Answer:
1/6 cubic unit
Step-by-step explanation:
Each plane describes the boundary of a triangular pyramid in the first octant. If we consider the x-y plane to be the base, that base will have an area that is 1/2 the product of the x- and y-intercepts. The height of the pyramid will be the z-intercept, so the volume is ...
V = (1/3)Bh = (1/3)((1/2)(x-intercept)(y-intercept))(z-intercept))
= (1/6)(x-intercept)(y-intercept)(z-intercept)
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We can write the equation of each plane in intercept form by dividing by the constant on the right:
x/(x-intercept) + y/(y-intercept) + z/(z-intercept) = 1
1st plane: x/1 + y/1 + z/1 = 1 . . . . . enclosed volume = (1/6)(1)(1)(1) = 1/6
2nd plane: x/1 + y/1 + z/2 = 1 . . . enclosed volume = (1/6)(1)(1)(2) = 2/6
The difference between the volumes enclosed by the planes is the volume of the region between them, so is ...
V = (2/6) -(1/6) = 1/6 . . . . cubic units
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We note that the x- and y-intercepts of both planes are the same, so the volume is that of a triangular wedge having an edge on the line x+y=1 in the plane z=0.
Answer: D.
Step-by-step explanation:
Using exponent rules an exponent to the power of a number will multiply by each other.
So the -4 and -9 will multiply.
The 6 in the numerator will now have a positive exponent of 36.
Now we can divide and when we do so the exponents will subtract from each other.
So 36 - 6 = 30
And the base of 6 does not change.
The simplified form is
Every positive real number has TWO<span>square roots; One is positive and one is negative. They are opposites of each other. </span>
10 is a square root of 100 because (10)(10) = 100, and ̶ 10 is also a square root of 100 because ( ̶ 10)( ̶ 10) = 100.
In general, “a” is a square root of “b” if a² = b, where “a” is a real number and b ≥ 0.
In conclusion:
<span> √(100) = </span>10<span> (the </span>positive<span> square root of 100) </span>and<span> </span>
<span> ̶ √(100) = ̶ (10) = </span>̶ 10<span> (the </span>negative<span> square root of 100)</span>
Answer:
no
Step-by-step explanation:
The time required for the hike Hank would like to take is ...
t = (d + elevation/1000)/2
= (6 + 3000/1000)/2
= 9/2
= 4.5 . . . . hours
Hank's hike is recommended to take 4.5 hours. If Hank only has 4 hours, he will not be able to complete the hike in the time available.
Answer:
23
Step-by-step explanation:
25.73−2.19
=25.73−2.19
=25.73+−2.19
=23.54