The equation of the plane that goes through these points is:
6x + 2y + z = 10.
<h3>How to find the equation of a plane given three points?</h3>
The equation of the plane is found replacing the points into the following equation:
ax + by + c = z.
For point A, we have that:
3b + c = 4.
For point B, we have that:
a + 2b + c = 0.
For point C, we have that:
-a + 6b + c = 4.
Hence the system is:
From the first equation, we have that:
c = 4 - 3b.
Replacing in the second, we have that:
a + 2b + 4 - 3b = 0
a - b = -4.
Replacing in the third, we have that:
-a + 6b + 4 - 3b = 4.
-a + 3b = 0.
a = 3b.
We have that a - b = -4, hence:
3b - b = -4
2b = -4
b = -2.
a = 3b, hence a = -6.
c = 4 - 3b -> c = 10.
Hence the equation is:
ax + by + c = z.
z = -6x - 2y + 10
6x + 2y + z = 10.
More can be learned about the equation of a plane at brainly.com/question/13854649
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Answer: -20/3
Step-by-step explanation:
Answer:
y = 5cos(πx/4) +11
Step-by-step explanation:
The radius is 5 ft, so that will be the multiplier of the trig function.
The car starts at the top of the wheel, so the appropriate trig function is cosine, which is 1 (its maximum value) when its argument is zero.
The period is 8 seconds, so the argument of the cosine function will be 2π(x/8) = πx/4. This changes by 2π when x changes by 8.
The centerline of the wheel is the sum of the minimum and the radius, so is 6+5 = 11 ft. This is the offset of the scaled cosine function.
Putting that all together, you get
... y = 5cos(π/4x) + 11
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The answer selections don't seem to consistently identify the argument of the trig function properly. We assume that π/4(x) means (πx/4), where this product is the argument of the trig function.
Answer:
The proportion would be 0.1
Step-by-step explanation:
Given, the function that shows the proportion of students in a psychology experiment who could remember an eight-digit number correctly for t minutes,

If t = 7 minutes,

Hence, the proportion that remembered the number for 7 minutes is 0.1 ( approx )
0.65625 is the decimal product of the fractions 3/4 & 7/8 whereas 7/8 can be simplified to 0.875 in decimal form... comparing both the values, we see that 7/8 is greater than the product of 3/4 and 7/8.