1.2 A pyramid, with the base similar to an obtuse-angled triangle as indicated by the diagram below. A = 110°, B = 40° and BC = 6 meters. The perpendicular height of the pyramid is 8 meters
1.Calculate the length of AB
2.Calculate the area of the base.
3.Calculate the volume of the pyramid
Answers
a) The length of the side AB is approximately 11.276 meters.
b) The area of the base of the pyramid is approximately equal to 6.161 square meters.
c) The volume of the pyramid is equal to 16.429 cubic meters.
What are the length of a side, the surface area and the volume of a pyramid?a) The picture shows a pyramid with a triangular base, the triangle has one obtuse angle and the length of the side AB can be found by the law of the sine:
6 / sin 110° = AB / sin 30°
AB = 6 × (sin 30° / sin 110°)
AB ≈ 3.193 meters
The length of the side AB is approximately 11.276 meters.
b) First, find the length of the side AC:
6 / sin 110° = AC / sin 40°
AC = 6 × sin 40° / sin 110°
AC ≈ 4.104 meters
Second, determine the area of the triangular base by Heron's formula:
s = 0.5 · (AC + BC + AB)
s = 0.5 · (4.104 m + 6 m + 3.193 m)
s = 6.649 m
A = √[s · (s - AC) · (s - BC) · (s - AB)]
A = √[6.649 · (6.649 - 4.104) · (6.649 - 6) · (6.649 - 3.193)]
A ≈ 6.161 square meters
The area of the base of the pyramid is approximately equal to 6.161 square meters.
c) The volume of the pyramid can be found by using the following expression:
V = (1 / 3) · A · h
Where:
A - Area of the pyramid base, in square meters.h - Height, in meters.If we know that A ≈ 6.161 square meters and h = 8 meters, then the volume of the pyramid is:
V = (1 / 3) · (6.161 m²) · (8 m)
V = 16.429 m³
The volume of the pyramid is equal to 16.429 cubic meters.
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Related Questions
Evaluate the variable expression when a = 2 and c = −3. 2a − (c + a)2
Answers
the expression of the variable for a = 2 and c = 3. 2a − (c + a)2
2a+b^2 2a +b2
2(-3) +(-2)^2 2(-3) + (-2)
-6 +4 -6 -4
-2 -10
An expression is a set of terms combined using the operations +, -, x or ÷, for example 4 x − 3 or 5 x 2 − 3 x y + 17 . An equation is a statement with an equals sign, which states that two expressions are equal in value, for example 4 b − 2 = 6 .
Either the options are incorrect, or the problem is poorly written.
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help please I don't quite understand the question much.
Answers
The profit in 2012 must be 4.5(in hundreds of dollars) to break even.
Profit for a company is defined as the difference between the revenue and cost of a product.
Let us take an example to learn more about profit.
A company sells a product at a price of 'S' dollars and the company spends 'C' dollars to manufacture the product. Here C includes the cost of raw materials, labor cost, transport etc.. Now the net profit for the company for selling one unit of this particular product is given by
Profit=S-C
When S>C the profit is positive.When S<C the profit is negative or loss .When S=C then the company breaks even.In the given chart it is shown the profit of the company is given as
2.5,1.75,-3.3 and -1.4 (in thousands of dollars) over 4 years.
Net profit over four years=[tex]2.5+1.75-3.3 -1.4=-0.45[/tex]
So over the past four years the company incurred a loss of
[tex]=0.45\times 1000\\[/tex]
[tex]=450[/tex] dollars
Now the company needs to break even in 2012.
So net profit must be zero over 5 years.
Therefore Profit in 2012=0-(-450)=450 dollars
Profit=4.5 (hundreds of dollars)
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(A) Find the slope of the line that passes through the given points_
(B) Find the point-slope form of the equation of the line.
(C) Find the slope-intercept form of the equation of the line.
(D) Find the standard form of the equation of the line.
