Answer:
Step-by-step explanation:
We can use the distance formula derived from the Pythagorean theorem
D = 
the two points given are
(0, 3) and (-2, -3)
<h2>
Answer:</h2><h3>
x = -9</h3>
<h2>Step-by-step explanation:</h2>
<h3><u>Step 1</u>: Simplify both sides of the equation.</h3><h3 /><h3>1/3x+1=−2</h3><h3 /><h3><u>Step 2</u>: Subtract 1 from both sides.</h3><h3 /><h3>1/3x+1−1=−2−1</h3><h3 /><h3>1/3x=−3</h3><h3 /><h3><u>Step 3</u>: Multiply both sides by 3.</h3><h3 /><h3>3*(1/3x)=(3)*(−3)</h3><h3 /><h3>x=−9</h3>
Answer:
35
Step-by-step explanation:
Make equations, l = w+5 and 2l + 2w = 150
Substitute w+5 into 2l + 2w = 150
Simplify to get 4w + 10 = 150
Subtract 10 from both sides to get 4w = 140
Divide both sides by 4 and you get 35 as width
The area of the triangle is
A = (xy)/2
Also,
sqrt(x^2 + y^2) = 19
We solve this for y.
x^2 + y^2 = 361
y^2 = 361 - x^2
y = sqrt(361 - x^2)
Now we substitute this expression for y in the area equation.
A = (1/2)(x)(sqrt(361 - x^2))
A = (1/2)(x)(361 - x^2)^(1/2)
We take the derivative of A with respect to x.
dA/dx = (1/2)[(x) * d/dx(361 - x^2)^(1/2) + (361 - x^2)^(1/2)]
dA/dx = (1/2)[(x) * (1/2)(361 - x^2)^(-1/2)(-2x) + (361 - x^2)^(1/2)]
dA/dx = (1/2)[(361 - x^2)^(-1/2)(-x^2) + (361 - x^2)^(1/2)]
dA/dx = (1/2)[(-x^2)/(361 - x^2)^(1/2) + (361 - x^2)/(361 - x^2)^(1/2)]
dA/dx = (1/2)[(-x^2 - x^2 + 361)/(361 - x^2)^(1/2)]
dA/dx = (-2x^2 + 361)/[2(361 - x^2)^(1/2)]
Now we set the derivative equal to zero.
(-2x^2 + 361)/[2(361 - x^2)^(1/2)] = 0
-2x^2 + 361 = 0
-2x^2 = -361
2x^2 = 361
x^2 = 361/2
x = 19/sqrt(2)
x^2 + y^2 = 361
(19/sqrt(2))^2 + y^2 = 361
361/2 + y^2 = 361
y^2 = 361/2
y = 19/sqrt(2)
We have maximum area at x = 19/sqrt(2) and y = 19/sqrt(2), or when x = y.
An average watering can is 5 liters so 5 liters
