Answer:
Sphere Formulas in terms of radius r:
Volume of a sphere: V = (4/3)πr.
Answer:
D is false
Step-by-step explanation:
f(x) = -2x2 + 4x + 6 should be written with a " ^ " to indicate exponentiation:
f(x) = -2x^2 + 4x + 6.
Because of the - sign, we know that the graph of this function opens down, so there is a maximum at the vertex. We can determine the x-value at the vertex by using the formula x = -b/(2a), which here is x = -4/(2*-2), or 1.
Evaluating f(x) = -2x^2 + 4x + 6 at x = 1, we get -2 + 4 + 6, or 8. So statement A is true: there's a max at (1, 8). This is also the vertex of the graph.
Let's now look at C and D. We evaluate f(x) at x = 3 and x - 2. If the output (y) value is 0, we know we have an x - intercept:
f(3) = -2(9) + 4(3) + 6 = 0. Yes, C is true, (3, 0) is an x-intercept.
f(-2) = -2(4) - 8 + 6 is not 0. Therefore D is false; (-2, 0) is not an x-intercept.
Look at B: Let x = 0 and find y: it's 6. Thus, (0, 6) is the y-intercept. B is true.
Answer:
<VUT = 50
Step-by-step explanation:
Tangent Chord Angle = 1/2 Intercepted Arc
< VUT = 1/2 (100)
<VUT = 50
Answer: d = 12
Step-by-step explanation: First isolate d/3 by subtracting 10 from both sides of the equation. That gives you d/3 = 4.
From here, since <em>d</em> is being divided by 5, multiply both sides of the equation by 5 so <em>d = 12</em>.
First make a triangle by connecting the center point of the circle to one of the end points of the chord.
This will make a right triangle. The new formed line is the radius of the circle and will be the hypotenuse of the right triangle too.
Since one of the legs of the right triangle is half the chord, divide the chord in to two.
9.6 / 2 = 4.8
Now we can calculate for the hypotenuse.
Pythagorean theorem states that a²+b² = c²
So
√2.4² + 4.8² = c
√5.76 + 23.04 = c
√28.8 = c
5.4 = c
C is the hypotenuse and the hypotenuse is known as the radius of the circle.
So the radius is 5.4
