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2 years ago

The expression 2x + 50 represents the elevation above sea level, in meters, of a rock climber after x minutes of climbing.

Mathematics

2 answers:

Gnesinka [82]2 years ago

8 0

2x+50 divided by x is 2+50/x

natka813 [3]2 years ago

3 0

The correct answer is 50 meters.

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At which points are the tangents drawn to the ellipse x 2 + y 2 = [ a ] x + [ a ] y parallel to

In-s [12.5K]

The given equation of the ellipse is x^2 + y^2 = 2 x + 2 y

At tangent line, the point is horizontal with the x-axis therefore slope = dy / dx = 0

So we have to take the 1st derivative of the equation then equate dy / dx to zero.

x^2 + y^2 = 2 x + 2 y

x^2 – 2 x = 2 y – y^2

(2x – 2) dx = (2 – 2y) dy

(2x – 2) / (2 – 2y) = 0

2x – 2 = 0

x = 1

To find for y, we go back to the original equation then substitute the value of x.

x^2 + y^2 = 2 x + 2 y

1^2 + y^2 = 2 * 1 + 2 y

y^2 – 2y + 1 – 2 = 0

y^2 – 2y – 1 = 0

Finding the roots using the quadratic formula:

y = [-(- 2) ± sqrt ( (-2)^2 – 4*1*-1)] / 2*1

y = 1 ± 2.828

y = -1.828 , 3.828

Therefore the tangents are parallel to the x-axis at points (1, -1.828) and (1, 3.828).

3 0

3 years ago

A scale drawing has a scale of 3 in.: 1 ft. What is the scale factor?

exis [7]

Answer:

1/4

Step-by-step explanation:

1 foot = 12 inches

the scale factor is 3" to 12" which simplifies to be 1/4

4 0

2 years ago

The length of a rectangle is one inch less than five times its width. If the perimeter of the rectangle is 46 inches, find its d

My name is Ann [436]

Answer:

19,4 or 4,19

Step-by-step explanation:

Let the width of the rectangle be 'w' in

According to the question length of the rectangle (l) is one inch less than five times it's width;

$\longrightarrow$ l = (5w - 1) in

Perimeter of rectangle = 46 inches

Formula of perimeter of rectangle = 2(Length + Width)

So,

$\rm \implies 2(Length + Width) = 46 \\ \\ \rm \implies 2(5w - 1 + w) = 46 \\ \\ \rm \implies 2(6w - 1) = 46 \\ \\ \rm \implies 6w - 1 = \dfrac{46}{2} \rm \implies 6w - 1 = 23 \\ \\ \rm \implies 6w = 23 + 1 \\ \\ \rm \implies 6w = 24 \\ \\ \rm \implies w = \dfrac{24}{6} \\ \\ \rm \implies w = 4 \: in$