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Yuri [45]
3 years ago
6

Peterkin park has a square fountain with a walkway aroind it. The fountain measures 12 feet on each side. The walkway is 3 1/2 f

eet wide.Find the area of the walkway
Mathematics
1 answer:
Black_prince [1.1K]3 years ago
3 0

Answer: 829.44 ft²

Step-by-step explanation:

Correction - The walkway is 31.2 feet wide.

To solve this, first find the area of the fountain:

Area of a square = Length * Width

= 12 * 12

= 144 ft²

The find the area of the walkway including the fountain:

= 31.2 * 31.2

= ‭973.44‬ ft²

To find the area of the walkway alone, subtract the area of the square from the area of the rectangle:

= 973.44 - 144

= 829.44 ft²

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The tangents to the curve with equation y = x^3-3x at the points A and B with x coordinates −1 and 4 respectively meet at the po
sladkih [1.3K]

Answer:

\displaystyle C=\left(\frac{26}{9}, 2\right)

Step-by-step explanation:

We need to find the equation of the tangent lines of Points A and B.

Differentiate the equation:

\displaystyle \frac{dy}{dx}=3x^2-3

Point A has an <em>x-</em>coordinate of -1. Hence, the slope of its tangent line is:

\displaystyle \frac{dy}{dx}\Big|_{x=-1}=3(-1)^2-3=0

Find the <em>y-</em>coordinate of Point A using the original equation:

y(-1)=(-1)^3-3(-1)=2

Hence, Point A is (-1, 2).

Thus, the tangent line at Point A is:

y-2=0(x-(-1))

Simplify:

y=2

Point B has an <em>x-</em>coordinate of 4. Hence, the slope of its tangent line is:

\displaystyle \frac{dy}{dx}\Big|_{x=4}=3(4)^2-3=45

Find the <em>y-</em>coordinate of Point B:

y(4)=(4)^3-3(4)=52

Thus, Point B is at (4, 52).

So, the tangent line at Point B is:

y-52=45(x-4)

Simplify:

y=45x-128

Point C occurs at the intersections of the tangent lines of Points A and B. Set the two equations equal to each other and solve for <em>x: </em>

2=45x-128

We acquire:

\displaystyle x=\frac{26}{9}

Since one of our equations is <em>y</em> = 2, the <em>y-</em>coordinate is 2.

Hence, Point C is:

\displaystyle C=\left(\frac{26}{9}, 2\right)

5 0
3 years ago
Read 2 more answers
Marianne has 5/8 pound of peas she cooks 2/3 of those peas for five people if each person is served an equal amount how much pea
Citrus2011 [14]
Weight of cooked peas is (2/3)(5 lb/8) = (10/24) lb, or (5/12) lb.

Divide this weight by 5 (people):


5
--
12
---------- = 1/12 lb, or   16/12 oz   = 1.33 oz, or 4/3 oz.
5




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3 years ago
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Lena [83]
I think the answer to this question is 10% but I don’t know if it’s right
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3 years ago
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Semmy [17]

Answer: Option b

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Step-by-step explanation:

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Note that in option b) the exponent of the variable x is n = 4 therefore the equation is nonlinear

Finally the answer is the option b

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3 years ago
10 ice cubes fit into 1/2 a tray. How many ice cubes fit per tray? 5<br> (1 Point)
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Answer:

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Step-by-step explanation:

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