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Illusion [34]
3 years ago
12

If the cube is divided into two equal parts by a plane parallel to the face defined by vertices 2, 3, 6, and 7, what will be the

area of the cross-section?
Mathematics
1 answer:
notsponge [240]3 years ago
5 0
The area of the cross-section is 169 sq. cm. 

That is the correct answer to this problem
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If it is 5 degrees outside, and the temperature will drop 12
kolezko [41]

Answer:

-7 degrees

Step-by-step explanation:

Dropping 12 degrees means that it will get colder by 12 degrees. The colder it gets, the lower the temperature. 5 degrees - the current temperature, is going to be dropped by 12 degrees. To calculate this: 5-12 = -7 (degrees)

7 0
3 years ago
Please show your work.​
Nastasia [14]

Answer:

1. 8.19, 2. 25.96, 3. 3.95

Step-by-step explanation:

use soh cah toa

1. cos is adjacent/hypotenuse

cos73=x/28

multiply both sides by 28

28cos73=x=8.186

2. sin is opposite over hypotenuse

sin68=x/28

multiply both sides by 28

28sin68=x=25.961

3. sin is opposite over hypotenuse

sin26=x/9

myltiply both sides by 9

9sin26=x=3.945

8 0
3 years ago
The price of products may increase due to inflation and decrease due to depreciation. Marco is studying the change in the price
likoan [24]

Answer:

A)  3%

B)  Product A

Step-by-step explanation:

<u>Exponential Function</u>

General form of an exponential function: y=ab^x

where:

  • a is the initial value (y-intercept)
  • b is the base (growth/decay factor) in decimal form
  • x is the independent variable
  • y is the dependent variable

If b > 1 then it is an increasing function

If 0 < b < 1 then it is a decreasing function

<u>Part A</u>

<u>Product A</u>

Assuming the function for Product A is <u>exponential</u>:

f(x) = 0.69(1.03)^x

The base (b) is 1.03.  As b > 1 then it is an <u>increasing function</u>.

To calculate the percentage increase/decrease, subtract 1 from the base:

⇒ 1.03 - 1 = 0.03 = 3%

Therefore, <u>product A is increasing by 3% each year.</u>

<u>Part B</u>

\sf percentage\:change=\dfrac{final\:value-initial\:value}{initial\:value} \times 100

To calculate the percentage change in Product B, use the percentage change formula with two consecutive values of f(t) from the given table:

\implies \sf percentage\:change=\dfrac{10201-10100}{10100}\times 100=1\%

Check using different two consecutive values of f(t):

\implies \sf percentage\:change=\dfrac{10303.01-10201}{10201}\times 100=1\%

Therefore, as 3% > 1%, <u>Product A recorded a greater percentage change</u> in price over the previous year.

Although the question has not asked, we can use the given information to easily create an exponential function for Product B.

Given:

  • a = 10,100
  • b = 1.01
  • n = t - 1 (as the initial value is for t = 1 not t = 0)

\implies f(t) = 10100(1.01)^{t-1}

To check this, substitute the values of t for 1 through 4 into the found function:

\implies f(1) = 10100(1.01)^{1-1}=10100

\implies f(2) = 10100(1.01)^{2-1}=10201

\implies f(3) = 10100(1.01)^{3-1}=10303.01

\implies f(4) = 10100(1.01)^{4-1}=10406.04

As these values match the values in the given table, this confirms that the found function for Product B is correct and that <u>Product B increases by 1% per year.</u>

4 0
2 years ago
Some banks now use continuous compounding of an amount invested. In this case, the equation that models the value of an initial
Komok [63]

Answer:

In this case, the equation that models the value of an initial investment of P dollars in t years at an annual interest rate of r is given by A = Pert.

Step-by-step explanation:

4 0
2 years ago
The ten sides of a regular decagon are colored with five different colors, so that all five colors are used, and sides that are
const2013 [10]

Answer:

  • <u>120</u>

Explanation:

Number the sides of the decagon: 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10, from top (currently red) clockwise.

  • The side number one can be colored of five different colors (red, orange, blue, green, or yellow): 5
  • The side number two can be colored with four different colors: 4
  • The side number three can be colored with three different colors: 3
  • The side number four can be colored with two different colors: 2
  • The side number five can be colored with the only color left: 1
  • Each of the sides six through ten can be colored with one color, the same as its opposite side: 1

Thus, by the multiplication or fundamental principle of counting, the number of different ways to color the decagon will be:

  • 5 × 4 × 3 × 2 ×1 × 1 × 1 × 1 × 1 × 1 = 120.

Notice that numbering the sides starting from other than the top side is a rotation of the decagon, which would lead to identical coloring decagons, not adding a new way to the number of ways to color the sides of the figure.

6 0
3 years ago
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