/2) for a perpendicular line. The red line has two points we can use to calculate slope, just to check.

(-3,-5) and (5,7)

Rise = (7 - (-5)) = 12

Run = (5-(-3)) = 8

Slope = (12/8) or (3/2)

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2 years ago

If point A is located at (-7,-3), and there are 12 points between A and B, what could be the possible coordinates for point B?

Ghella [55]

(5,-3) , (-19,-3) , (-7,9), (-7,-15)

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3 years ago