The midpoint, where the rest area is, will just be the average of the coordinates of Springfield and Columbus.
Rest Area=((1+7)/2, (-4+1)/2)
Rest Area=(4, -1.5)
The distance between the two cities can be found using the Pythagorean Theorem, which used in the manner is often referred to as the "distance" formula between two points.
d^2=(x2-x1)^2+(y2-y1)
d^2=(7-1)^2+(1--4)^2
d^2=36+25
d^2=61
d=√61 and we are told that each unit is equal to 5.38mi so the distance from Springfield to Columbus is:
D=5.38√61 mi
D≈42.02mi (to nearest hundredth of a mile)
The 12th term in the sequence is -26.
Given,
B (n) = -4 – 2(n – 1)
We have to find the 12th term in the sequence:
To find the nth term in an arithmetic sequence:
An arithmetic sequence's nth term is determined by the formula a = a + (n - 1)d. The common difference, or d, is the difference between any two consecutive terms in an arithmetic series; it can be calculated by deducting any pair of terms starting with a and an+1.
Here,
First term, a = -4
Common difference, d = -2
nth term = 12
Now, let’s find 12th term
B(n) = -4 -2(n – 1)
B(12) = -4 – 2(12 – 1)
B(12) = -4 -2(11)
B(12) = -4 -22
B(12) = -26
That is, the 12th term in the sequence is -26.
Learn more about arithmetic sequence here:
brainly.com/question/11570734
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Let
. The gradient of
at the point (1, 0, 0) is the normal vector to the surface, which is also orthogonal to the tangent plane at this point.
So the tangent plane has equation

Compute the gradient:

Evaluate the gradient at the given point:

Then the equation of the tangent plane is

Answer:
x = 4
Step-by-step explanation:
Using the sine ratio on right triangle KJL
and the exact value sin30° = 
sin30° =
=
=
=
( cross- multiply )
2JL = 8
( divide both sides by 2 )
JL = 4
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Using the sine ratio in right triangle JLM
and the exact value sin45° = 
sin45° =
=
=
=
( cross- multiply )
x ×
= 4
( divide both sides by 
x = 4