(4,2) and (11,8)
Answers
a) The slope of the line is 6 / 7.
b) The point-slope form of the equation of the line is y - 2 = (6 / 7) · (x - 4).
c) The slope-intercept form of the equation of the line is y = (6 / 7) · x - 17 / 7.
d) The point-slope form of the equation of the line is - 6 · x + 7 · y + 17 = 0.
How to find the equation of the line in three different forms
There are three different forms of the equation of the line:
Point-slope
y - y' = m · (x - x') (1)
Slope-intercept
y = m · x + k (2)
Standard
a · x + b · x + c = 0 (3)
Where:
m - Slopek - y-Intercepta) The slope that passes through the two given points is found by secant line formula:
m = [8 - 2] / [11 - 4]
m = 6 / 7
b) The point-slope form of the equation of the line is:
y - 2 = (6 / 7) · (x - 4)
c) The slope-intercept form of the equation of the line is:
y - 2 = (6 / 7) · x - 24 / 7
y = (6 / 7) · x - 17 / 7
d) The standard form of the equation of the line is:
7 · y = 6 · x - 17
- 6 · x + 7 · y + 17 = 0
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what is the HCF of 225 495 and 810
Answers
Step-by-step explanation:
Factor of 225
= 3 × 3 × 5 × 5
Factor of 495
= 3 × 3 × 5 × 11
Factor of 810
= 3 × 3 × 3 × 3 × 2 × 5
Now ,
HCF = Common Factor
= 3 × 3 × 5
= 45
[tex]...[/tex]
☘️☘️☘️...
Using the associative property, rewrite the following expression. You do NOT need to simplify it. -3y - 6y + 10y
Answers
Another form of the given expression using associative property is 10y + (-3y -6y)
Associative propertyAssociative property shows that if two or more property are added or multiplied, the result remains the same. For instance;
a +(b + c) = (a+b) + c
Given the expression below;
-3y - 6y + 10y
Group to have
(-3y - 6y) + 10y
10y - 3y - 6y
This can also be grouped as;
(10y - 3y) - 6y = 10y + (-3y -6y)
Hence another form of the given expression using associative property is 10y + (-3y -6y)
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3/4 + 7/8 + 3/4 + 1/2 + 7/8
Answers
Answer:
=
15/4
(Decimal: 3.75)
Step-by-step explanation:
In 2006, the number of federal hazardous waste sites in California was 3 less than twice the number of sites in Washington. How many hazardous waste sites were there in Washington if there were 19 such sites in California?
Answers
Answer:
11
Step-by-step explanation:
2x-3=19
2x=22
x=11
Find a polynomial function of degree 5 with -2 as a zero of multiplicity 3, 0 as a zero of multiplicity 1, and 2 as a zero of multiplicity 1
(Use 1 for the leading coefficient.)
Answers
The polynomial function with degree 5 is formed as:
f (x) = x (x + 2)³ (x - 2).
What are termed as the polynomial functions?Polynomials are algebraic representations that contain indeterminates and constants.A polynomial is an algebraic expression in which all of the variable exponents have become whole numbers.Any polynomial's variable exponents must be non-negative integers.A polynomial's degree is the highest and greatest exponent of a variable in such a polynomial.The degree is used to approximate the optimal number of solutions to a polynomial function using Descartes' Rule of Signs.(-2) is derived from the factor (x + 2); because it has a multiplicity of three, you must account for that zero three times; thus, it is composed as (x + 2)³.
0 is derived from the factor x.
2 is derived from of the factor (x - 2).
The factored polynomial function is:
f (x) = x (x + 2)³ (x - 2)
Thus, the polynomial function with degree 5 is composed.
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The length of a rectangle is 4yd longer than its width.
If the perimeter of the rectangle is 68yd, find its length and width.
Answers
Pentagon Question
The sides add to 63, so:
[tex]11+3x+11+x+2+2x+3=63 \\ \\ 6x+27=63 \\ \\ 6x=36 \\ \\ x=6 \\ \\ \implies AB=2(6)+3=15[/tex]
Rectangle Question
If the width is w, then the length is w+4.
