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NARA [144]
3 years ago
6

martin reads 19 pages of a novel in 12 minutes. complete the proportion and use it to find x, the number of pages he reads in 42

minutes
Mathematics
1 answer:
Korvikt [17]3 years ago
3 0

Answer:

67 pages in 42 minutes

Step-by-step explanation:

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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.

5 0
3 years ago
Can please someone help me out and explain it step by step. Thank you
Anit [1.1K]

Answer:x=7, \ y=-2

Step-by-step explanation:

Given

Equations are 3x-y=23 and 2x+3y=8

take 3x-y=23

y=3x-23

Put the value of y in another equation

\Rightarrow 2x+3(3x-23)=8\\\Rightarrow 2x+9x-69=8\\\Rightarrow 11x=77\\\Rightarrow x=7

Put the value of x in y

y=3(7)-23=21-23=-2

Hence, x=7, \ y=-2

7 0
3 years ago
Round to the place value of the underlined digit 301.587
DerKrebs [107]

round too? hundreds? thousand? ones? where do we round too? i need to know so i can help you :)


4 0
3 years ago
Solve the system using substitution.<br> 2x = 5y + 14<br> x = 5y
andrew-mc [135]

Answer:

<h2>y = 2.8</h2><h2>x = 14</h2>

Step-by-step explanation:

To solve an equation, we can only have one variable. In this case, we are given the system 2x = 5y + 14. However, we are given the value of x in terms of y. We can substitute 10y in for 2x and solve.

10y = 5y + 14

First, we need to get all the variables on one side of the equation, so we subtract 5y.

5y = 14

Divide by 5

y = 14/5 or 2 4/5 or 2.8

Now for the x part.

2x = x + 14

Subtract 1x

x = 14

Now we check our answer.

2(14) = 5(2.8) + 14

28 = 14 + 14

28 = 28

Because 28 equals 28, our solutions are correct.

7 0
3 years ago
The Kings Dominion Gold Pass costs $89. If you buy it the first week of
Eddi Din [679]

Answer:

$75.65

Step-by-step explanation:

1 - .15 = .85 = 85% of the price is what you pay

89 • .85 = $75.65

7 0
3 years ago
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