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3 years ago

Joanna has a total of 7 rolls of coins worth $23. She has rolls of dimes worth $5 each, and

Mathematics

1 answer:

yawa3891 [41]3 years ago

6 0

Answer:

3 rolls of dimes and 4 rolls of nickels

Step-by-step explanation:

Number of rolls of dimes = x

Number of rolls of nickels = y

Total number of rolls = 7

x + y = 7 -------------------(i)

Total amount = $ 23

5x + 2y = 23 ----------------(ii)

Multiply equation (i) by -2. So when we are adding, y will be eliminated and you will get the number of rolls of dimes.

(i)*(-2) -2x - 2y = -14

(ii) <u>5x + 2y = 23</u> {Now add}

3x = 9

x = 9/3

x = 3

Plug in the value of x in equation (i)

3 +y = 7

y = 7- 3

y = 4

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A solid right pyramid has a square base. The length of the base edge is4 cm and the height of the pyramid is 3 cm period what is

Illusion [34]

Answer:

The volume of this pyramid is 16 cm³.

Step-by-step explanation:

The volume $V$ of a solid pyramid can be given as:

$\displaystyle V = \frac{1}{3} \cdot b \cdot h$ ,

where

$b$ is the area of the base of the pyramid, and
$h$ is the height of the pyramid.

Here's how to solve this problem with calculus without using the previous formula.

Imaging cutting the square-base pyramid in half, horizontally. Each horizontal cross-section will be a square. The lengths of these squares' sides range from 0 cm to 3 cm. This length will be also be proportional to the vertical distance from the vertice of the pyramid.

Refer to the sketch attached. Let the vertical distance from the vertice be $x$ cm.

At the vertice of this pyramid, $x = 0$ and the length of a side of the square is also $0$ .
At the base of this pyramid, $x = 3$ and the length of a side of the square is $4$ cm.

As a result, the length of a side of the square will be

$\displaystyle \frac{x}{3}\times 4 = \frac{4}{3}x$ .

The area of the square will be

$\displaystyle \left(\frac{4}{3}x\right)^{2} = \frac{16}{9}x^{2}$ .

Integrate the area of the horizontal cross-section with respect to $x$

from the top of the pyramid, where $x = 0$ ,
to the base, where $x = 3$ .

$\displaystyle \begin{aligned}\int_{0}^{3}{\frac{16}{9}x^{2}\cdot dx} &= \frac{16}{9}\int_{0}^{3}{x^{2}\cdot dx}\\ &= \frac{16}{9}\cdot \left(\frac{1}{3}\int_{0}^{3}{3x^{2}\cdot dx}\right) & \text{Set up the integrand for power rule}\\ &= \left.\frac{16}{9}\times \frac{1}{3}\cdot x^{3}\right|^{3}_{0}\\ &= \frac{16}{27}\times 3^{3} \\ &= 16\end{aligned}$ .

In other words, the volume of this pyramid is 16 cubic centimeters.

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2 years ago

a scale model of the human heart os 196 in. The scale is 32:1, what is the approximate actual size of the heart

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If it is a 32:1 then the answer is somewhere around 6.125 inches

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X = 196/32
X= 6.125

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2 years ago

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cluponka [151]

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3 years ago

Silas just bought a used car for $5000. It loses value at a rate of 30% per year. The value of the car in n years is modeled by

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Answer:

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2 years ago

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EleoNora [17]

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2 years ago

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