This means that 2(w+w+4)=68.
[tex] 2(2w+4)=68 \\ \\ 2w+4=34 \\ \\ 2w=30 \\ \\ w=15[/tex]
So, the length is 19 and the width is 15.
My child is struggling with the answer.
Answers
Using the relation between velocity, distance and time, the distances are given as follows:
A. d = 13/3 miles.
B. d = 4.25 miles.
C. d = M x 5/60(first five minutes) + N x 15/60(last 15 minutes).
What is the relation between velocity, distance and time?Velocity is distance divided by time, that is:
v = d/t.
Hence the distance is:
d = vt.
In item a, considering the time in hours, we have that:
v = 13, t = 20/60 = 1/3.
Hence:
d = 13/3 miles.
In item b, we have different definitions, then:
d = 15 x 5/60(first five minutes) + 12 x 15/60(last 15 minutes).
d = 15/12 + 15/5
d = 4.25 miles.
For item c, we have that:
d = M x 5/60(first five minutes) + N x 15/60(last 15 minutes).
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A television sells for $550. Instead of paying the total amount at the time of the purchase, the same television can be
bought by paying $200 down and $50 a month for 14 months. How much is saved by paying the total amount at the
time of the purchase?
Answers
One-seventh of a number, increased by twelve?
Answers
Answer:
x/7+12
Step-by-step explanation:
One seventh refers to 1/7.
Since we do not know what "a number" is it, it is written as "x."
Whenever you see the word "increased" think addition.
So in this case,
x / 7 + 12
Chef Smith will be serving a breakfast banquet for 300 guests. Each guest will be served a two-egg
omelet. How many dozen eggs should Chef Smith order?
Answers
Answer: 50
Step-by-step explanation:
Answer:
50
Step-by-step explanation:
300(2) bcuz 300 guests and each person gets 2
600(12) bcuz 300(2) is 600 and a dozen is 12
=50
which expression represents an irrational number
Answers
Convert 50°F to degrees Celsius.
If necessary, round your answer to the nearest tenth of a degree.
Here are the formulas.
C=5/9(F-32)
F=9/5C+32
Answers
Answer:
10°C
Step-by-step explanation:
F = 50
C = 5/9 * (F - 32) = 5/9 * (50 - 32) = 5/9 * 18 = 5 * 2 = 10
The 5000 that invested in Fund A returned a 3% profit. The amount that invested in Fund B returned a 10% profit. How much did she invest in Fund B, if both funds together returned a 5% profit?
Answers
The investment in Fund B is $2000.
To understand the given question we first have to understand the logic of percentage and how it affect the return on Investment.
If an investment fund returns a profit on an investment then the profit is calculated by multiplying the investment with the profit(in decimal form).
For Example: If the investment is A and profit is x % then the profit is calculated by:
Profit =A×([tex]\frac{x}{100}[/tex])
Now in the given problem, let us consider the amount of investment into the Fund B be x.
Profit in Fund B=10%
Profit in Fund A is 3%.
Investment in Fund A=$5000
Total profit from both investments=3% of 5000+10% of x
[tex]=\frac{3}{100}\times 5000 + \frac{10}{100}\times x\\ =150+0.1x[/tex]
Now the total investment=5000+x
The combined profit for both the Investments is 150+0.1x
But the combined profit is 5% for both investments.
profit=[tex]5\% of(5000+x)[/tex]
[tex]=\frac{5}{100}\times (5000+x)\\=0.05\times5000+0.05x\\=250+0.05x[/tex]
Now the profit is same, so if we equate both the expressions of profit we get a linear equation in x.
[tex]\therefore 250+0.05x=150+0.1x\\or,250-150=0.1x-0.05x\\or,100=0.05x\\or,x=2000[/tex]
Thus we can conclude that she invested $2000 in the Fund B.
