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2 years ago

Happy snow day! My project

Mathematics

1 answer:

attashe74 [19]2 years ago

7 0

Answer:

21 Snowmen

Step-by-step explanation:

The perimeter of your yard is 25ft + 28ft + 25ft + 28ft = 106ft

Each snowman is 5ft across, so divide 106ft by 5ft.

106ft / 5ft = 21 with a remainder of 1ft

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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

Someone please help me with this and show work I don’t get it I’ll give brainliest

kenny6666 [7]

Answer: THAT IS RIGHT OK BYE MAN

Step-by-step explanation: OK BYE

4 0

3 years ago

Write an equation with a variable on both sides of the equal sign that has infinitely many solutions. Solve the equation and exp

inn [45]

Equation:

2x + 6 = 4x/2 + 12/2

To solve this, we need to transpose like terms to the same side.

2x - 4x/2 = 12/2 - 6
2x - 2x = 6 - 6
0 = 0

Since both sides are zero, it means that the equation has infinite number of solutions.

8 0

3 years ago

Read 2 more answers

Please help!

Alinara [238K]

It is D. ,that one makes the most sense to me

4 0

3 years ago

Write a function t(I) that determines the number of

forsale [732]

Using the table, we will see that the function is:

t(l) = 3*l

<h3>How to write the function?</h3>

Here we only have a table to work with, so we need to use that.

In the table, we can see the pairs:

t(1) = 3
t(2) = 6
t(3) = 9
t(4) = 12

So, in each new level, we just add 3 more toothpicks. Even more, we can see that the number of toothpicks is 3 times the value of l (the level) for all the cases in the table. So this is a linear function.

From that we can conclude that the function will be:

t(l) = 3*l

If you want to learn more about linear functions, you can read:

brainly.com/question/4025726

6 0

2 years ago