A blueprint of a shopping complex shows the bottom edge of the roof to be 68 feet above the ground. If the roof rises to a point 122 feet above the ground over a horizontal distance of 4.5 yards, what is the slope of the roof?41.2128
Answers
SOLUTION
Given:
A blueprint of a shopping complex shows the bottom edge of the roof to be 68 feet above the ground. If the roof rises to a point 122 feet above the ground over a horizontal distance of 4.5 yards, what is the slope of the roof?
[tex]Slope\text{ =}\frac{rise}{run}[/tex][tex]\begin{gathered} Rise\text{ =122-68=54 feet} \\ Run=4.5yards=13.5feet \end{gathered}[/tex][tex]\therefore Slope=\frac{54}{13.5}=4feet[/tex]
Final answer:
Related Questions
The table lists recommended amounts of food to order for 25 party guests. Amanda and Syndey are hosting a graduation party for 40 guests. They know there will also be guests stopping by who may have come from other parties. For ordering purposes, they will count each of these "drop-in" guests as half a guest. How much of each food item should Amanda and Syndey order for a graduation party with 45 drop-in guests?
Answers
Amanda and Sydney are hosting a graduation party for 40 guests.
Also, they have 45 drop-in guests (each of these will count as half a guest).
Then, the total number of guests is:
[tex]40+\frac{45}{2}=\frac{40\times2+1\times45}{1\times2}=\frac{80+45}{2}=\frac{125}{2}[/tex]The table shows the recommended amounts of food for 25 party guests:
Fried Chicken: 24 pieces
Deli meats: 4 1/3 pounds
Lasagna: 10 3/4 pounds.
Let's find the proportion for 125/2 guests:
a. Fried chicken:
[tex]\begin{gathered} \frac{24\text{ pieces}}{25\text{ guests}}=\frac{x\text{ pieces}}{125/2\text{ guests}} \\ \text{Set the product of the diagonals equal to each other:} \\ 24\times\frac{125}{2}=x\times25 \\ \frac{24\times125}{2}=x\times25 \\ 1500=x\times25 \\ \text{Divide both sides by 25} \\ \frac{1500}{25}=\frac{x\times25}{25} \\ \text{Simplify} \\ 60=x \end{gathered}[/tex]Then, they'll need to order 60 units of fried chicken for the party.
b. Deli meats:
Start by converting the mixed number 4 1/3 into a fraction:
[tex]4\frac{1}{3}=\frac{4\times3+1}{3}=\frac{12+1}{3}=\frac{13}{3}[/tex]Now, apply proportions:
[tex]\begin{gathered} \frac{13/3\text{ pounds}}{25\text{ guests}}=\frac{x\text{ pounds}}{125/2\text{ guests}} \\ \text{Set the product of the diagonals equal to each other:} \\ x\times25=\frac{13}{3}\times\frac{125}{2} \\ x\times25=\frac{13\times125}{3\times2} \\ x\times25=\frac{1625}{6} \\ \text{Divide both sides by 25} \\ \frac{x\times25}{25}=\frac{1625}{6\times25}=\frac{1625}{150}=\frac{65}{6} \\ \text{Simplify} \\ x=\frac{65}{6} \end{gathered}[/tex]You also can convert this fraction into a mixed number:
[tex]\begin{gathered} \text{When you divide 65/6 you obtain a quotient of 10 and remainder 5.} \\ \text{Then the whole part is 10 and the fraction is 5/6} \\ \frac{65}{6}=10\frac{5}{6} \end{gathered}[/tex]Then, they'll need to order 10 5/6 pounds of deli meats for the party.
