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2 years ago

Write an equation that represents the distance d and Miles traveled by the monarch butterfly and t days

Mathematics

1 answer:

loris [4]2 years ago

3 0

Complete question :

When the monarch butterfly is migrating to the south, it has an average speed of 80 miles per day. Write an equation that shows the realtionship between the number of days (t) and the distance (in miles) it has traveled (d)

Answer:

d = 80t

Step-by-step explanation:

Given :

Average speed = 80 miles per hour

Distance traveled (in miles) = d

Number of days = t

Equation which shows the Relationship between Number of days and distance traveled :

Recall :

Speed = distance / time

Speed = 80 ; distance = d ; time = t

80 = d/t

80 * t = d

d = 80t

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Find the equation of the tangent line to the curve (a lemniscate)

olya-2409 [2.1K]

Answer:

$m=\frac{9}{13}$ and $b=\frac{40}{13}$

Step-by-step explanation:

The equation of curve is

$2(x^2+y^2)^2=25(x^2-y^2)$

We need to find the equation of the tangent line to the curve at the point (-3, 1).

Differentiate with respect to x.

$2[2(x^2+y^2)\frac{d}{dx}(x^2+y^2)]=25(2x-2y\frac{dy}{dx})$

$4(x^2+y^2)(2x+2y\frac{dy}{dx})=25(2x-2y\frac{dy}{dx})$

The point of tangency is (-3,1). It means the slope of tangent is $\frac{dy}{dx}_{(-3,1)}$ .

Substitute x=-3 and y=1 in the above equation.

$4((-3)^2+(1)^2)(2(-3)+2(1)\frac{dy}{dx})=25(2(-3)-2(1)\frac{dy}{dx})$

$40(-6+2\frac{dy}{dx})=25(-6-2\frac{dy}{dx})$

$-240+80\frac{dy}{dx})=-150-50\frac{dy}{dx}$

$80\frac{dy}{dx}+50\frac{dy}{dx}=-150+240$

$130\frac{dy}{dx}=90$

Divide both sides by 130.

$\frac{dy}{dx}=\frac{9}{13}$

If a line passes through a points $(x_1,y_1)$ with slope m, then the point slope form of the line is

$y-y_1=m(x-x_1)$

The slope of tangent line is $\frac{9}{13}$ and it passes through the point (-3,1). So, the equation of tangent is

$y-1=\frac{9}{13}(x-(-3))$

$y-1=\frac{9}{13}(x)+\frac{27}{13}$

Add 1 on both sides.

$y=\frac{9}{13}(x)+\frac{27}{13}+1$

$y=\frac{9}{13}(x)+\frac{40}{13}$

Therefore, $m=\frac{9}{13}$ and $b=\frac{40}{13}$ .

5 0

2 years ago

Given that f(x) = x2 + 9x + 18 and g(x) = x + 6, find f(x) – g(x) and

Diano4ka-milaya [45]

Answer:

x^2+8x+12

Step-by-step explanation:

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2 years ago

In March for every 2 days it rained out of 5 days. A total of 30 days were calculated, How many days did it rain?

icang [17]

Answer:

37 days it rained for sure

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3 years ago

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amm1812

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6 0

2 years ago

Looking for the answer and explanation for this equation 7xy=? x=1 y=3

Dmitrij [34]

If you plug in the x and y, you get
7(1)(3)
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6 0

2 years ago

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