Find the vertex, focus, directrix, and focal width of the parabola. x = 4y2.

Answers

Answer 1

Answer: - Vertex : ( 0, 0 ).
- Focus: ( p/2, 0 );
y² = 1/4 x
y² = 2 p x ⇒ 2 p = 1/4
p = 1/8
p/2 = 1/16
F ( 1/16, 0)
- Directrix:
x = - p/2 x
x = - 1/16 x
- The focal length:
2 p = 2 · 1/8 = 1/4

Answer 2

Answer:

Answer:

The vertex is (0,0), focus of the parabola is $((1)/(16),0)$ , directrix of the parabola is $y=-(1)/(16)$ , focal width is $(1)/(4)$ .

Step-by-step explanation:

The given equation of parabola is

$x=4y^2$

It can be written as

$y^2=(1)/(4)x$ ....(1)

The general equation of parabola is

$(y-k)^2=4p(x-h)$ ... (2)

Where, (h,k) is vertex, (h+p,k) is focus, y=h-p is directrix and |4p| is focal width.

On comparing (1) and (2), we get

$h=0,k=0$

The vertex is (0,0).

$4p=(1)/(4)$

$p=(1)/(16)$

Focus of the parabola is

$(h+p,k)=(0+(1)/(16),0)=((1)/(16),0)$

Therefore focus of the parabola is $((1)/(16),0)$ .

Directrix of the parabola is

$y=h-p=0-(1)/(16)=-(1)/(16)$

Directrix of the parabola is $y=-(1)/(16)$ .

Focal width is

$|4p|=|4* (1)/(16)|=(1)/(4)$

Focal width is $(1)/(4)$ .

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Could someone help me understand how to solve questions like these? Thank you!

Answers

Answer:

$y=-(1)/(4)x+(5)/(4)$

Step-by-step explanation:

You solve a question like this by finding the slope and intercept of the desired line and putting those values into the answer form.

The relationship between slopes of perpendicular lines is that one is the negative reciprocal of the other.

The slope-intercept form of the equation for a line is ...

y = mx + b . . . . . . where m is the slope and b is the y-intercept

The given line is in "slope-intercept form," so you can identify the slope as 4 and the y-intercept as 6. (For this question, the y-intercept of the given line is irrelevant.)

Using the relationship between slopes of perpendicular lines, you now know the slope of the line you want is m = -1/(slope of given line) = -1/4. This is the coefficient of x in the slope-intercept form, so fills the blanks on the left.

To make the line go through the point (1, 1), you need to choose a y-intercept that makes (x, y) = (1, 1) a solution to the equation. For a y-intercept of "b", that means ...

y = -1/4x + b

1 = -1/4·1 + b . . . . . . . . fill in the values of x and y at the given point

1 + 1/4 = b = 5/4 . . . . . add 1/4 to both sides of the equation

Now you know the equation you want is ...

$y=-(1)/(4)x+(5)/(4)$

Which of the following is not a congruence transformation? A.Translating
B.Rotating
C.Dilating

Answers

The answer is C.) Dilating
because dilating doesn't make them congruent anymore, but they change size to be either smaller or bigger than one another, but the shape itself does not change.

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The health care Jimmy’s employer offers is a fee-for-service plan in which Jimmy and his family must pay for $12,500 in health related services in a calendar year before the insurance company begins to pay. Jimmy and his family have several health related issues that demand $685.00 each month. If one of Jimmy’s children were to become seriously injured at the end of the year, how much more would Jimmy and his family need to pay before the insurance company begins to assume responsibility?a.
$984.58
b.
$4,280.00
c.
$11,815.00
d.
$14,417.92

Answers

The answer is Letter B - $4,280.00.

Total the amount they could incur because of health issues in a year then deduct it from 12,500.

= 685 x 12 months
= 8,220; they incur $8,220 for their health related issues in a year

= 12,500 - 8,220
= 4,280; amount they need to pay before the insurance company assumes responsibility.

PLEASE HELPPP!You’re buying hand lotion. The lotion comes in rectangular pyramid-shaped bottles. Bottle A has a base of 1 in x 2 in, and a height of 6 in. Bottle B is a wider bottle with a base of 1.5 in x 3 in, and a height of 4 inches. Which bottle has more lotion?

Answers

Answer:

Bottle B has a larger volume of lotion therefore the correct answer

Step-by-step explanation:

1×2×6=12/3=4 Bottle A

1.5×3×4=18/3=6 Bottle B

Answer:

Bottle B contains 6 in3 of lotion, and Bottle A contains 4 in3. Bottle B contains more.

Step-by-step explanation:

(x^2 - x^(1/2))/(1-x^(1/2))

Answers

$\frac { \left( { x }^( 2 )-{ x }^{ \frac { 1 }{ 2 } } \right) }{ \left( 1-{ x }^{ \frac { 1 }{ 2 } } \right) }$

$\n \n =\frac { \left( { x }^( 2 )-\sqrt { x } \right) }{ \left( 1-\sqrt { x } \right) } \cdot 1$

$\n \n =\frac { \left( { x }^( 2 )-\sqrt { x } \right) }{ \left( 1-\sqrt { x } \right) } \cdot \frac { \left( 1+\sqrt { x } \right) }{ \left( 1+\sqrt { x } \right) }$

$\n \n =\frac { { x }^( 2 )+{ x }^( 2 )\sqrt { x } -\sqrt { x } -x }{ 1+\sqrt { x } -\sqrt { x } -x }$

$\n \n =\frac { -\sqrt { x } \left( 1-{ x }^( 2 ) \right) -x\left( 1-x \right) }{ \left( 1-x \right) }$

$\n \n =\frac { -\sqrt { x } \left( 1+x \right) \left( 1-x \right) -x\left( 1-x \right) }{ \left( 1-x \right) }$

$\n \n =\frac { \left( 1-x \right) \left\{ -\sqrt { x } \left( 1+x \right) -x \right\} }{ \left( 1-x \right) }$

$\n \n =-\sqrt { x } \left( 1+x \right) -x\n \n =-{ x }^{ \frac { 1 }{ 2 } }\left( 1+{ x }^{ \frac { 2 }{ 2 } } \right) -x$

$\n \n =-{ x }^{ \frac { 1 }{ 2 } }-{ x }^{ \frac { 3 }{ 2 } }-x\n \n =-\sqrt { x } -\sqrt { { x }^( 3 ) } -x$

x² - x^(1/2) = x²
1 - x^(1/2)

In a right triangle, the length of the hypotenuse is 20 inches and the length of one leg is 15 inches. What is the length of the other leg in inches?

Answers

Solutions

To solve this problem we have to use the Pythagorean theorem. You can only use the Pythagorean theorem in Right Triangles. The longest side of the triangle is called the "hypotenuse". C² is the longest side so it is the hypotenuse . To calculate c² we have to do α² + β² = c².

Given

In a right triangle, the length of the hypotenuse is 20 inches and the length of one leg is 15 inches.

$c^2 = 20 in$

$a^2 = 15 in$

$b^2 = Unknown$

------------ Calculations

$b^2 = c^2 - a^2$

$b^2 = c^2(20) - a^2(15)$

$b^2 = 400 - 225$

$b^2 = 175$

$b = √(175)$

$b = 13.2287565553$

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Karissa eats 400 bananas per day. using f(x)=400x•422, where x is the amount of time in days, and f(x) is the amount of potassium in karissa's bones in Mg. how much radiation has she built up over 14 days, if there is 0.1 mSv of radiation per 422 milligrams of potassium.equation: f(x)=400x•422

Help, please. I really need help one this