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4 years ago

Pls answer this with an explanation if you can pg4 pt3

Mathematics

1 answer:

Vitek1552 [10]4 years ago

5 0

Answer:

Step-by-step explanation:

$\geqslant$ means greater or equal to.

Since c is greater or equal to 2, the arrow has to start from 2 and point to the right, where the numbers are increasing. Note that the dot at 2 has to be coloured since the symbol is $\geqslant$ and not $>$ .

Option A shows c >2

Option C shows c <2

Option D shows c ≤2

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Find 2 positive real numbers that differ by 1 and have a product of 1

velikii [3]

A) x -y =1
B) x * y =1
B) y = 1/x

A) x -(1/x) = 1
Multiplying both sides by "x"
A) x^2 -1 = x
A) x^2 -x -1 = 0

Solving by the quadratic formula
x = 1.618 and
y = .618

Interestingly, the number 1.6180339... is called the "phi ratio" or the "golden ratio".
https://en.wikipedia.org/wiki/Golden_ratio

6 0

3 years ago

How to find the vertex calculus 2What is the vertex, focus and directrix of x^2 = 6y

son4ous [18]

Solution:

Given:

$x^2=6y$

Part A:

The vertex of an up-down facing parabola of the form;

$\begin{gathered} y=ax^2+bx+c \\ is \\ x_v=-\frac{b}{2a} \end{gathered}$

Rewriting the equation given;

$\begin{gathered} 6y=x^2 \\ y=\frac{1}{6}x^2 \\ \\ \text{Hence,} \\ a=\frac{1}{6} \\ b=0 \\ c=0 \\ \\ \text{Hence,} \\ x_v=-\frac{b}{2a} \\ x_v=-\frac{0}{2(\frac{1}{6})} \\ x_v=0 \\ \\ _{} \\ \text{Substituting the value of x into y,} \\ y=\frac{1}{6}x^2 \\ y_v=\frac{1}{6}(0^2) \\ y_v=0 \\ \\ \text{Hence, the vertex is;} \\ (x_v,y_v)=(h,k)=(0,0) \end{gathered}$

Therefore, the vertex is (0,0)

Part B:

A parabola is the locus of points such that the distance to a point (the focus) equals the distance to a line (directrix)

Using the standard equation of a parabola;

$\begin{gathered} 4p(y-k)=(x-h)^2 \\ \\ \text{Where;} \\ (h,k)\text{ is the vertex} \\ |p|\text{ is the focal length} \end{gathered}$

Rewriting the equation in standard form,

$\begin{gathered} x^2=6y \\ 6y=x^2 \\ 4(\frac{3}{2})(y-k)=(x-h)^2 \\ \text{putting (h,k)=(0,0)} \\ 4(\frac{3}{2})(y-0)=(x-0)^2 \\ Comparing\text{to the standard form;} \\ p=\frac{3}{2} \end{gathered}$

Since the parabola is symmetric around the y-axis, the focus is a distance p from the center (0,0)

Hence,

$\begin{gathered} Focus\text{ is;} \\ (0,0+p) \\ =(0,0+\frac{3}{2}) \\ =(0,\frac{3}{2}) \end{gathered}$

Therefore, the focus is;

$(0,\frac{3}{2})$

Part C:

A parabola is the locus of points such that the distance to a point (the focus) equals the distance to a line (directrix)

Using the standard equation of a parabola;

$\begin{gathered} 4p(y-k)=(x-h)^2 \\ \\ \text{Where;} \\ (h,k)\text{ is the vertex} \\ |p|\text{ is the focal length} \end{gathered}$

Rewriting the equation in standard form,

Since the parabola is symmetric around the y-axis, the directrix is a line parallel to the x-axis at a distance p from the center (0,0).

Hence,

$\begin{gathered} Directrix\text{ is;} \\ y=0-p \\ y=0-\frac{3}{2} \\ y=-\frac{3}{2} \end{gathered}$

Therefore, the directrix is;

$y=-\frac{3}{2}$

3 0

1 year ago

Help please! Use the area to find the value of x:

olga55 [171]

Answer:

x = 6

Step-by-step explanation:

A = 1/2bh

36 = 1/2(12)(x)

x = 6

3 0

3 years ago

Charlie is evaluating the product of 0.09 and 0.05. He multiplies, and before placing the decimal, arrives at an answer of 45. A

yKpoI14uk [10]

Answer:

Result = 0.0045

Step-by-step explanation:

Given

$0.09 * 0.05$

Required

Determine the result

Following Charlie's steps:

0.09 is a 2 decimal placed digit

and

0.05 is a 2 decimal placed digit

So, the product is as follows:

9 --------- 2 decimal place

5 --------- 2 decimal place

------------------------------------------

45 --------- 4 decimal place

Shifting the decimals in 45 to 4 decimal places will give us: 0.0045

<em>Hence, the final answer is 0.0045</em>

4 0

3 years ago

Please help would mean a lot

jarptica [38.1K]

Answer:

1/2

Step-by-step explanation:

output devided by input

3 0

2 years ago