c. Lasagna
Convert the mixed number to fraction:
[tex]10\frac{3}{4}=\frac{10\times4+3}{4}=\frac{40+3}{4}=\frac{43}{4}[/tex]Apply proportions:
[tex]\begin{gathered} \frac{43/4\text{ pounds}}{25\text{ guests}}=\frac{x\text{ pounds}}{125/2\text{ guests}} \\ \text{Set the product of the diagonals equal to each other:} \\ x\times25=\frac{43}{4}\times\frac{125}{2} \\ x\times25=\frac{43\times125}{4\times2} \\ x\times25=\frac{5375}{8} \\ \text{Divide both sides by 25} \\ \frac{x\times25}{25}=\frac{5375}{8\times25}=\frac{5375}{200}=\frac{215}{8} \\ \text{Simplify} \\ x=\frac{215}{8} \end{gathered}[/tex]You also can convert this fraction into a mixed number:
[tex]\begin{gathered} \text{When you divide 215/8 you obtain a quotient of 26 and remainder 7.} \\ \text{Then the whole part is 26 and the fraction is 7/}8 \\ \frac{215}{8}=26\frac{7}{8} \end{gathered}[/tex]Then, they'll need to order 26 7/8 pounds of lasagna for the party.
Consider the following function.f(x) = |x − 9|Find the derivative from the left at x = 9. If it does not exist, enter NONE.Find the derivative from the right at x = 9. If it does not exist, enter NONE.
Answers
The form of the derivative of the absolute equation is
[tex]\begin{gathered} f(x)=\lvert x-a\rvert \\ \frac{dx}{dy}=\frac{\lvert x-a\rvert}{x-a} \\ \frac{dy}{dx}=\frac{x-a}{\lvert x-a\rvert} \end{gathered}[/tex]For the given function
[tex]f(x)=\lvert x-9\rvert[/tex]We will find the derivative from the left at x = 9
[tex]\frac{dy}{dx}=\frac{x-9}{\lvert x-9\rvert}[/tex]Substitute x by 9
[tex]\begin{gathered} \frac{dy}{dx}=\frac{9-9}{\lvert9-9\rvert} \\ \frac{dy}{dx}=\frac{0}{0} \end{gathered}[/tex]Then dy/dx does not exist (None)
The derivative from right at x = 9
[tex]\frac{dx}{dy}=\frac{\lvert x-9\rvert}{x-9}[/tex]Substitute x by 9
[tex]\begin{gathered} \frac{dx}{dy}=\frac{\lvert9-9\rvert}{9-9} \\ \frac{dx}{dy}=\frac{0}{0} \end{gathered}[/tex]Then dx/dy does not exist (None)
The table gives a set of outcomes and their probabilities. Let A be the event "the outcom less than or equal to 2". Let B be the event "the outcome is a divisor of 3". Find P(AB). Outcome Probability 1 0.2 2 0.6 3 0.2
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Given the table:
Outcome Probability
1 0.2
2 0.6
3 0.2
Let A be the event "the outcome less than or equal to 2.
Let B be the event "the outcome is a divisor of 3.
Let's find P(A ∩ B).
To find P(A ∩ B) let's first find P(A) and P(B).
Numbers less than or equal to 2 = 2 and 1
Outcomes less than or equal to 2 = P(2) or P(1)
Probability the outcome is less than or equal to 2 = P(A) = 0.2 + 0.6 = 0.8
Divisor of 3 = 1 and 3
Outcome is a divisor of 3 = P(1) and P(3)
Probability the outcome is a divisor of 3 = P(B) = 0.2 x 0.2 = 0.04
To find P(A ∩ B), we have:
P(A ∩ B) = P(A) x P(B) = 0.04 x 0.8 = 0.032
ANSWER:
0.032
Find the principal P that corresponds to the future value F= $1,300 under r = 4% interest compounded daily for t = 3 years. Round your final answer to two decimal places.