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What is the range of the function f(x) = 4x – 5 over the interval of 1 < x ≤ 5? Give your answer in interval notation.
Answers
Answer:
Hello,
Step-by-step explanation:
[tex]1 < x\leq 5 \ \\\Longrightarrow\ 4 < 4x \leq 20 \ \\\Longrightarrow\ -1 < 4x-5 \leq 15 \\\Longrightarrow\ -1 < f(x) \leq 15 \\\\range=]-1; 15][/tex]
The range of the function f(x) = 4x - 5 will range from -1 to 15.
What are the function and range?The expression that established the relationship between the dependent variable and independent variable is referred to as a function. In the function as the value of the independent variable varies the value of the dependent variable also varies.
A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.
Given that the function f(x) = 4x – 5 and the interval is 1 < x ≤ 5. The range will be calculated as,
1 < x ≤ 5
4 < 4x ≤ 20
4-5<4x - 5< 20-5
-1 < 4x - 5 < 15
Therefore, the range of the function f(x) = 4x - 5 will range from -1 to 15.
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How do I solve this absolute value in quality problem
|2t + 2/3|≤4
Answers
Answer: -7/3≤t≤5/3
Step-by-step explanation:
|2t + 2/3|≤4
2t + 2/3≤4
(2t + 2/3≤4)*3
6t+2≤12
6t≤10
t≤10/6
t≤5/3
2t + 2/3>=-4
(2t + 2/3>=-4)*3
6t + 2>=-12
6t>=-14
t>=-14/6
t>=-7/3
-7/3≤t≤5/3
The lateral surface area of cone A is exactly 1/2 the lateral surface area of
cylinder B.
OA. True
OB. False
Answers
Answer:
B. False
Step-by-step explanation:
You want to compare the lateral surface areas of a cone and cylinder, where the slant height of the cone is twice the height of the cylinder. Your proposition is that the cone's lateral area is half that of the cylinder.
Cone lateral areaEffectively, the lateral area of a cone is the area of a triangle whose base is the circumference of the cone, and whose height is the cone's slant height. The formula for the lateral area of a cone of radius r and slant-height s is ...
A = πrs
For the given dimensions (s=2h), the lateral area is ...
A = πr(2h) = 2πrh
Cylinder lateral areaThe lateral area of a cylinder is the area of a rectangle whose base is the circumference of the cylinder, and whose height is the cylinder's height. The formula for the lateral area of a cylinder of radius r and height h is ...
A = 2πrh
ComparisonThe lateral areas of the given figures are both 2πrh, so one is not half the other.
The proposition is False.
8.2% of what amount is $2.87
Answers
Answer:
35Step-by-step explanation:
8.2% of what amount is $2.87
we find unity and multiply by 1002.87 : 8.2 * 100 =
35
Find an equation of variation in which y varies jointly as x and z, and y= 48 when x = 8 and z=6
Answers
Answer:
y = xzStep-by-step explanation:
Joint variation equation:
y = kxz, where k- coefficient of variationGiveny = 48,x = 8,z = 6Find the value of k by plugging in the given values:
48 = 8*6k48 = 48kk = 1The equation is:
y = xzYou have two strands of decorative lights. Strand A changes color every 8 seconds and Strand B changes color every 12 seconds. Both strands just changed color. After how many seconds will the strands change color at the same time again?
Answers
Answer:
24 seconds
Step-by-step explanation:
Strand A: 3 × 8 secons =24 seconds
Strand B: 2 × 12 seconds= 24 seconds
Which list shows the numbers in increasing order?
A) -0.5, 1.5, -2, -0.75, √7
C) -2, -0.75, -0.5, 1.5, √7
B) -0.5, -2, -0.75, 1.5, √7
D) √7, 1.5, -0.5, -0.75, -2
Answers
Answer:
Step-by-step explanation:
its ''C''
Find the equation of the line that contains the point (6, -2) and is perpendicular to the line y = - 2x + 8.
O y = -x
Oy=2x-14
O y =
x-5
O y = - 2x + 10
Answers
keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above
[tex]y = \stackrel{\stackrel{m}{\downarrow }}{-2}x+8\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{-2\implies \cfrac{-2}{1}} ~\hfill \stackrel{reciprocal}{\cfrac{1}{-2}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{1}{-2}\implies \cfrac{1}{2}}}[/tex]
so, we're really looking for the equation of a line whose slope is 1/2 and that it passes through (6 , -2)
[tex](\stackrel{x_1}{6}~,~\stackrel{y_1}{-2})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{1}{2} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-2)}=\stackrel{m}{ \cfrac{1}{2}}(x-\stackrel{x_1}{6}) \implies y +2= \cfrac{1}{2} (x -6) \\\\\\ y+2=\cfrac{1}{2}x-3\implies \LARGE \begin{array}{llll} y=\cfrac{1}{2}x-5 \end{array}[/tex]
What is the slope of the line represented by the equation y =4/5x-3?
Answers
Answer:
4/5 is the slope of the line
How many groups of 3/8 are in 1?
Answers
Answer:
2 groups of 3/8 are in one
Step-by-step explanation:
making up 6/8 because you can add another 3/8 to it.
Ch. 1. Problems 6, 7 & 9
6. The only swimmng pool at a motel is outdoors. It is 5.0 m wide and 12.0 m long. If the weekly
evaporation is 2.35 inches how many gallons of water must be added to the pool if it does not rain? If during the next week the pool still loses two. 35 inches of water to evaporation, even with 20 mm of rainfall, how many liters of water must be added?
Answers
Answer:
946 gal
629 gal
Step-by-step explanation:
volume that evaporates = LWH
volume = (5.0 m × 100 cm/m × inch / 2.54 cm) × (12.0 m × 100 cm/m × inch / 2.54 cm) × 2.35 inch
volume = 218,550 in.³
volume = 218,550 in.³ × 1 gal / 231 in.³
volume = 946 gallons
You must add 946 gallons.
The loss to evaporation is 2.35 in.
The amount of rain is 20 mm
The net loss is
2.35 in. × 25.4 mm / inch - 20 mm = 39.69 mm
39.69 mm × 1 inch / 25.4 mm = 1.563 in.
The net loss now is 1.563 in. instead of 2.35 in.
We find the fraction of the the previous loss is the loss with rain and multiply by the previous loss.
1.563/2.35 × 946 gal = 629 gal
With rain, then 629 gallons of water must be added.
The posts of a hockey goal are 6 ft. apart. A player attempts to score by shooting the puck from a
point that is 19 ft from one post and 24 ft from the other post. Within what angle & must the shot be
made? Express your answer to the nearest degree.
Answers
The angle at which the shot was made should be 17.53° degrees.
Let C denote the point where the player attempts to put in a goal.
Let A and B denote the two goalposts.
We are given the posts of a hockey goal are 6 ft apart.
The distance between the player and one goalpost is 19 ft.
The distance between the player and the other goalpost is 24 ft.
Then, we have AC = 19 ft, BC = 24 ft, and AB= 6 ft.
Refer to the diagram.
Let θ be the angle made when trying to shoot the goal towards goalpost A.
Then we have tan(θ) = 6/19
⇒ θ = 17.53° degrees.
Therefore, the angle at which the shot was made should be 17.53° degrees.
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Allison ran 5 miles in 40 minutes before running an additional 3 miles in 27 minutes is this proportional are not pls help ASAP
Answers
Answer:
no it is not proportional...
Step-by-step explanation:
5 miles/40 minutes is 1/8
3 miles/27 minutes is 1/9...
[tex]-6y + 4 = | 4y + 12 |[/tex]
Answers
Answer: its not equal.
Step-by-step explanation:
-6y + 4 = 2 (-3y + 2)
|4y + 12| = 4 (y + 3)
