Answer:
All the points that lie on the line:
Step-by-step explanation:
In order to find the maximum rate of change, we need to find the gradient of the function. The gradient of a function of two variables is defined to be:
So:
Hence:
Since we need to find all the points at which the direction of fastest change of the function is . Then:
Therefore:
So, we can conclude, that all the points where the direction of fastest change of lie on the line:
Answer:
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Step-by-step explanation:
Answer:
x = 38°
Step-by-step explanation:
Let's find the internal angles of the triangle, at the base.
We see that one external angle is 134° and we need to find its supplementary angle (a+b = 180°) so:
134° + α = 180°
α = 46°
Now the other base angle:
β + 84° = 180°
β = 96°
We also know that the sum of all angles in a triangle is always 180°:
α + β + x = 180°
x = 180° - α - β = 38°
The total surface area of the remaining solid is 48(4+✓3) centimeters square.
<h3>How to calculate the surface area?</h3>
Through a regular hexagonal prism whose base edge is 8 cm and the height is 12 cm, a hole in the shape of a right prism.
The formula for the total surface area will be:
= Total surface area=2(area of the base)+ parameter of base × height
where,
Height= 8cm
Parameter of base=12(2) = 24
Area of the base= 6×✓3/4×4² = 64✓3/4
The surface area of the remaining solid will be:
= 2(64✓3/4) + 24 × 8
= 2(64✓3/4 + 192
With the hole is a rhombus prism with the following parameters:
diagonal 1 = 6, diagonal 2 = 8, height = 12
The volume is:
V1 =0.5 × d1 × d2 × h
V1 = 0.5 × 6 × 8 × 12
V1 = 96
The dimensions of the hexagonal prism are:
Base edge (a) = 8
Height (h) = 12
The volume is
V2 = (3✓(3)/2)a²h
V2 = (3✓3)/2) × 8² × 12
V2 = 1152✓3
The remaining volume is
V = V2 -V1
V = 1152✓3 - 96
Learn more about the hexagonal prism on:
brainly.com/question/27127032
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Let the red cat be represented by x.
Let the yellow cat be represented by y.
Let the white cat be represented by z.
Which means :
Thus, the first statement is correct.
Thus, the second statement is a lie.
Thus, the third statement is correct.
Therefore, <u>the second one is a lie</u>.