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The formula to find the principal is:
[tex]FV=P(1+i)^n[/tex]Where
FV is future value
P is principal
i is the rate of interest
n is the time frame
Given,
FV = 1300
i = r = 4%, or 4/100 = 0.04
n = t = 3
Plugging into formula and solving gives us:
[tex]\begin{gathered} FV=P(1+i)^n \\ 1300=P(1+0.04)^3 \\ 1300=P(1.04)^3 \\ P=\frac{1300}{1.04^3} \\ P=1155.695 \end{gathered}[/tex]Rounding to 2 decimal places:
$1155.70
Fnd the volume of each cylinder below.9.18 in15 in
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9) We can calculate the volume as the product of the base area and the height.
The base is a circle with radius r=18 in. Then, its area is:
[tex]A_b=\pi r^2=\pi\cdot18^2=324\pi[/tex]Then, we can calculate the volume V as:
[tex]V=A_b\cdot h=324\pi\cdot15=4860\pi[/tex]10) In this case the circular base is on the side, but we can still use the same principle to calculate the volume.
The area of the base with diameter D = 11 in is:
[tex]A_b=\frac{\pi D^2}{4}=\frac{\pi\cdot11^2}{4}=\frac{\pi\cdot121}{4}=\frac{121}{4}\pi[/tex]Then, we can calculate the volume V as:
[tex]V=A_b\cdot h=\frac{121}{4}\pi\cdot21=\frac{2541}{4}\pi=635.25\pi[/tex]Answer:
9) V = 4860π
10) V = 635.25π
3x-22x + 1A8If x=8, then the length of AB is
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Ok the length of AB is given by the equation:
[tex]3x-2[/tex]If x=8 then we simply have to replace this value in the equation:
[tex]\bar{AB}=3\cdot8-2=22[/tex]And that's the length of segment AB.
which of the following represents a line that is parallel to the line with equation y = – 3x + 4 ?A. 6x +2y = 15B. 3x - y = 7 C. 2x - 3y = 6D. x + 3y = 1
Answers
In order to have parallel lines, the slopes of the lines need to be the same.
In order to check the slope for each option, let's put the equations in the slope-intercept form:
[tex]y=mx+b[/tex]Where m is the slope and b is the y-intercept.
So we have that:
A.
[tex]\begin{gathered} 6x+2y=15 \\ 2y=-6x+15 \\ y=-3x+7.5 \end{gathered}[/tex]B.
[tex]\begin{gathered} 3x-y=7 \\ y=3x-7 \end{gathered}[/tex]C.
[tex]\begin{gathered} 2x-3y=6 \\ 3y=2x-6 \\ y=\frac{2}{3}x-2 \end{gathered}[/tex]D.
[tex]\begin{gathered} x+3y=1 \\ 3y=-x+1 \\ y=-\frac{1}{3}x+\frac{1}{3} \end{gathered}[/tex]So the only option with a line with a slope of -3 is Option A.
Every week Ben collects a few pounds of paper to recycle. The graph below shows the total number of pounds of paper(y) that Ben collected in a certain amount of time (x), in weeks:
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To obtain the amount of paper that would most likely be collected in 10 weeks, the following steps are necessary:
Step 1: Select two points that lie on the straight line and use the two points to derive the equation of the straight line, as follows:
Such two points could be: (x1, y1) = (0, 30) and (x2, y2) = (120, 3)
Using the following formula, we can derive the equation of the straight line:
[tex]\frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}[/tex]Thus:
[tex]\begin{gathered} \frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1} \\ \Rightarrow\frac{y-30_{}}{x-0_{}}=\frac{120_{}-30_{}}{3_{}-0_{}} \\ \Rightarrow\frac{y-30_{}}{x_{}}=\frac{90_{}}{3_{}_{}} \\ \Rightarrow\frac{y-30_{}}{x_{}}=30 \\ \Rightarrow y-30=30\times x \\ \Rightarrow y=30x+30 \end{gathered}[/tex]The above equation can be re-written as:
[tex]\begin{gathered} y=30x+30 \\ \Rightarrow\text{Amount of paper collected = 30 }\times number\text{ of w}eeks\text{ + 30 } \end{gathered}[/tex]Step 2: Use the derived equation to obtain the value of the amount of paper collected in 10 weeks, as follows:
In 10 weeks, we will have :
[tex]\begin{gathered} \text{Amount of paper collected = 30 }\times number\text{ of w}eeks\text{ + 30 } \\ \Rightarrow\text{Amount of paper collected = 30 }\times10\text{ + 30 } \\ \Rightarrow\text{Amount of paper collected = 300 + 30 }=330 \\ \Rightarrow\text{Amount of paper collected = 3}30 \end{gathered}[/tex]Therefore, the amount of paper that would most likely be collected in 10 weeks is 330
Sound is measured in decibels, using the formula d = 10 log() where P is the intensity of the sound and P, is the weakest sound the human ear can hear. A horn has a decibel warning of20. How many times more intense is this horn compared to the weakest sound heard to the human ear?
