Answer:
Step-by-step explanation:
Step 1 - As both triangles have lengths the same size, they both add together to equal a rectangle. Therefore:
4 x 3 = 12
Which is the area of the triangles.
Step 2 - Calculating the area of a circle uses the formula:
Where r is the radius of the circle.
Plug the known variables in:
However, this is the area of a full circle. The figure is only half a circle so we must divide this by two:
28.26 ÷ 2 = 14.13
Now, add the area of the semi-circle to the area of the triangles:
14.13 + 12 = 26.13
Therefore, the area of the figure is .
Hope this helps!
Compute the derivative dy/dx using the power, product, and chain rules. Given
x³ + y³ = 11xy
differentiate both sides with respect to x to get
3x² + 3y² dy/dx = 11y + 11x dy/dx
Solve for dy/dx :
(3y² - 11x) dy/dx = 11y - 3x²
dy/dx = (11y - 3x²)/(3y² - 11x)
The tangent line to the curve is horizontal when the slope dy/dx = 0; this happens when
11y - 3x² = 0
or
y = 3/11 x²
(provided that 3y² - 11x ≠ 0)
Substitute y into into the original equation:
x³ + (3/11 x²)³ = 11x (3/11 x²)
x³ + (3/11)³ x⁶ = 3x³
(3/11)³ x⁶ - 2x³ = 0
x³ ((3/11)³ x³ - 2) = 0
One (actually three) of the solutions is x = 0, which corresponds to the origin (0,0). This leaves us with
(3/11)³ x³ - 2 = 0
(3/11 x)³ - 2 = 0
(3/11 x)³ = 2
3/11 x = ³√2
x = (11•³√2)/3
Solving for y gives
y = 3/11 x²
y = 3/11 ((11•³√2)/3)²
y = (11•³√4)/3
So the only other point where the tangent line is horizontal is ((11•³√2)/3, (11•³√4)/3).
The image of the car park showing the 2 angles is attached.
Answer:
Their lines are parallel.
Step-by-step explanation:
From the attached image, we can see that ∠1 and ∠2 form a pair of alternate exterior angles. Thus; ∠1 = ∠2.
Now since they are congruent, it means that their lines will be parallel.
Thus, we can conclude that their lines are parallel.
Answer:
$32.39
Step-by-step explanation:
She has a 15-gallon tank and it has 1/5 a tank of gas left (so about 3/15)
Because she needs to refill it and already has 1/5, she'll only need to pay for 4/5 a tank of gas (12/15).
So the equation should be 12 times $2.699.
12 × 2.699 = 32.388
Then, round to the nearest cent.
32.388 = $32.39
Hope this helped !
Answer:
B and C
Step-by-step explanation:
