Answers
Answer:
Exact surface area = 500+20pi square cm
=============================================================
Explanation:
A = area of the bottom face = 10*12 = 120B = area of the left face = 7*12 = 84C = area of the right face = 7*12 = 84D = area of the front face = 7*10-0.5*pi*2^2 = 70 - 2piE = area of the back face = 7*10-0.5*pi*2^2 = 70 - 2piF = area of the top face = 2*3*12+0.5*2*pi*2*12 = 72+24piAll areas mentioned are in square cm, which can be abbreviated to cm^2.
Faces A,B,C are straight forward as they are simply rectangles. The remaining 3 other faces are a bit tricky.
Faces D and E involve subtracting off the area of a semicircle of radius 2 from a 7 by 10 rectangle area. The formula pi*r^2 is the area of a full circle, while 0.5*pi*r^2 is the area of a semicircle. From there, I then plugged in r = 2.
The top face is really a combination of 3 different pieces (two flat, one curved in the middle). Each flat part is of area 3*12 = 36, so that doubles to 2*3*12 when accounting for both flat parts. The curved portion will involve the lateral surface area of a cylinder formula which is
LSA = 2*pi*r*h
but since we're only dealing with half the lateral area, we multiply that by 0.5 to get 0.5*2*pi*r*h. From there, I plugged in r = 2 and h = 12.
-----------------------
In summary we have these six areas for the faces
bottom = 120left = 84right = 84front = 70 - 2piback = 70 - 2pitop = 72 + 24piAdd up those sub areas to get the full surface area of this particular 3D solid.
120+84+84+(70-2pi)+(70-2pi)+(72+24pi)
(120+84+84+70+70+72)+(-2pi-2pi+24pi)
500+20pi
This is the exact surface area in terms of pi. If you want the approximate version of this, then you could replace pi with 3.14 and compute to get 562.8 cm^2
Use more decimal digits in pi to get a more accurate value. If you use your calculators version of pi, then you should get somewhere around 562.831853 cm^2
In this case, I think it's better to stick with the exact surface area (unless your teacher instructs otherwise).
Related Questions
Given two consecutive integers whose sum is 45, find the smaller of the two integers.
Answers
Answer:
22 and 23
Step-by-step explanation:
let two consecutive number be
x and x+1
now,according to the question
x+x+1=45
or,2x=45-1
or,2x=44
or,x=44/2
:-x=22
Hence, the two consecutive numbers are
22 and 23
What is the image point of (5, 1) after a translation right 5 units and down 2 units?
Submit Answer
PLS HELP ASAP
Answers
Answer:
(10,-1)
Step-by-step explanation:
A translation to the right is (x+5)
A translation down 2 is (y-2)
(5+5, 1-2)
(10,-1)
Answer:
(10, - 1 )
Step-by-step explanation:
A translation right 5 units means add 5 to the x- coordinate
A translation down 2 units means subtract 2 from the y- coordinate
(5, 1 ) → (5 + 5, 1 - 2 ) → (10, - 1 )
Instructions: Find the missing side of the triangle.
25
20
х
X =
Answers
Answer:
x = 15
Step-by-step explanation:
Using Pythagoras' identity in the right triangle
x² + 20² = 25²
x² + 400 = 625 ( subtract 400 from both sides )
x² = 225 ( take the square root of both sides )
x = [tex]\sqrt{225}[/tex] = 15
Find two numbers whose sum is sixty eight and whose difference is twenty two
Answers
Answer:
45 and 23
Step-by-step explanation:
Let x equal the first number and y equal the second number.
We can set the following equations up with our information:
[tex]x+y=68[/tex]
[tex]x-y=22[/tex]
Adding the two equations together, we get:
[tex]2x=90[/tex]
Dividing by two, we receive [tex]x=45[/tex]
We can plug this into our first equation to get [tex]45+y=68[/tex].
Subtracting 45 from both sides, we get [tex]y=23[/tex].
The two numbers are 45 and 23, solved using system of equations.
What is a system of equations?A system of equations is a set of equations, involving similar variables used to solve for the variables simultaneously.
How to solve the question?In the question, we are asked to find the two numbers, whose sum is 68 and the difference is 22.
We assume the two numbers to be x and y.
The sum of the two numbers is given to be 68.
This can be shown as an equation, x + y = 68 ... (i).
The difference of the two numbers is given to be 22.
This can be shown as an equation, x - y = 22 ... (ii).
Equations (i) and (ii) together makes a system of equation in the variables x and y.
To solve for the system of equation, we add (i) and (ii), to get:
x + y = 68
x - y = 22
_________
2x = 90,
or, x = 45.
Substituting x = 45 in (i), we get:
x + y = 68,
or, 45 + y = 68,
or, y = 23.
Thus, the two numbers are 45 and 23, solved using system of equations.
Learn more about system of equations at
https://brainly.com/question/13729904
#SPJ2
make x the subject of the formula x(a-b)=a(b-x).
Answers
Answer:
Hello,
Step-by-step explanation:
[tex]x(a-b)=a(b-x)\\\\x(a-b)=ab-ax\\\\x(a-b)+ax=ab\\\\x(a-b+a)=ab\\\\x(2a-b)=ab\\\\\\x=\dfrac{ab}{2a-b} \ if\ 2a-b\neq 0[/tex]
Answer:
[tex]{ \sf{x(a - b) = a(b - x)}} [/tex]
Open the brackets:
[tex]{ \sf{ax - bx = ab - ax}} \\ { \sf{2ax - bx= ab }}[/tex]
Factorise out x:
[tex]{ \sf{x(2a - b) = ab}} \\ { \sf{x(2a - b) = ab}} \\ { \sf{x = \frac{ab}{2a - b} }}[/tex]
Over what interval is the function in this graph increasing?
AY
5
O A. -33x2
B. -43x3-2
O C. -5 sxs 5
OD. -2 sxs 3
Answers
Answer:
D
Step-by-step explanation:
As the graph depicts, the function is increasing in the interval [-2,3]
factorize: xy-3x - 5y + 15
Answers
Answer:
Step-by-step explanation:
xy-3x-5y+15
x(y-3)-5(y-3)
(y-3)(x-5)
Complete the equation to represent finding x, the greater integer. x(x – ) = 143 What is the greater integer?
Answers
Answer:
[tex]x * (x - 2) = 143[/tex]
Where [tex]x = 13[/tex]
Step-by-step explanation:
Given
[tex]x (x - \_) = 143[/tex]
Required
Complete the blank
The complete question implies that the product include 2 consecutive odd numbers.
Two numbers whose products equal 143 are: 11 and 13
i.e. [tex]11 * 13 = 143[/tex]
So, we have:
[tex]x * (x - \_) = 13 * 11[/tex]
By comparison, we have:
[tex]x = 13[/tex]
[tex]x - \_ = 11[/tex]
Collect like terms
[tex]\_ = x - 11[/tex]
Substitute 13 for x
[tex]\_ = 13 - 11[/tex]
[tex]\_ = 2[/tex]
So, the complete equation is:
[tex]x * (x - 2) = 143[/tex]
Where [tex]x = 13[/tex]
Answer:
2
and
13
Step-by-step explanation:
Got it right on edge.
A company wants to determine the level of interest among its employees for an annual summer picnic. The company wants to survey
200 employees.
What is the best way to randomly choose these 200 employees?
Answers
Answer: Use employee identification numbers to randomly select 200 employees
Step-by-step explanation:
Random sampling refers to a sampling technique whereby each sample has an equal chance of being selected. It is an unbiased representation of the entire population and this is vital in drawing conclusion.
From the options given, the best way to randomly choose these 200 employees will be to use employee identification numbers to randomly select 200 employees.
Which polygon has an interior angle sum of 1080°?
Answers
Answer:
its octagon. first and last one it has total 8 sides
Choose the correct description of the graph of the compound inequality:
x-3<-9 or x+5>equal to 12
Answers
Answer:
C
Step-by-step explanation:
x - 3 < -9
simplifies to x < -6, which is to the left with an open circle
x + 5> 12
simplifies to x > 7, which is to the right a closed circle
Given the following coordinates complete the reflection transformation.
Answers
Answer:
see explanation
Step-by-step explanation:
Under a reflection in the x- axis
a point (x, y ) → (x, - y ) , then
A (- 1, - 5 ) → A' (- 1, 5 )
B (2, - 3 ) → B' (2, 3 )
C (3, - 5 ) → C' (3, 5 )
Under a reflection in the y- axis
a point (x, y ) → (- x, y ) , then
A' (- 1, 5 ) → A'' (1, 5 )
B' (2, 3 ) → B'' (- 2, 3 )
C' (3, 5 ) → C'' ( - 3, 5 )
1) Let f be the function defined by the
graph shown at right, with y = f(x).
a) What is the value of f(-9)?
-14-13-12-)1-10-9
10 11 12
b) How many solutions are there to
the equation f(x) = -2? (Just
state how many there are.)
c) State any and all intervals on which fis decreasing
d State any and all values of x for which fax>0. Ilse intervals to do this
Answers
Write a short account on farmer with the help of statement given, it says that the Indian farmer is born in dept lives in dept and die in dept.
plese help. need help.
Answers
Answer:
sir Malcolm darling
Step-by-step explanation:
he has said Indian farmer is born in dept lives in dept and die in dept.
Find the value of y.
Answers
y=65
write an inequality and show on a number line all numbers greater (-3) but less than equal to3
Answers
Answer:
-3<x<_3
You plot this on a number line by writing and open circle on -3 and drawing and arrow from that open circle all the way until 3 and them draw a closed circle on 3.
Step-by-step explanation:
Rewrite this equation in the form y = ax + b.
2y = 4x - 8
Enter the correct answer.
OOÐ
DONE
Clear all
ĐOO
?
Answers
Answer:
y = 2x -4
Step-by-step explanation:
2y = 4x - 8
Divide each side by 2
2y/2 = 4x/2 - 8/2
y = 2x -4
please help, i really dont understand. will give brainliest.
At Sarah's cafe, customers can choose one of the following entrees: burrito, pasta, soup or taco. They can also order a side dish. They have a choice of french fries, salad, potato salad or coleslaw. Finally customers get to choose one of the following drinks and a choice of soda, coffee, water, milk or juice.
For dinner, the cafe offers diners a special, customers can order 2 sides with their entree. In how many different ways can dinner be ordered?
*The answer is not 120 btw*
Answers
Answer:
I've done the math and it's 120, people say it's 120 and online 120, I really wanna help but I just
Find the distance between (3, −7)
and (4, 1). Write your answer using a radical sign.
Answers
Answer:
sqrt(65)
Step-by-step explanation:
To find the distance between the two points
d = sqrt( (x2-x1)^2+ (y2-y1)^2)
= sqrt( (4-3)^2 +(1 - -7)^2)
= sqrt( 1^2 + (1+7)^2)
= sqrt( 1+8^2)
= sqrt(1+64)
sqrt(65)
[tex] \large\begin{gathered} {\underbrace{\boxed{ \bf {\red{Distance \: = \: \sqrt{(x_2 \: - \: x_1) ^{2} \: + \: (y_2 \: - \: y_1) ^{2} } }}}}}\end{gathered}[/tex]
Substuting the values[tex] \bf \longrightarrow \: Distance \: = \: \sqrt{ \bigg(4 \: - \: 3 \bigg) ^{2} \: + \: \bigg(1 \: - \: [ - 7 ]\bigg) ^{2} }[/tex]
[tex] \bf \longrightarrow \: Distance \: = \: \sqrt{ (1) ^{2} \: + \: (1 \: + \: 7 ) ^{2} }[/tex]
[tex] \bf \longrightarrow \: Distance \: = \: \sqrt{ 1 \: + \: (8 ) ^{2} }[/tex]
[tex] \bf \longrightarrow \: Distance \: = \: \sqrt{ 65 }[/tex]
[tex]\Large \purple \diamond \: \: \underbrace {\rm {{{\color{blue}{Distance \: = \: \sqrt{65} }}}}} \: \: \purple \diamond[/tex]
the expression below is a factorization of what trimonial (5x+6)(3x-2)
Answers
Answer:
[tex]15x^2 + 8x -12[/tex]
Step-by-step explanation:
(5x+6)(3x-2)
"foil" it out
F: 5x * 3x = 15x^2
O: 5x * -2 = -10x
I: 6*3x = 18x
L: 6 * -2 = -12
Answer:
15x² + 8x - 12
Step-by-step explanation:
(5x + 6)(3x - 2)
Each term in the second factor is multiplied by each term in the first factor, that is
5x(3x - 2) + 6(3x - 2) ← distribute both parenthesis
= 15x² - 10x + 18x - 12 ← collect like terms
= 15x² + 8x - 12
How much wrapping paper did he use ,in square inches
Answers
Answer:
96.76 square inches
Step-by-step explanation:
5.2x5.2=27.04
6.7x5.2/2=17.42
17.42x4=69.68
69.68+27.04=96.76
Hope this helps <3 Comment if you want more thanks and be sure to give brainliest (4 left) <3
simplify the radical expressions pleaseeeeee help I haven’t done algebra in 2 years
Answers
For the next one you can’t have a radical in the denominator so just multiply by root 3/ root 3, which gives you 6 root 3/3 which simplifies into 2 root 3.
Need help ASAP plz
Answers
Answer:
C) postulate
An axiom or a postulate is an accepted statement of fact.
OAmalOHopeO
Answer:
Im pretty sure its definition
(PLEASE HELP you don't have to graph I just need the equations) Dr. Gilmore just got his PhD, and he wants to print copies of his thesis in hardcover book
format. He could use Belmont Printing, paying a setup fee of $40 and $4 for every book
printed. Alternately, he could go through Fairfax University, paying an up-front fee of $30
and $6 per book. It turns out that, given the number of books Dr. Gilmore wants to print, the
two options cost the same amount. How many books is that?
Write a system of equations, graph them, and type the solution.
Answers
yeah yeah that’s what she was saying she didn’t yyyyyyyyu
I don’t know what to write but ye I need help with this question. Thanks
Answers
Answer: the first table.
Step-by-step explanation:
The terms in the domain (x) should have only one range (y)
Answer:
A) x: -3, 0, -2, 8
y: -1, 0, -1, 1
Step-by-step explanation:
Function has only one output for each input.
OAmalOHopeO
A hot air balloon is flying at an altitude of 2926 feet. If the angle of depression from the pilot in the balloon to a house on the ground below is 25°
25
°
, how far is the house from the pilot? Round to the nearest tenth.(1 point)
Choices:
The house is 1236.6 feet from the pilot.
The house is 6274.8 feet from the pilot.
The house is 3228.5 feet from the pilot.
The house is 6923.5 feet from the pilot.
Answers
Answer:
The house is 6274.8 feet from the pilot.
Step-by-step explanation:
Samantha thought of a number N, divided it by 5, and add 4. Then she told the result R to Kelly. Find the domain and range of this function.
Answers
The domain of the function is the input values for which the function exists. For the function above, the domain exists on all real values. Hence the domain of the function will be D = [tex]\{-\infty, \infty\}[/tex]
The range of the function is the output values for which the function exists. For the function above, the range also exists on all real values. Hence the range of the function will be R = [tex]\{-\infty, \infty\}[/tex]
The number N thought by Samantha divided by5 is expressed as;
[tex]\dfrac{N}{5}[/tex]
If the result is added to 4 and stored as R, then;
[tex]R = \dfrac{N}{5}+4[/tex]
This gives the required result
The domain of the function is the input values for which the function exists. For the function above, the domain exists on all real values. Hence the domain of the function will be D = [tex]\{-\infty, \infty\}[/tex]
The range of the function is the output values for which the function exists. For the function above, the range also exists on all real values. Hence the range of the function will be R = [tex]\{-\infty, \infty\}[/tex]
Learn more on domain and range here: https://brainly.com/question/13856645
Triangle ABC is translated right 8 units and down 15 units to triangle XYZ. Triangle ABC
has these angle measures:
m∠A=45∘
m∠B=53∘
m∠C=82∘
What is the measure of angle Y?
Answers
9514 1404 393
Answer:
53°
Step-by-step explanation:
The names of the triangles indicate that angle B corresponds to angle Y. Translation does not affect side lengths or angle measures, so angle Y is the same measure as angle B.
m∠Y = 53°
Answer: 53
Step-by-step explanation:
PLEASE FAST lenear equations
Answers
Answer:
y = 43
Step-by-step explanation:
(y-4)/3 = (y+9)/4
4(y-4) = 3(y+9)
4y-16 = 3y+27
4y-3y = 27+16
y = 43
who can help me out with this one?
Answers
Answer:
(x + 1)² + (y - 2)² = 9
Step-by-step explanation:
Equation of the circle with center (h, k):
(x - h)² + (y -k)² = r² where r is radius
Center(-1 , 2) ; r =3
(x - [-1])² + (y - 2)² = 3²
(x + 1)² + (y - 2)² = 9