Answers
We have the following:
The formula is the following
[tex]d=10\log (\frac{P}{P_o})[/tex]From what the statement tells us, the value of d is equal to 20, now we replace and solving for P / Po
[tex]\begin{gathered} 10\log (\frac{P}{P_o})=20 \\ \frac{10}{10}\log (\frac{P}{P_o})=\frac{20}{10} \\ \log (\frac{P}{P_o})=2\rightarrow\log (x)=2\rightarrow x=10^2\rightarrow x=100 \\ \frac{P}{P_o}=100 \\ P=100\cdot P_o \end{gathered}[/tex]Therefore, the sound of the horn is about 100 more intense than the weakest sound heard to the human ear.
Parallelogram ABCD was translated to parallelogram AB'C'D'.How many units and in which direction were the x-coordinates of parallelogram ABCD moved?
Answers
Number of units: 7
Direction: left of the x coordinate
Explanation:Given:
Parallelogram ABCD was translated to parallelogram AB'C'D'
To find:
the number of units and in which direction were the x-coordinates of parallelogram ABCD moved
To determine the number of units, we will use the diagram below:
From A to A', B to B', C to C' and D to D', the number of units for the movement in the x coordinate is 7. The vertical position didn't change. This means to movement in the coordinate.
The parallelogram ABCD was moved to the left of the x axis to get parallelogram A'B'C'D'
Number of units: 7
Direction: left of the x coordinate
7 units to the left
Find the exact value of cos -1050.OA.-3OB.-12/2OC. 1OD. 1/3Reset Selection
Answers
Solution:
Given;
[tex]\cos(-1050)[/tex]Rewrite the expression using;
[tex]\cos(-x)=\cos x[/tex]Thus;
[tex]\begin{gathered} \cos(-1050)=\cos(1050) \\ \\ \cos(1050)=\cos(330) \end{gathered}[/tex]Then;
[tex]\cos(330)=\frac{\sqrt{3}}{2}[/tex]CORRECT OPTION: D
two trains leave town 906 miles aprt at the same time and travel each other. one train travels 21 mi/h faster than other. if they meet in 6 hours, what is the rate of each train?
Answers
Let
x be the speed of the slower train
x + 21 be the speed of the faster train
They meet in 6 hours which means that their speed is
[tex]\frac{906}{6}=151[/tex]The sum of their therefore is
[tex]\begin{gathered} x+(x+21)=151 \\ 2x+21=151 \\ 2x=151-21 \\ 2x=130 \\ \frac{2x}{2}=\frac{130}{2} \\ x=65\frac{\operatorname{mi}}{\operatorname{h}}\text{ (speed of slower train)} \\ \\ x+21=65+21=86\frac{\operatorname{mi}}{\operatorname{h}}\text{ (speed of faster train)} \end{gathered}[/tex]m/cour16121/quizzes/2919544/take22A totem pole casts a shadow 45 feet long at the same time that a 6-foot-tallmancasts a shadow that is 3 feet long. Find the height of the totem pole.Height of the totemfeetHint: set a proportion like this oneshadow totemshadow manactual height totem actual height manucation
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The totem pole with its shadow form a right triangle, and the same happens with the man and its shadow. Since it happens at the same time of the day, the "inclination" of the sunlight is the same for both, and those two triangles are similar, which means that their corresponding ratiso betweens sides are the same.
