Answer:
Kayla is correct; the center is a fixed point in the middle of the sphere.
Step-by-step explanation:
Kayla is correct. Raymond is wrong because a point cannot be a radius: a radius is a line segment from the center to the surface.
The center is the fixed point in the middle of the sphere.
Answer:
49/8 is the value of k
Step-by-step explanation:
We have the system
x = -2y^2 - 3y + 5
x=k
We want to find k such that the system intersects once.
If we substitute the second into the first giving us k=-2y^2-3y+5 we should see we have a quadratic equation in terms of variable y.
This equation has one solution when it's discriminant is 0.
Let's first rewrite the equation in standard form.
Subtracting k on both sides gives
0=-2y^2-3y+5-k
The discriminant can be found by evaluating
b^2-4ac.
Upon comparing 0=-2y^2-3y+5-k to 0=ax^2+bx+c, we see that
a=-2, b=-3, and c=5-k.
So we want to solve the following equation for k:
(-3)^2-4(-2)(5-k)=0
9+8(5-k)=0
Distribute:
9+40-8k=0
49-8k=0
Add 8k on both sides:
49=8k
Divide both sides by 8"
49/8=k
So find g(0) and g(3)
G(0) = 0^2 -5(0) +3 = 3
And g(3) = 3^2 - 5(3) +3 = 9 - 15 + 3 = 3 so there is no change in g(x) for that interval.
H(0) = 8(0) + 10 = 10
And h(3) = 8(3) + 10 = 34
So the change in h(x) for that interval is 24.
Answer:
$33.81
Step-by-step explanation:
2.49*3 = 7.47 dollars for 3 pounds of strawberries
3.19*2 = 6.38 dollars for 2 pounds of blueberries
4.99*4 = 19.96 dollars for 4 pounds of pineapple
7.47 + 6.38 + 19.96 = 33.81 dollars spent in total
Answer:
d
Step-by-step explanation:
This is point-slope form, and these coordinates make both sides equal to 0.
