What is .35 as a decimal and fraction

Find the dimensions of the rectangle of largest area that has its base on the x-axis and its other two vertices above the x-axis

stealth61 [152]

Complete question is;

Find the dimensions of the rectangle of largest area that has its base on the x-axis and its other two vertices above the x-axis and lying on the parabola. (Round your answers to the nearest hundredth.) y = 6 - x²

Answer:

height = 4 and base = 2√2

Step-by-step explanation:

Area of a rectangle is given by;

A = base(b) × height(h)

To start off, we will first have to consider half of the rectangle.

Due to the fact that it is bounded by a parabola which is symmetric over the y-axis, it means that the rectangle will have the same area on the right and left hand sides.

So if we maximize the area of the first quadrant, it means that we are also maximizing the area of the entire rectangle.

Now, since we are dealing with the base and other 2 vertices on the x-axis, it means that the base(b) of this half rectangle will be x.

The height of this rectangle is the y coordinate of the corner that is directly above the x coordinate, which is also on the rectangle.

Therefore, the coordinates of the upper corner will be (x, y), or (x, 6 - x²). Thus our half base is x and full height is 6 - x². Area will be;

A = x(6 - x²)

A = 6x - x³

We will maximize this area by finding the derivative and equating to zero.

Thus;

A' = 6 - 3x²

At A' = 0,we have;

6 - 3x² = 0

3x² = 6

x² = 6/3

x² = 2

x = √2

Thus, from y = 6 - x², we have;

y = 6 - (√2)²

y = 6 - 2

y = 4

Since x is half base, it means our full width is 2x = 2 × √2 = 2√2

So, height = 4 and base = 2√2

8 0

3 years ago

Noel is a computer repairman. To fix a computer, he charges a customer $40 per hour, plus a fixed fee of $15, represented by the

SVETLANKA909090 [29]

Answer: the answer would be A. the number of hours Noel worked

sorry i responded so late but i hope this helps you

Step-by-step explanation:

4 0

3 years ago

(4+4)÷22×2<br><br> plss someone answer hurry <3

sineoko [7]

Answer:

first is 4+4=8.........second is 22×2=11 ..........third is 8÷11=0.7272727273 u can do it 0.72

Step-by-step explanation:

hope this help

7 0

3 years ago

Read 2 more answers

So, I undestood slope right. But, I get confused with the other points that intersect there is multiple of them. How do i look f

ivanzaharov [21]

Answer:

slope = 2

Step-by-step explanation:

Find 2 points on the line that land perfectly on the grid. I'll choose these 2 here:

(-2, -1) and (0, 3)

Rise is the change in the y value from one point to the other, and run is the change in the x. Looking at these 2 points, y went from -1 to 3. That is a <em>rise</em> of 4. The x went from -2 to 0, so that is a <em>run</em> of 2. "rise over run" means rise literally over run in a fraction like this:

$m=\frac{rise}{run}$

The more proper way to calculate slope looks like this, but it's really the same thing in the end:

$m=\frac{y2-y1}{x2-x1}$

where (x1, y1) and (x2, y2) are your 2 points.

Finally, the slope of this line is:

$m=\frac{3--1}{0--2}\\\\m=\frac{4}{2}\\\\m=2$

That's a rise of 4 over a run of 2, and that simplifies to just a slope of 2.

8 0

3 years ago

Eric, Shenna, and Yael are playing a game. Eric has half as many points as Shenna. Shenna has three fewer points than Yael. Alto

Anon25 [30]

Using algebraic equations, the number of points Yael has is calculated as: 29 points.

<h3>How to Use Algebraic Equations to Solve Word Problems?</h3>

In the given world problem, we known the following:

E = Eric

S = Shenna

Y = Yael

Their total points would be: E + S + Y = 68

S = 2(E) (Shenna has twice the points of Erik)

Y = S + 3 (Yael has three points more than Shenna)

We would therefore have the following algebraic equation:

E + 2E + (S + 3) = 68

Substitute S with 2E

E + 2E + 2E + 3 = 68

Solve for E

5E + 3 = 68

5E = 68 - 3

5E = 65

5E/5 = 65/5

E = 13

Eric's points is: 13

Yael's points = Y = S + 3

Y = S + 3 = 2E + 3

Plug in the value of E

Y = 2(13) + 3

Y = 26 + 3

Y = 29

Yael has 29 points.

Learn more about algebraic equation on:

brainly.com/question/2164351

#SPJ1

5 0

1 year ago