Using the hint given on the problem, we can estabilish the following equation for the height of the totem(let's call it h).
[tex]\frac{45}{h}=\frac{3}{6}[/tex]Now, we just need to solve for h.
[tex]\begin{gathered} \frac{45}{h}=\frac{3}{6} \\ \frac{45}{h}=\frac{1}{2} \\ \frac{h}{45}=2 \\ h=2\cdot45 \\ h=90 \end{gathered}[/tex]The height of the totem pole is 90 ft.
Watch help videoFind the value of y in the diagram below.Y +9Y + 9Y +9y +9Y +9116Answer: Submit Answer
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The equation from the box obtained is
[tex]y+9+y+9+y+9+y+9+y+9=116[/tex][tex]5y+45=116[/tex][tex]5y=71[/tex][tex]y=14.2[/tex]Simplify (sqrt)98m^12 using factor tree or splitting up using perfect squares. Quick answer showing work = amazing review :)
Answers
The expression is:
[tex]\sqrt[]{98m^{12}}[/tex]We need to use a factor tree to solve the problem. We will draw it as shown below:
According to the factor tree we can represent the 98 as:
[tex]\sqrt[]{2\cdot7^2m^{12}}[/tex]We can now remove the terms that have a power of 2 and a power of 12. For that we need to divide the exponents by 2.
[tex]7^{}\sqrt[]{2}m^6[/tex]The simplified expression is 7*sqrt(2)*m^6.
Part BNow you’ll attempt to copy your original triangle using two of its angles:Choose two of the angles on ∆ABC, and locate the line segment between them. Draw a new line segment, DE¯, parallel to the line segment you located on ∆ABC. You can draw DE¯ of any length and place it anywhere on the coordinate plane, but not on top of ∆ABC.From points D and E, create an angle of the same size as the angles you chose on ∆ABC. Then draw a ray from D and a ray from E through the angles such that the rays intersect. You should now have two angles that are congruent to the angles you chose on ∆ABC.Label the point of intersection of the two rays F, and draw ∆DEF by creating a polygon through points D, E, and F.Take a screenshot of your results, save it, and insert the image in the space below.
Answers
Step 1)
We used angles alpha and betta from the original triangle
Step 2)
Then,
Step 3)
Notice that the two triangles are similar due to the AAA postulate. (The length of DE is different than that of AB)
01 Question 11 What is the area of the shaded region? 12cm 6 cm 10cm 8cm 128cm? 96cm2 X 144cm? a 112cm?
Answers
We can calculate the area of the shaded region as the difference between the area of the rectangle (sides 12 cm and 10 cm) and the area of the triangle in the corner.
The triangle has base of b=12-8=4 cm and height h=10-6=4 cm.
