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3 years ago

A building has a length of 40 m. The length of its scale model is 25 cm. What scale factor was used to make the scale model?

Mathematics

1 answer:

Marizza181 [45]3 years ago

8 0

The answer is 1 cm = 1.6m. We know this because the scale model was 25 cm and the building was 40m. To simplify, our proportion is 40 meters /25 centimeters to x meters/1 centimeter. 40/25= 1.6, so we can say that x (the scale factor) is 1 cm to 1.6 m.

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Find the indicated limit, if it exists.

kondor19780726 [428]

Answer:

d) The limit does not exist

General Formulas and Concepts:

Calculus

Limits

Right-Side Limit: $\displaystyle \lim_{x \to c^+} f(x)$
Left-Side Limit: $\displaystyle \lim_{x \to c^-} f(x)$

Limit Rule [Variable Direct Substitution]: $\displaystyle \lim_{x \to c} x = c$

Limit Property [Addition/Subtraction]: $\displaystyle \lim_{x \to c} [f(x) \pm g(x)] = \lim_{x \to c} f(x) \pm \lim_{x \to c} g(x)$

Step-by-step explanation:

*Note:

In order for a limit to exist, the right-side and left-side limits must equal each other.

Step 1: Define

Identify

$\displaystyle f(x) = \left\{\begin{array}{ccc}5 - x,\ x < 5\\8,\ x = 5\\x + 3,\ x > 5\end{array}$

Step 2: Find Right-Side Limit

Substitute in function [Limit]: $\displaystyle \lim_{x \to 5^+} 5 - x$
Evaluate limit [Limit Rule - Variable Direct Substitution]: $\displaystyle \lim_{x \to 5^+} 5 - x = 5 - 5 = 0$

Step 3: Find Left-Side Limit

Substitute in function [Limit]: $\displaystyle \lim_{x \to 5^-} x + 3$
Evaluate limit [Limit Rule - Variable Direct Substitution]: $\displaystyle \lim_{x \to 5^+} x + 3 = 5 + 3 = 8$

∴ Since $\displaystyle \lim_{x \to 5^+} f(x) \neq \lim_{x \to 5^-} f(x)$ , then $\displaystyle \lim_{x \to 5} f(x) = DNE$

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Limits

5 0

3 years ago

Explain why 256 + 4 is equivalent to (200 + 4) + (40+4) + (164)

laiz [17]

The expression 256 + 4 is equivalent to (200 + 4) + (40+4) + (16+4) according to distributive and commutative property of addition.

Given the expression 256 + 4. This can be solved using the partial sum expressed as:

256 + 4

= (200 + 40 + 16) + 4

According to the commutative property, A+B = B+A

The arrangement does not affect the result. Hence;

(200 + 40 + 16) + 4 = 4 + (200 + 40 + 16)

Using the distributive law;

4 +(200 + 40 + 16) = (200 + 4) + (40 + 4) + (16 + 4)

Hence the expression 256 + 4 is equivalent to (200 + 4) + (40+4) + (16+4) according to distributive and commutative property of addition.

Learn more on partial sum here: brainly.com/question/6958503

4 0

3 years ago

Write 83 50 as a decimal.

Katyanochek1 [597]

Answer:

0.83,0.50

Step-by-step explanation:

Since there are 2 digits in 83, the very last digit is the "100th" decimal place.

So we can just say that .83 is the same as 83/100.

So your final answer is: .83 can be written as the fraction

7 0

3 years ago

Read 2 more answers

Maddyross91 ! i’ll give brainliest please help

frosja888 [35]

Answer:

Symbol

Step-by-step explanation:

the object symbolizes something else

4 0

3 years ago

Read 2 more answers

Find the sample standard deviation:

zlopas [31]

Answer:

Step-by-step explanation:

Given the sample data 2 6 15 9 11 22 1 4 8 19, before we can get the standard deviation, we need to first calculate the mean.

mean = 2 +6 +15 +9 +11 +22 +1 +4 +8 +19/10

mean = 97/10

mean = 9.7

Standard deviation for ungrouped data is expressed using the formula;

$S = \sqrt{ \dfrac{\sum(x-\overline x)^2}{n-1} }$

$\overline x \ is\ the \ mean\\n \ is \ sample \ size$

$S = \sqrt{\frac{(2-9.7)^2+(6-9.7)^2+(15-9.7)^2+(9-9.7)^2+(11-9.7)^2+(22-9.7)^2+(1-9.7)^2+(4-9.7)^2+(8-9.7)^2+(19-9.7)^2}{10-1} }\\ S = \sqrt{\frac{(-7.7)^2+(-3.7)^2+(5.3)^2+(-0.7)^2+(1.3)^2+(12.3)^2+(-8.7)^2+(-5.7)^2+(-1.7)^2+(9.3)^2}{10-1} }\\\\S = \sqrt{\dfrac{59.29+13.69+28.09+0.49+1.69+151.29+75.69+32.49+2.89+86.49}{10-1} }\\\\\\S = \sqrt{\dfrac{452.1}{9} }\\\\S = \sqrt{50.23}\\ \\S = 7.08\\\\S \approx 7.1$

Hence the standard deviation of the sample data is 7.1

7 0

3 years ago