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A 13.5-m fire truck ladder is leaning against a wall. Find the distance d the ladder goes up the wall (above the fire truck)

larisa86 [58]

To solve this problem you must apply the proccedure shown below:

1. You have the the 13.5-m fire truck ladder is leaning against a wall and the ladder makes an angle of 39 degrees 45 ' with the horizontal.

2. Then you have:

39 degrees 45'=39.75°

Sin(39.75°)=d/13.5
d=13.5xSin(39.75°)
 d=8.63

8 0

3 years ago

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A video game arcade offers a yearly membership with reduced rates for game play. A single membership costs $60 per year. Game to

Nastasia [14]

Let

x-------> the number of game tokens purchased for a member of the arcade

y-------> the function of the yearly cost in dollars

we know that

the function y of the yearly cost in dollars is equal to

$y =\frac{1}{10} x +60$

This is the equation of the line

using a graph tool

see the attached figure

Statements

case a) The slope of the function is $1.00

The statement is False

The slope of the function is equal to $\frac{1}{10} \frac{\$}{tokens}$

case b) The y-intercept of the function is $60

The statement is True

we know that

The y-intercept of the function is the value of the function when the value of x is equal to zero

so

for $x=0$

$y =\frac{1}{10}*0 +60$

$y =\$60$

case c) The function can be represented by the equation y =(1/10)x + 60

The statement is True

The equation of the function is equal to $y =\frac{1}{10} x +60$

case d) The domain is all real numbers

The statement is False

The value of x cannot be negative, therefore the domain is the interval

[0,∞)

case e) The range is {y| y ≥ 60}

The statement is True

The range of the function is the interval-------> [60,∞)

see the attached figure

8 0

3 years ago

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How to find the area of a square whose perimeter is 7 meters

yKpoI14uk [10]

Answer:

A≈3.06

P Perimeter

7

Using the formulas

A=a2

P=4a

Solving forA

A=1

16P2=1

16·72=3.0625

8 0

2 years ago

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PLEASE HELP!!!! a bag holds 25 potatoes, if the potatoes in the bag are split among 5 people, how many people does each person g

Airida [17]

Answer:

25 potatoes split between 5 people would be 25÷5=5. So each person will get 5 potatoes.

6 0

3 years ago

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Explain proportionality to me 7th grade math

kari74 [83]

If two quantities a and b are directly proportional to one another, then both a and b change in the same direction.

For example, if the amount/volume of coffee I have in a cup is directly proportional to the total volume of the cup, then the larger the cup gets, the more coffee I can fill it with. On the other hand, if the cup gets smaller, the amount of coffee it can hold also gets smaller.

Both a and b don't necessarily change at the same rate, though, which means one of these needs to get appropriately scaled by some factor k, so that

a = kb

Continuing the coffee example: Suppose I only fill my cup halfway. If the total volume of the cup is a, then the amount of coffee I pour in is b = 1/2 a. So the relationship of these two quantities is governed by the equation,

a = 2b

and in this case, k = 2.

If instead a and b are inversely proportional, this means as one quantity changes, the other changes in the opposite direction.

Suppose I have two cups that I use for coffee that can both hold the same amount k if they are filled completely, but one cup is taller than the other. In order for both cups to be able to hold the same volume of coffee, the taller cup must have a thinner profile.

The cups are cylindrical, so that their volumes are equal to the products of the area of their base a and their height b. If one cup is twice as tall as the other, then for the smaller cup we could have

ab = k

and for the taller one,

a (2b) = k

But in order to get the same volume, the quantity a for the shorter cup must be cut in half to preserve equality:

(1/2 a) (2b) = ab = k

So one quantity is doubled (increases), while the other gets halved (decreases).

5 0

3 years ago