Then, we can calculate the area of the shaded area as:
[tex]\begin{gathered} A=A_r-A_t \\ A=b_r\cdot h_r-\frac{b_t\cdot h_t}{2} \\ A=12\cdot10-\frac{4\cdot4}{2} \\ A=120-\frac{16}{2} \\ A=120-8 \\ A=112\operatorname{cm}^2 \end{gathered}[/tex]Answer: 112 cm^2
at the rate shown in the table how many books were sold in 3 weeks
Answers
210 books were sold in 3 weeks
Explanation
Step 1
you can easily solve this by using a rule of three
number of weeks=1
sold books=70
then, the rate is
[tex]\text{rate}=\frac{70\text{ books}}{1\text{ we}ek}=70\text{ book}s\text{ per w}eek[/tex]Step 2
Let
x represents the number of books sold in 3 weeks,then the rate is
[tex]\text{rate}=\frac{x}{3\text{ w}eeks}[/tex]as the rates are equal
[tex]\begin{gathered} 70=\frac{x}{3} \\ Multiply\text{ both sides by 3} \\ 70\cdot3=\frac{x}{3}\cdot3 \\ x=210 \end{gathered}[/tex]I hope this helps you
given the following trig equation, find the Exact value of the remaining 5 trig functionstan (theta) = 5/6 and cos theta < 0Start by drawing the triangle in standard position and use the Pythagorean theorem to find the remaining side. A. label the exact value of all 3 sides of the triangle drawn in the correct quadrantB. DETERMINE the EXACT value of the remaining 5 trig functions! (sin) (cos) (tan) (sec) (csc) (cot)
Answers
tan (theta) = 5/6 and cos theta < 0
tan (theta) = 5/6 ==> theta = tan^-1(5/6) = 39.80557109
theta = 39.80557109
cos(theta) = cos(39.80557109) = 0.7682212796
It says that cos(theta) < 0, so the 39.80557109 degrees is in rality an angle of 90 + 39.80557109 = 120.80557109
sin (theta) = sin (120.80557109) = 0.858910105
cos(theta) = cos(120.80557109) = −0.5121263824
tan(theta) = tan(120.80557109) = −1.677144811
sec(theta) = sec(120.80557109) = −1.952643008
csc(theta) = csc(120.80557109) = 1.164266195
cot(theta) = cot(120.80557109) = −0.5962514348
What is the value of u? H 88 U +64 I K к 88 50 J U =
Answers
HK = KJ
So:
u+64 = 5u
Solve for u
Combine like terms:
64 = 5u-u
64= 4u
Divide both sides by 4
64/4 =4u/4
16 = u
Pythagorean Theorem Task Card #1 A pool table is 9 feet long and 5 feet wide. How far is it from one corner pocket to the diagonally opposite corner pocket? Round to the nearest tenth.
Answers
A right triangle is made where the two legs are 9 ft (a) and 5 ft (b), and we have to find the hypotenuse (c). Using Pythagorean Theorem:
c² = a² + b²
c² = 9² + 5²
c² = 81 + 25
c = √106
c ≈ 10.3 ft
10. Linek is graphed below. Write an equation for line m that is perpendicular to line (there are multiple correct answers).
Answers
step 1
Find the equation of line k
the slope of line k is
m=-3/4 ------> previous answer
step 2
If two lines are perpendicular, then their slopes are opposite reciprocal
so
the slope of the line m must be equal to
m=4/3
I will assume a point (3,4)
Find the equation in slope intercept form
y=mx+b
we have
m=4/3
point (3,4)
substitute
4=(4/3)*(3)+b
solve for b
4=4+b
b=0
therefore
y=(4/3)x -----> equation in slope intercept form ( this line is perpendicular to line k)Find the equation in point slope form
y-y1=m(x-x1)
we have
m=4/3
point (3,4)
substitute
y-4=(4/3)*(x-3) -----> equation in point slope form ( this line is perpendicular to line k)Find the equation in standard form
Ax+By=C
where
A is a positive integer
B and C are integers
we have
y=(4/3)x
Multiply by 3 both sides
3y=4x
4x-3y=0 ------> equation in standard formy=(4/3)xy-4=(4/3)*(x-3)4x-3y=0the product of 8 and a number increased by 17
Answers
You have the following stament:
The product of 8 and a number increased by 17
In order to write the previous statment in an algebraic way, you take into account that "the product of 8 and a number" means the multiplication of 8 and a variable, which is "increased" by 17. That is, number 8 is multiplying the sum of a variable and 17.
