Answer:
The smallest solution is -6
Step-by-step explanation:
2/3 x^2=24
Multiply by 3/2 on each side
3/2 *2/3 x^2=24 *3/2
x^2 = 36
Take the square root of each side
sqrt(x^2) = ±sqrt(36)
x = ±6
x = -6, 6
The smallest solution is -6
If you learned about the 45-45-90 triangle (which is isosceles), then the faster way is to know that the hypotenuse (side opposite of right angle) is √2 times either one of the sides.
3√2 = (√2)x
x = 3
But if you didn't learn the 45-45-90 triangle yet, that's ok.
Recall the trigonometric ratios for right triangles: sine (sin), cosine (cos), tangent (tan).
If your angle is x, then
sin(x) = opposite side / hypotenuse
cos(x) = adjacent side / hypotenuse
tan(x) = opposite side / adjacent side
Remember the hypotenuse is the side opposite and across from the right angle (3√2 in this case).
An acronym to remember this is SohCahToa.
In this problem, the angle given is 45°, and you need to find the length of the adjacent side x. The hypotenuse is also given as 3√2.
Because we have the adjacent side and the hypotenuse, we use cosine to relate those two sides
cos(45°) = x / (3√2)
x = (3√2)cos45°
If you plug this into your calculator (in degree mode), then
x = 3
Data: (Cylinder)
h (height) = 8 cm
r (radius) = 5 cm
Adopting:
V (volume) = ?
Solving:(<span>Cylinder volume)
</span>
<span>Note: Now, let's find the volume of a hemisphere.
</span>
Data: (hemisphere volume)
V (volume) = ?
r (radius) = 5 cm
Adopting:
If: We know that the volume of a sphere is
, but we have a hemisphere, so the formula will be half the volume of the hemisphere
Formula: (<span>Volume of the hemisphere)
</span>
Solving:
<span>Now, to find the total volume of the figure, add the values: (cylinder volume + hemisphere volume)
</span>
Volume of the figure = cylinder volume + hemisphere volume
Volume of the figure = 628 cm³ + 261.6 cm³
Answer:
Slope formula: (b) m = y2 – y1 / x2 – x1
Point-Slope Formula: (c) y – y1 = m (x – x1)
Slope Intercept Form: (a) y = mx + b