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lisabon 2012 [21]
3 years ago
15

goldie's pizza place is known throughout the city. The small Baby Bear pizza has a radius of 6 inches and sells for $10. Mama Be

ar pizza sells for $12.50 and has an 8 inch radius. The large papa bear pizza is 18 inches in diameter and Sella for 17 dollars. What size has the most pizza edge per dollar? What is the circumference of this pizza?
Mathematics
2 answers:
shutvik [7]3 years ago
3 0
\bf \textit{circumference of a circle}\\\\
C=2\pi r\qquad r=radius=\frac{diameter}{2}\\\\
-----------------------------\\\\

\begin{array}{lcccclllll}
&radius&\$&Cmfc&\frac{Cmfc}{\$}\\
&---&---&-----&-----\\
\textit{Baby Bear}&6&10&2\pi \cdot 6&\frac{2\pi \cdot 6}{10}\\\\
\textit{Mama Bear}&8&12.50&2\pi \cdot 8&\frac{2\pi \cdot 8}{12.50}\\\\
\textit{Papa Bear}&
\begin{array}{llll}
diameter=18\\
radius=\frac{18}{2}=9
\end{array}&17&2\pi \cdot 9&\frac{2\pi \cdot 9}{17}
\end{array}

notice, Papa Bear is 18inches in diameter, but radius is half that

and "edge per dollar" simply means, how much circumference per dollar
or \bf \cfrac{Cmfc}{\$}

Serga [27]3 years ago
3 0
Baby bear: 6r and sells for $10
Mama bear:8r and sells for $12.50
Papa bear:18d and sells for $17
B.B Bear: $1.67
M.M Bear:$1.56
P.P Bear:$1.89
Answer:Papa bear pizza
Circumference:
Formula:C:pi(d)
C:18 times 3.14 equals 56.52
Circumference of Papa Bear:56.52
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Pachacha [2.7K]

Answer:

a = 9.849

b = 20.25

c = 491.03

Step-by-step explanation:

By using Pythagoras theorem in the right triangle BDC,

(Hypotenuse)² = (Leg 1)² + (Leg 2)²

BC² = BD² + DC²

a² = 9² + 4²

a = \sqrt{(81+16)}

a = \sqrt{97}

a = 9.8489

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By mean proportional theorem,

\frac{\text{DC}}{\text{BD}}=\frac{\text{BD}}{\text{AD}}

AD × DC = BD²

b × 4 = 9²

b = \frac{81}{4}

b = 20.25 units

BY Pythagoras theorem in ΔADB,

AB² = AD² + BD²

c² = b² + 9²

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c² = 410.0625 + 81

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6 0
3 years ago
Consider the points A(5, 3t+2, 2), B(1, 3t, 2), and C(1, 4t, 3). Find the angle ∠ABC given that the dot product of the vectors B
Vilka [71]

Answer:

66.42°

Step-by-step explanation:

<u>Given:</u>

A(5, 3t+2, 2)

B(1, 3t, 2)

C(1, 4t, 3)

BA • BC = 4

Step 1: Find t.

First we have to find vectors BA and BC. We do that by subtracting the coordinates of the initial point from the coordinates of the terminal point.

In vector BA B is the initial point and A is the terminal point.

BA = OA - OB = (5-1, 3t+2-3t, 2-2) = (4, 2, 0)

BC = OC - OB = (1-1, 4t-3t, 3-2) = (0, t, 1)

Now we can find t because we know that BA • BC = 4

BA • BC = 4

To find dot product we calculate the sum of the produts of the corresponding components.

BA • BC = (4)(0) + (2)(t) + (0)(1)

4 = (4)(0) + (2)(t) + (0)(1)

4 = 0 + 2t + 0

4 = 2t

2 = t

t = 2

Now we know that:

BA = (4, 2, 0)

BC = (0, 2, 1)

Step 2: Find the angle ∠ABC.

Dot product: a • b = |a| |b| cos(angle)

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|BA| |BC| cos(angle) = 4

To get magnitudes we square each compoment of the vector and sum them together. Then square root.

|BA| = \sqrt{4^2 + 2^2 + 0^2} = \sqrt{20} = 2\sqrt{5}

|BC| = \sqrt{0^2 + 2^2 + 1^2} = \sqrt{5}

2\sqrt{5}\sqrt{5}\cos{(m\angle{ABC})} = 4

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\cos(m\angle{ABC}) = \frac{4}{10}=\frac{2}{5}

m\angle{ABC} = cos^{-1}{(\frac{2}{5})}

m\angle{ABC} = 66.4218^{\circ}

Rounded to two decimal places:

m\angle{ABC} = 66.42^\circ

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