One afternoon, Olive, who is 2 feet 3 inches tall, casts a shadow that is 6 feet 1 inch long. At the same time of

Which point of intersection is the solution to the system that of equations y= 2/5x-1/2 and y=-1/3x+2/3

Mrrafil [7]

Answer:

x = 35/22

y = 3/22

Step-by-step explanation:

y= 2/5x-1/2 ................(1)

y=-1/3x+2/3 ...............(2)

10*(1)

10y = 4x -5 ...................(1A)

3*(2)

3y = -x +2 ....................(2A)

To find intersection, solve for y & x

4(2A) + (1A)

12y+10y = -4x+4x +8-5

22y = 3

y = 3/22

Substitute in (1)

3/22 = 2/5x -1/2

multiply by 110

15 = 44x - 55

70 = 44x

x = 70/44 = 35/22

5 0

3 years ago

A. Find y in terms of x if

givi [52]

Answer:

A. $y(x) =\sqrt{ 2(\frac{x^5}{5} -\frac{6^5}{5})}$

B.Therefore the solution is defined on the interval:

6≤ x ≤ +∞

Step-by-step explanation:

Given differential equation is

$\frac{dy}{dx} = x^4y^{-1}$

$\Rightarrow \frac{dy}{dx} =\frac{ x^4}{y}$

$\Rightarrow y dy = x^4dx$

Integrating both sides:

$\Rightarrow\int y dy = \int x^4dx$

$\Rightarrow \frac{y^2}{2} =\frac{x^5}{5} +C$ ........(1)

Given y(0)= 6

it means y=0 when x=6

Putting x=6 and y=0 in the equation (1)

$\therefore \frac{0^2}{2} =\frac{6^5}{5} +C$

$\Rightarrow C=-\frac{6^5}{5}$

Equation (1) become:

$\Rightarrow \frac{y^2}{2} =(\frac{x^5}{5} -\frac{6^5}{5})$

$\Rightarrow y} =\sqrt{ 2(\frac{x^5}{5} -\frac{6^5}{5})}$

Therefore $y(x) =\sqrt{ 2(\frac{x^5}{5} -\frac{6^5}{5})}$

(B)

The quantity under root must greater than or equal to zero.

Therefore,

$2(\frac{x^5}{5} -\frac{6^5}{5})} \geq0$

$\Rightarrow \frac{x^5}{5} -\frac{6^5}{5}} \geq0$

$\Rightarrow \frac{x^5}{5} \geq\frac{6^5}{5}}$

$\Rightarrow x^5\geq {6^5$

$\Rightarrow \sqrt[5]{x^5} \geq \sqrt[5]{6^5}$

$\Rightarrow x\geq {6$

When x≥0 then the value of $2(\frac{x^5}{5} -\frac{6^5}{5})}$ is real other wise the value of $2(\frac{x^5}{5} -\frac{6^5}{5})}$ is imaginary.

Therefore the solution is defined on the interval:

6≤ x ≤ +∞

8 0

4 years ago

Jim wants to buy an electric saw marked $98.00. If the salesperson offers him a discount of 15%, how much will he have to pay fo

Schach [20]

Since the discount is 15%, that means that they will pay 85% of the original price ( 100% - 15% = 85%).

Multiply the original price by 85% to find the discounted price:

98.00 x 0.85 = 83.30

They will pay $83.30 for the saw.

6 0

3 years ago

Read 2 more answers

Given h(x) =1/2 x + 4 find h(-4) + 2.

Lynna [10]

Hi there! :)

$\large\boxed{h(-4) + 2 = 4}$

h(x) = 1/2x + 4

Substitute in -4 for "x" to solve for h(-4):

h(-4) = 1/2(-4) + 4

h(-4) = -2 + 4

h(-4) = 2

Since we are solving for h(-4) + 2, add:

2 + 2 = 4.

8 0

3 years ago

Read 2 more answers

3y+6(3y-2) = 2(y-1)-7<br><br> solve for y , reduce answer to integer or fraction.

Alexxandr [17]

=3y+18y-12=2y-2-7
=21y-12=2y-9
=21y-2y=-9+12
=19y=3
Y=0,16

4 0

4 years ago

Read 2 more answers