Answer:
(see attached workings)
y = -4x + 2
y = (4/5)x + 2/5
Step-by-step explanation:
- Rewrite the function to make y the subject.
- Find the x values of the points when y=-2 by substituting y=-2 into the rewritten function
- Differentiate the function
- Input the found values of x into the differentiated function to find the gradients of the tangents to the curve at y=-2
- Use the equation of a straight line and the points where y=-2 and the found gradients to find the equation of the tangent lines.
See attached for complete step-by-step.
Answer:
The volume of water that remains on the cone is 523.6 cm³
Step-by-step explanation:
To solve this problem you have to keep in mind the formules that describes the volume of a cone and the volume of a sphere.
Volume of a cone = (πr²h)/3
Volume of a sphere = (4/3)πr³
So, if the base of the cone has a diameter of 10 cm, its radius is 5 cm. Its altitude is 10 cm. ⇒Volume = (πr²h)/3 ⇒ Volume = [π(5²)10) ⇒
Volume = 785.4 cm³. This is the initial volume of water.
Now if the sphere fits in the cone and half of it remains out of the water, the other half is inside the cone. Estimating the volume of the sphere and dividing it by two, you find the volume of water that was displaced.
Volume of a sphere = (4/3)πr³, here the radius is the same of the base of the cone (5 cm).
⇒ Volume = (4/3)π(5³) ⇒ Volume = 523.6 cm³ ⇒ The half of this volume is 261.8 cm³. This is the volume of water displaced.
⇒ The volume of water that remains on the cone is 523.6 cm³ (785.4 cm³- 261.8 cm³)
I think it's D. The area of A is k2 times the area of rectangle B
Answer:
Step-by-step explanation:
hello :
f(x)=3x^2-6x+13
1) a=3 and b= -6
2) the x coordinate of the vertex is : x= -b/2a so : x= -(-6)/6 = 1
3) the y coordinate by x= 1 is : f(1) = 3(1)²-6(1)+13 = 10