Thus, you have:
The product of 8 and a number increased by 17:
8(x + 17)
ХI went to the bank 4 times last week and withdrew a total of $160. What was theaverage amount withdrew each time? Write and solve an expression to find theanswer
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A ball is shot out of a cannon at ground level. it's height H in feet after t seconds is given by the function H(t) = 96t - 16t^2. Find H(1), H(5), H(2), and H(4). Why are some of the outputs equal? H(1) = ______ feetH(2)= ______ feetH(4)= ______ feet H(5)= ______ feet
Answers
Follow the function we have that
[tex]\begin{gathered} H(1)=96(1)-16(1)^2 \\ =96-16=80 \end{gathered}[/tex]So H(1) = 80 feet. Now
[tex]\begin{gathered} H(2)=96(2)-16(2)^2 \\ =192-64=128 \end{gathered}[/tex]So H(2) = 128 feet. Now
[tex]\begin{gathered} H(4)=96(4)-16(4)^2 \\ =384-256=128 \end{gathered}[/tex]So H(4) = 128 feet. Now
[tex]\begin{gathered} H(5)=96(5)-16(5)^2 \\ =480-400=80 \end{gathered}[/tex]So H(5) = 80 feet.
Simply this expression 4(1-3x)+7x-8
Answers
Answer:
-5x-4
Step-by-step explanation:
4(1-3x)+7x-8
Distribute the 4
4(1)+4(-3x)+7x-8
4-12x+7x-8
Combine like terms
-12x+7x+4-8
-5x-4
hopes this helps please mark brainliest
five to the third power
Answers
We need to find the value of 5 to the third power, to do this let's remember that the third power of a number means multiplying this number three times by itself, that is:
[tex]5^3=5\times5\times5=125[/tex]The answer is 125
DreviousRandom numbers are useful forA creatingOB. beingOC. modelingOD. sellingReset Selectionreal-world situations that involve chance.
Answers
Given random numbers, it is important to remember that Random Numbers are defined as those numbers that each have the same probability of being selected.
In Statistics, random numbers are useful to model different real-world situations.
An example of random numbers is the numbers of a lottery.
Another example of random numbers is the numbers obtained by rolling a numbered dice.
Hence, the answer is: Option C.
Select the correct choice and fill in the answer box
Answers
To begin with, let us look at a few definitions that will help
A relation is a function if each x-value is paired with exactly one y-value. A vertical line test on a graph can be used to determine whether a relation is a function.
If we use a graph to check, we will have
We can see that there is no overlapping of coordinates. The table satisfies the vertical line test.
Hence, it is a function
The domain and range of function is the set of all possible inputs and outputs of a function respectively. The domain and range of a function y = f(x) is given as domain= {x ,x∈R }, range= {f(x), x∈Domain}.
The domain of the function, D is given by
[tex]D=\mleft\lbrace-1,0,1,2,3\mright\rbrace[/tex]The range, R is given by
[tex]R=\mleft\lbrace-6,-1,2,5,8\mright\rbrace[/tex]The Rainforest Pyramid at Moody Gardens is a rectangular pyramid that has glass sides to allow the sunlight to enter the building. The base of the building is approximately 320 feet wide and 200 feet long. The height of each side is approximately 140 feet. How many square feet of glass were needed to cover the lateral sides of the pyramid?
Answers
We have the following diagram for a rectangular pyramid:
Where:
• h is the height of the pyramid,
,• s is the slant height, the height of the sides.
The area of the sides (without the base) of the pyramid is given by:
[tex]A=\frac{1}{2}\cdot p\cdot s\text{.}[/tex]Where p is the perimeter of the base.
We have a rectangular pyramid with:
• base with sides a = 320 ft and b = 200 ft,
,• slant height (heigh of the sides ) s = 140 ft.
The perimeter of the base is:
[tex]p=2\cdot(a+b)=2\cdot(320ft+200ft)=1040ft\text{.}[/tex]Replacing the value of p and s in the formula of the area we get:
[tex]A=\frac{1}{2}\cdot(1040ft)\cdot140ft=72800ft^2.[/tex]Answer
It was needed 72800 ft² of glass.