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umka21 [38]
3 years ago
6

A sheet cake and a birthday cake are both made from the same batter. The sheet cake is in the shape of a rectangular prism that

is 12 inches long, 9 inches wide, and 2 inches tall. The birthday cake is in the shape of a cylinder with a base radius of 4.5 inches and a height of 4 inches.
If the sheet cake has a total of 3,600 calories, approximately how many calories are in the birthday cake?

a. 1,880
b. 2,960
c. 3,770
d. 4,240
Mathematics
2 answers:
NISA [10]3 years ago
7 0
Volume of the sheet cake:
V ( prism ) = 12 * 9 * 2 = 216 in³
Volume of the birthday cake:
V ( cylinder ) = r² * π * h = 4.5² * 3.14 * 4 = 254.34 in³
Then we will use the proportion :
216 : 254.34 = 36000 : x
216 x = 254.34 * 3600
216 x = 915,660
x = 915.660 : 216
x = 4,239.17 ≈ 4,240
Answer:
d. 4,240
skad [1K]3 years ago
4 0

Answer:

The answer is 4240

Step-by-step explanation:

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Find the coordinates of p so that p partitions AB in the ratio 1 to 3 with a(-5,4) and(7,-4)
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Which expression represents the number 2i4−5i3+3i2+−81‾‾‾‾√ rewritten in a+bi form?
vichka [17]

Answer:

The expression -1+14i represents  the number 2i^4-5i^3+3i^2+\sqrt{-81} rewritten in a+bi form.

Step-by-step explanation:

The value of i is i=\sqrt{-1}[tex] or [tex]i^{2}=-1[\tex].Now [tex]i^{4} in term of i^{2}[\tex] can be written as, [tex]i^{4}=i^{2}\times i^{2}

Substituting the value,

i^{4}=\left(-1\right)\times \left(-1\right)

Product of two negative numbers is always positive.

\therefore i^{4}=1

Now i^{3} in term of i^{2}[\tex] can be written as, [tex]i^{3}=i^{2}\times i

Substituting the value,

i^{3}=\left(-1\right)\times i

Product of one negative  and one positive numbers is always negative.

\therefore i^{3}=-i

Now \sqrt{-81} can be written as follows,

\sqrt{-81}=\sqrt{\left(81\right)\times\left(-1\right)}

Applying radical multiplication rule,

\sqrt{ab}={\sqrt{a}}\sqrt{b}

\sqrt{\left(81\right)\times\left(-1\right)}={\sqrt{81}}\sqrt{-1}

Now, \sqrt{\left(81\right)=9 and \sqrt{-1}}=i

\therefore \sqrt{\left(81\right)\times\left(-1\right)}=9i

Now substituting the above values in given expression,

2i^4-5i^3+3i^2+\sqrt{-81}=2\left(1\right)-5\left(-i\right)+3\left(-1\right)+9i

Simplifying,

2+5i-3+9i

Collecting similar terms,

2-3+5i+9i

Combining similar terms,

-1+14i

The above expression is in the form of a+bi which is the required expression.

Hence, option number 4 is correct.

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3 years ago
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