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3 years ago

What are the coordinates of the x-intercept and y-intercept of the line -3y-x=-9

Mathematics

1 answer:

PIT_PIT [208]3 years ago

8 0

Answer:

Step-by-step explanation:

The x-intercept exists when y = 0; the coordinate takes on the form ( , 0)

The y-intercept exists when x = 0; the coordinate takes on the form (0, ).

We will fill in the blanks in a sec.

If the x-intercept exists when y = 0, then we fill in 0 for y and solve for x:

-3(0) - x = -9 so

-x = -9 and

x = 9

The coordinate is (9, 0) for the x-intercept.

If the y-intercept exists when x = 0, then we fill in 0 for x and solve for y:

-3y - 0 = -9 so

-3y = -9 and

y = 3

The coordinate is (0, 3) for the y-intercept.

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A Norman window has the shape of a rectangle surmounted by a semicircle. Suppose the outer perimeter of such a window must

Feliz [49]

The base length that will maximize the area for such a window is 168.03 cm. The exact largest value of x when this occurs is 233.39 cm

Suppose we make an assumption that:

(x) should be the width of the rectangle base;
(h) should be the height of the rectangle

Also, provided that the diameter of the semi-circle appears to be the base of the rectangle, then;

the radius $\mathbf{r = \dfrac{x}{2}}$

and, the perimeter of the window can now be expressed as:

$\mathbf{x + 2h + \pi r = x + 2h + \dfrac{\pi x }{2}}$

$\mathbf{= \Big ( 1 + \dfrac{\pi}{2}\Big) x + 2h}$

Given that the perimeter = 600 cm

∴

$\mathbf{ \Big ( 1 + \dfrac{\pi}{2}\Big) x + 2h= 600}$

$\mathbf{ h = 300 - \Big( \dfrac{1}{2} + \dfrac{\pi}{4}\Big) x}$

Since h > 0, then:

$\mathbf{ h = 300 - \Big( \dfrac{1}{2} + \dfrac{\pi}{4}\Big) x>0}$

By rearrangement and using the inverse rule:

$\mathbf{ x< \dfrac{ 300}{\Big( \dfrac{1}{2} + \dfrac{\pi}{4}\Big) } }$

$\mathbf{ x= \dfrac{ 1200}{\Big( 2 +\pi \Big) } }$

$\mathbf{ x= 233.39 \ cm }$

Thus, the largest length x = 233.39 cm

However, the area of the window is given as:

$\mathbf{A(x) = xh + \dfrac{1}{2} \pi r^2}$

$\mathbf{A = x \Big [ 300 - \Big ( \dfrac{1}{2}+\dfrac{1}{4} \Big) x \Big ] +\dfrac{1}{2}\pi \Big(\dfrac{x}{2} \Big )^2}$

$\mathbf{A (x) = 300x - \Big( \dfrac{1}{2} + \dfrac{\pi}{8}\Big) x^2 \ cm^2}$

Now, at maximum, when the area A = 0. Taking the differentiation, we have:

$\mathbf{\dfrac{d}{dx} 300x - \dfrac{d}{dx} \Big( \dfrac{1}{2} + \dfrac{\pi}{8}\Big) x^2 \ =0}$

$\mathbf{ 300 - 2x \Big( \dfrac{1}{2} + \dfrac{\pi}{8}\Big) \ =0}$

Making x the subject of the formula, we have:

$\mathbf{x = \dfrac{1200}{4 +\pi}}$

x = 168.03 cm

Taking the second derivative:

$\mathbf{\dfrac{d}{dx} \Big [300 -2x \Big( \dfrac{1}{2} + \dfrac{\pi}{8}\Big) \Big]}$

$\mathbf{= -2 \Big( \dfrac{1}{2}+\dfrac{\pi}{8}\Big )$

Therefore, we can conclude that the maximum area that exists for such a window is 168.03 cm

Learn more about derivative here:

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3 years ago

Vernon writes −2 3/10 as a fraction using the same method he knows for positive mixed numbers. His work is shown: Multiply the w

love history [14]

Answer: no

Step-by-step explanation: to change a fraction back to a improper fraction

multiply the whole number by the denominator and then add it to the numerator but be careful with negative. You can check this process by changing the improper fraction back to proper. If i change -17/10 i get -1 7/10. the correct answer is -23/10.

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3 years ago

What is the greatest common factor of 120 and 168

GaryK [48]

Answer:

Step-by-step explanation:

gcf for that is 24 I think

5 0

2 years ago

Read 2 more answers

What is 50%+100094648%

nataly862011 [7]

Answer:

Percent : 10,009,514‬

Decimal : 1000946.98

Step-by-step explanation:

7 0

3 years ago

You multiply a number by 3 subtract 6 then add 2 the results is 20 what's the number

e-lub [12.9K]

You multiply a number by 3 subtract 6 then add 2 the results is 20

what's the number ?

Let the number = x

multiply a number by 3

so, it becomes 3x

subtract 6 , so, 3x - 6

then add 2

so, 3x - 6 + 2

The result will be 20

So,

3x - 6 + 2 = 20

solve for x

3x - 4 = 20

Add 4 to both sides

3x - 4 + 4 = 20 + 4

3x = 24

Divide both sides by 3

3x/3 = 24/3

So,

x = 8

5 0

1 year ago