In the diagram below Please help I’ll give brainliest
1 answer:
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Answer:
b = 4.6 ft
h = 2.3 ft
Step-by-step explanation:
The volume of the tank is given by:
Where 'b' is the length of the each side of the square base, and 'h' is the height of the tank.
The surface area can be written as:
The value of b for which the derivate of the expression above is zero is the value that yields the minimum surface area:
The value of h is then:
Rounded to the nearest tenth, the dimensions are b = 4.6 ft and h = 2.3 ft.
Answer:
The angular speed of the wheel in radians per second is 0.66.
Step-by-step explanation:
Recall the following statement:
A linear speed (v) is given by,
...... (1)
Here, represents the angular speed of the wheel and <em>r</em> represents the radius of the wheel.
From the given information:
Linear speed (v) = 33 cm/s
Radius of the wheel (r) = 50 cm
Now to find the angular speed in radian per second.
Divide both sides by 50.
Hence, the angular speed of the wheel in radians per second is 0.66.
The shape of the graph of quadratic functions is the shape of a parabola.
The steps for drawing a graph of the function f(x) = 2·(x + 4)² - 3 arranged in the correct order are;
- (a) Plot the vertex (-4, -3)
- (b) Apply the 2·x² pattern, from the vertex go right 1 up 2 and plot (-3, -1)
- (c) Apply the 2·x² pattern again, from the vertex go right 2 up 8 and plot (-2, 5)
- (d) Apply the 2·x² pattern a 3rd time, from the vertex go right 3 up 18 and plot (-1, 15)
- (e) Draw the axis of symmetry x = -4
- (f) Reflect the points over the axis of symmetry and plot (-5, -1), (-6, 5), and (-7, 15)
- (g) Draw a U shaped parabola.
Reasons:
The given function is; f(x) = 2·(x + 4)² - 3
The function is given in the vertex form; f(x) = a·(x - h)² + k
Therefore, the vertex, (h, k) = (-4, -3)
Step (a);
The vertex can be plotted on the graph
- Plot the vertex (-4, -3)
Step (b);
Given that the quadratic term is 2·x², the pattern that can be used for the points from the vertex is therefore, 2·x²
From the vertex (-4, -3) apply the 2·x² pattern by going to the right 1 unit and up 2 × 1² = 2 units to get the point (-4 + 1, -3 + 2) = (-3. -1)
- Apply the 2·x² pattern, from the vertex go right 1 up 2 and plot (-3, -1)
Step (c);
To get the next point, the 2·x² pattern is applied with x = 2, to the vertex to get; (-4 + 2, -3 + (2×2²)) = (-2, 5)
- Apply the 2·x² pattern again, from the vertex go right 2 up 8 and plot (-2, 5)
Step (d);
A third point on the graph relative to the vertex is obtained again by applying the 2·x² pattern again to the vertex with x = 3, to get;
(-4 + 3, -3 + (2 × 3²)) = (-1, 15)
- Apply the 2·x² pattern a 3rd time, from the vertex go right 3 up 18 and plot (-1, 15)
Step (e);
The axis of symmetry can be drawn with a vertical line passing through the vertex, which is the line, x = -4
The line x = -4 can be drawn on the graph next
- Draw the axis of symmetry x = -4
Step (f);
The points obtained relative to the vertex (-3, -1), (-2, 5), (-1, 15) can reflected about the axis of symmetry x = -4, to get;
(-3, -1) (-5, -1)
(-2, 5) (-7, 5)
(-1, 15) (-7, 15)
- Reflect the points over the axis of symmetry and plot (-5, -1), (-6, 5), and (-7, 15)
Step (g);
The parabola that is U shaped can be drawn from the points plotted in the steps above.
- Draw a U shaped parabola
Learn more about drawing the graph of a quadratic function here: