Consider a window the shape of which is a rectangle of height h surmounted by a triangle having a height t that is 0.9 times the width w of the rectangle. if the cross-sectional area is a, determine the dimensions of the window which minimize the perimeter.
The cross-sectional area is (h × w ) + ((1 ÷ 2) × 0.9 × w²) and the dimensions of the window which minimize the perimeter is (A - [tex]c_{0}[/tex][tex]w_{0}^{2}[/tex]) ÷ [tex]w_{0}[/tex] = 2√A[tex]c_{1}[/tex]([tex]c_{2}[/tex] - [tex]c_{0}c_1[/tex]) = 0.60592√A.
height of rectangle = h
height of the triangle = t
T = 0.9
width of the rectangle = w
The formula of Cross-sectional area is,
A = h × w + (1 ÷ 2)T × w
A = (h × w ) + ((1 ÷ 2) × 0.9 × w²)
Perimeter,
P = w + (2 × h) + 2√(T² + (w ÷ 2)²)
P = w + (2 × h) + 2√((0.9)² + (1 ÷ 2)²)
P = 2h + 2√((0.9)² + (1 ÷ 2)² + 1) × w
Therefore, [tex]C_{0}[/tex] = 0.9 ÷ 2, [tex]C_{1}[/tex] = 2, [tex]C_{2}[/tex] = 2√((0.9)² + (1 ÷ 2)² + 1)
minP=[tex]c_1[/tex]h+[tex]c_2[/tex]w
A = (h × w) + [tex]c_{0}[/tex]w²
substituting h = (A - [tex]c_{0}[/tex]w²) ÷ hw in P,
P = [tex]c_1[/tex]w + ([tex]c_1[/tex](A - [tex]c_{0}[/tex]w²) ÷ w)
Differentiating both sides,
(dP ÷ dw) = -2[tex]c_{0}[/tex][tex]c_{1}[/tex] + [tex]c_{2}[/tex] - ([tex]c_{2}[/tex](A - [tex]c_{0}[/tex]w²) ÷ w²) = 0
[tex]w_{0}[/tex] = (√[tex]c_{1}[/tex]A ÷ (√[tex]c_{2}[/tex] - [tex]c_{0}c_1[/tex])) = 0.962445√A
and consequently,
[tex]h_{0}[/tex] = (A - [tex]c_{0}[/tex][tex]w_{0}^{2}[/tex]) ÷ [tex]w_{0}[/tex] = 2√A[tex]c_{1}[/tex]([tex]c_{2}[/tex] - [tex]c_{0}c_1[/tex]) = 0.60592√A
Learn more about the maxima and minima at
https://brainly.com/question/18687565?referrer=searchResults
#SPJ4
Be Precise: Yesterday, Noah ran 2½ miles in 3/5 hour. Emily ran 3 3/4 miles in 5/6 hour. Anna ran 3 1/2 miles in hour. How fast, in miles per hour, did each person run? Who ran the fastest? Help pleaseeee
Answer:
Step-by-step explanation:
Noah- 4 1/6 miles/hour
Emily- 8 1/10 miles/hour
Anna- 3 1/2 miles/ hour
Emily ran the quickest.
Answer:
Anna was the fastest.
Step-by-step explanation:
Following are the steps we take to determine each one's speed:
speed=distance/time
Noah went 4 1/6 miles an hour, Emily went 4 1/2 miles an hour, and Anna went 5 5/9 miles an hour. Therefore, Anna was the fastest.
algebra 2 please help!
Answer:
The answer is C, I had this same quiz today and I got 100%
For a floral arrangement class, Alicia has to create an arrangement of twigs and flowers that has a total of 9 objects.
Alicia wants the arrangement to have twice as many flowers as twigs. Write and solve a system of equations to find the number of twigs and flowers that Alicia will need.
By solving a system of two simultaneous linear equations, it can be calculated that
Alicia will need 3 twigs and 6 flowers
What is simultaneous linear equation?
At first it is important to know about linear equation
Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.
A one degree equation is known as linear equation.
Two or more linear equations, which can be solved together to obtain common solution are known as simultaneous linear equation.
Here, a system of two simultaneous linear equation needs to be solved
Let the number of twigs Alicia needed be x and the number of flowers Alicia needed be y
Alicia has to create an arrangement of twigs and flowers that has a total of 9 objects.
x + y = 9 ..... (1)
Alicia wants the arrangement to have twice as many flowers as twigs
2x = y .... (2)
Putting the value of x in (1)
x + 2x = 9
3x = 9
[tex]x = \frac{9}{3}[/tex]
x = 3
Putiing the value of x in (2),
y = 2 [tex]\times[/tex] 3
y = 6
Alicia will need 3 twigs and 6 flowers
To learn more about simultaneous linear equation, refer to the link:
https://brainly.com/question/26310043
#SPJ1
what could be the maximum number of deaths if only 27% of the people in a population of eighteen million is susceptible?
The maximum number of deaths could be 5840000.
What is susceptible?Being prone to something indicates you are more likely to get sick from it, such as an infection or an earache.Has something ever been given to you that you didn't want? Well, that is probably going to be the case since the word "susceptible" means "likely to be influenced or affected by." If you're easily swayed by flattery, all someone needs to do to get what they want from you is to pay you one or two compliments. Crack-prone materials won't last very long in good condition.acc to our question-
total popuation= 8000000susceptinlr percentage= 278000000 * 27/10021600008000000 - 21600005840000.hence,The maximum number of deaths could be 5840000.
learn more about susceptible click here:
https://brainly.com/question/4054549
#SPJ4
Which equation has the solution x = 5?
Select each correct answer.
x/5+5=6
18−2x=9
3x + 1 = 9
32−4x=12
25/x+4=9
11 + 6x = 22
room attendants at your hotel typically clean one room every 20 minutes. one-fifth of the rooms take 40% longer to clean due to various issues. how much time will it take to clean 175 rooms?
Does the point (-2, 7) lie on the graph of y = -2x+1
The point (-2, 7) is not on the graph of y = -2x + 1
How to determine if the point is on the graph?From the question, we have the following equation
y = -2x + 1
This equation represents the equation of the graph
Also, we have the following points
(-2, 7)
This point implies that
(x, y) = (-2, 7)
Substitute (x, y) = (-2, 7) in the equation y = -2x + 1
So, we have
7 = -2 x -2 + 1
Evaluate
7 = 5
This is false
Hence, the point is not on the graph
Read more about linear graphs at
https://brainly.com/question/14323743
#SPJ1
Suppose that 12 inches of wire costs 36 cents. At the same rate, how many inches of wire can be bought for 21 cents?
The amount of wire that can be bought from 21 cents is 7 inches.
It is given in the question that 12 inches of wire costs 36 cents.
We have to find the amount of wire that can be bought from 21 cents.
We will use the unitary method to solve this question.
Amount of wire that can be bought from 1 cent = 12/36 = 1/3 inches
Hence, according to the data given in the question, we can write,
The amount of wire that can be bought from 21 cents = (1/3)*21 = 7 inches.
Unitary method
The unitary method is a mathematical problem-solving technique where the value of a single unit is found out from the value of multiple units prior to finding the necessary result.
To learn more about unitary method, here:-
https://brainly.com/question/22056199
#SPJ1
PLEASE HELP I WILL GIVE BRAINLIEST
Find x and y
*image is linked below*
The value of x and y in the triangle given are 15 and 4 respectively
Equivalent TrianglesAn Equilateral triangle is a triangle in which all three sides are equal and angles are also equal. The value of each angle of an equilateral triangle is 60 degrees therefore, it is also known as an equiangular triangle. The equilateral triangle is considered as a regular polygon or a regular triangle as angles are equal and sides are also equal.
In the triangle given, we can equate equal sides and find the missing sides on the triangle.
12/18 = y + 12 / 18 + 6
12/18 = y + 12 / 24
2/3 = y + 12 / 24
solve for y
y = 4
Taking another side and solve for x
12 / x = 12 + y / x + 5
but y = 4
12 /x = 12 + 4 / x + 5
12/x = 16 / x + 5
x = 15
Learn more on equivalent triangles here;
https://brainly.com/question/14285697
#SPJ1
X Solve for x. *
please solve for c and explain
Check the picture below.
3² × 3 = 3² Find the value of x.
The value of x in 3² × [tex]3^{x}[/tex] = 3² is 0.
According to the question,
We have the following information:
3² × [tex]3^{x}[/tex] = 3²
We know that when two numbers with the same base are in multiplication then the powers of the numbers are added. So, in this case, 2 will be added to x. And this expression of addition will be equal to the powers of the number on the right hand side.
Now, we have the following expression:
2+x = 2
x = 2-2
x = 0
Hence, the value of x in 3² × [tex]3^{x}[/tex] = 3² is 0.
To know more about value of x here
https://brainly.com/question/3162971
#SPJ1
Can anyone write the equation of the graph?
The equation of the graph is f(x) = |x - 3| + 5
How to determine the equation of the graph?The graph represents the given parameter
From the graph, we have the following highlights:
The graph is an absolute value graphThe graph has its minimum point at (3, 5)This means that
Vertex = (3, 5)
Rewrite the vertex as
(h, k)
An absolute value function is represented as
f(x) = a|x - h| + k
Substitute the known values in the above equation
So, we have the following equation
f(x) = a|x - 3| + 5
On the graph, we have
(x, f(x)) = (2, 6)
So, we have
6 = a|2 - 3| + 5
This gives
a = 1
So, we have
f(x) = 1 * |x - 3| + 5
Evaluate
f(x) = |x - 3| + 5
Hence, the graph has an equation of f(x) = |x - 3| + 5
Read more about absolute value functions at
https://brainly.com/question/3381225
#SPJ1
consider tbe graph of a function that is positive over its entire domain. can the graph have an x-intercept?
The graph whose domain is positive will not have any x - intercept.
What is graph of a function?
At first it is important to know about function
A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.
There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.
Graph of a function is the set of all points of the form (x, f(x)).
The graph is positive in its entire domain
f(x) > 0 for all x
So the graph will never cut the x axis at any point.
So the graph will not have any x intercept.
To learn more about graph of a function, refer to the link-
https://brainly.com/question/19040584
#SPJ9
Select the correct answer. Which statement is true about this equation? 3(-y + 7) = 3(y + 5) + 6 A. The equation has one solution, y = 0. B. The equation has one solution, y = -1. C. The equation has no solution. D. The equation has infinitely many solutions.
The statement which is true about this equation is that: C. The equation has no solution.
What is no solution?In Mathematics, no solution is sometimes referred to as zero solution. Additionally, an equation is considered as having no solution when the right hand side and left hand side of the equation are not the same or equal.
This ultimately implies that, an equation would have no solution or zero solution when both sides of the equal sign are not the same and the variables cancel out.
From the information provided above, we have this equation:
3(-y + 7) = 3(y + 5) + 6
Opening the bracket, we have the following:
-3y + 21 = 3y + 15 + 6
Next, we would rearrange the equation by collecting like terms as follows:
-3y + 21 = 3y + 21 (no solution)
-3y - 3y = 21 - 21
-6y = 0
y = -0/6
y = 0
Read more on equation here: brainly.com/question/28949611
#SPJ1
Find the surface area of this cuboid.
4 cm
2 cm
2 cm
Answer:
40 cm²
Step-by-step explanation:
Let,
length ( l ) = 4 cm
Height ( h ) = Width ( w ) = 2 cm
To find : Surface are of cuboid : -
Formula : -
Surface are of cuboid = 2 [ lh + hw + wl ]
Surface are of cuboid
= 2 [ ( 4 )( 2 ) + ( 2 )( 2 ) + ( ( 2 )( 4 ) ]
= 2 [ 8 + 4 + 8 ]
= 2 [ 20 ]
= 2 x 20
= 40 cm²
a bike path is 12.5 miles. Dominic is 70% of the way to the end how far is Dominic on the path
Dominic is on the 8.75 mile of the bike path
How to determine how far on the path is the distance?From the question, the given parameters are:
Proportion of distance = 70% of the bike path Bike path = 12.5 milesThe above parameters implies that
Dominic's position = 70% of the total distance
Represent the total distance with x
So, we have the following representation
Dominic's position = 70% * x
Where
x = 12.5
So, we have
Dominic's position = 70% * 12.5
Evaluate the products
Dominic's position = 8,75
Hence, Dominic's position is 8,75 miles
Read more about proportions at
https://brainly.com/question/16828793
#SPJ1
If f(x) = e¹/x then f(x)=
The derivative of f(x) is option A.
What is derivative?
The instantaneous pace at which one quantity changes in relation to another is referred to as a derivative in mathematics.
Main Body:
Since the derivative of [tex]e^{x}[/tex] is just [tex]e^{x}[/tex] , application of the chain rule to a composite function with [tex]e^{x}[/tex] as the outside function means that:
[tex]\frac{dy}{dx} (e^{f(x)} )= e^{f(x) }.f'(x)[/tex]
Now the derivative of 1/x = [tex]\frac{-1}{x^{2} }[/tex]
Hence derivative of f(x) = [tex]-e^{\frac{1}{x} } /x^{2}[/tex].
To learn more about derivative click on the link below.
https://brainly.com/question/23819325
#SPJ13
Calculate the length of the unknown side of this right-angled triangle.
9 cm
8 cm
Making a certain shade of paint requires mixing 3 parts silver with 4 parts green. Meg uses this data to start this table of equivalent ratios. A 2-column table has 3 rows. Column 1 is labeled Silver paints (parts) with entries 3, blank, blank. Column 2 is labeled Green paint (parts) with entries 4, blank, blank. Which ratios are equivalent to 3 parts silver paint to 4 parts green paint? Check all that apply. 4:5 6:8 5:6 9:12
The ratios that are equivalent to 3 parts silver paint to 4 parts green paint are: 6:8 and 9:12.
What is a ratio?A ratio can be defined as a mathematical expression that's used to denote the proportion of two (2) or more quantities with respect to one another and the total quantities.
Generally speaking, a proportional relationship can be represented by the following mathematical expression:
x = ky
Where:
x represents the silver paints (parts).y represents the green paint (parts).k represents the constant of proportionality.In this context, the constant of proportionality or ratio of the quantity of silver paint (parts) to green paints (parts) can be calculated as follows:
Constant of proportionality (k) = x/y
Constant of proportionality (k) = 3/4
Now, we can determine the equivalent ratios as follows:
Equivalent ratio = 4/5 ≠ 3/4
Equivalent ratio = 6/8 = 3/4 (divide by 2)
Equivalent ratio = 5/6 ≠ 3/4
Equivalent ratio = 9/12 = 3/4 (divide by 3).
Read more on ratio here: brainly.com/question/28083504
#SPJ1
the answer is 6:8 and 9:12
Step-by-step explanation: hope this helped ;D
sec^2 54 - 1, can anyone please help me with question asap
The numeric value of the expression sec²(54º) - 1, using a trigonometric identity, is given as follows:
tan²(54º) = 1.8944.
How to solve the expression using a trigonometric identity?Before applying the trigonometric identity, we have to define the secant and the tangent of an angle, as follows:
The secant of an angle is given by the division of one by the cosine of the angle.The tangent is given by the division of the sine of the angle by the cosine of the angle.The identity that exists between the squares of these measures is given as follows:
tan²(x) + 1 = sec²(x).
Hence, isolating the tangent:
tan²(x) = sec²(x) - 1.
In this problem, the expression is given as follows:
sec²(54º) - 1
Applying the identity, the expression is given as follows:
sec²(54º) - 1 = tan²(54º).
Using a calculator, the numeric value of the expression is given as follows:
tan²(54º) = 1.8944.
More can be learned about trigonometric identities at https://brainly.com/question/7331447
#SPJ1
Which postulate can be used to prove the two triangles are congruent?
Answer:
SAS
Step-by-step explanation:
If two sides and the included and the included angle of one triangle are congruent to two sides and the included angle of another triangle , then the triangles are congruent. The included angle is the angle formed by the two sides.
EF = BC
∠ F = ∠ C
DF = AC
then the two triangles are congruent by the SAS postulate.
Answer:
SAS
Step-by-step explanation:
On triangle one and two, they both start by having a congruent side, then a congruent angle, then another congruent side, thus making these triangles congruent by Side Angle Side.
It can't be AAS because there is only one angle, we know is congruent.
It can't be SSS because there are only two sides, we know are congruent.
It can't be HL because there is no right angle, meaning these aren't right triangles.
calculate the %cw for a sample of 1040 steel that has an original diameter of 12 mm and a final diameter of 10 mm.
The new yield strength of the 1040 steel will be the intercept on the curve for 30.56 %of cold work which is between700 to 800 MPA
Given original diameter do = 12 mm
Ao = [tex]\pi[/tex]/4 x 12² = 113.097 mm²
Deformed diameter d =10mm
Ad = [tex]\pi[/tex]/4 x 10² = 78.54 mm²
Degree of cold work %CW = (Ao - Ad/Ao)X 100
=(113. 097 - 78. 54/113.097) x 100
= 30.56%
% CW is 30.56 %
Therefore, the intercept on the curve for 30.56% of cold work, which is between 700 and 800 MPA, will represent the new yield strength of the 1040 steel.
Learn more about intercept on the curve :
https://brainly.com/question/28715687
#SPJ4
What is the expression d/3+4
Answer:
d+12/3
Step-by-step explanation:
*= multiply /= fraction ALL OVER= fraction over fraction
find the common denominator-
d/3+4
d/3+3*4/3
combine fractions with the common denominator
d/3+3*4/3 ALL OVER d+3*4/3
multiply
d+3*4/3 ALL OVER d+12/3
Editors preparing a report on the economy are trying to estimate the percentage of businesses that plan to hire
additional employees in the next 60 days. They are willing to accept a margin of error of 1% but want 95% confidence.
How many randomly selected employers will they need to contact?
n= (Round up to the nearest integer.)
The number of randomly selected employers that would have to be contacted is 9604
How to solve for the value of nThe confidence level is 95%
1 - 0.95 = 0.05
We have to get the z value at 0.05
0.05/2 = 0.025
Using the standard normal table, the critical value at 0.025 = 1.96
We have to define the probability as P = 50% = 0.5
we have to define q = 1 - 50% = 0.5
The formula that would be used to find the value of n is given as
[tex]n = pq\frac{Zc}{E} ^2[/tex]
These variables used are:
pq = variance of population
E = margin of error = 0.01
critical value = Zc = 1.96
[tex]n = 0.5*0.5 (\frac{1.96}{0.01})^2[/tex]
= 0.25 * 38416
= 9604
Hence the sample space is given as 9604
Read more on confidence interval here:
https://brainly.com/question/26658887
#SPJ1
720 divided by 50 gives the same answer as x divided by 100
what is the value of X
Answer:
Value of x is 1440
Step-by-step explanation:
According to the question,
720 ÷ 50 gives same answer as x ÷ 100
[tex] \therefore[/tex]
[tex] \rm \implies \dfrac{720}{50} = \dfrac{x}{100} \\ \\ \rm \implies x = \frac{720}{50} \times 100 \\ \\ \rm \implies x = 720 \times 2 \\ \\ \rm \implies x = 1440[/tex]
Give the coordinates of each image.
7. R4180°, 0) (GH) for G(2, -9), H(-1, 3)
please explain i dont understand
The coordinates of each image are G'(-2,9), and H'(1,-3).
What are the coordinates?
A pair of numbers that use the horizontal and vertical separations from the two reference axes to define a point's location on a coordinate plane. typically expressed by the x-value and y-value pair (x,y).
Here, we have
R₍₁₈₀°,₀ (GH)
H(-1,3)
G(2,-9)
Now we need to the rotation of 180° about the origin.
By following the rule, we get,
(x , y) ⇒ (-x , -y)
After solving,
G(2,-9) ⇒ G'(-2,9)
H(-1,3) ⇒ H'(1,-3)
Hence, the coordinates of each image are G'(-2,9), and H'(1,-3).
To learn more about the coordinates from the given link
https://brainly.com/question/25528482
#SPJ13
let nn denote the smallest positive integer that is divisible by both 44 and 9,9, and whose base-1010 representation consists of only 44's and 99's, with at least one of each. what are the last four digits of nn?
The last four digits of the number nn are 4944
Given that,
Let nn stand for the lowest positive integer that can be represented in base-1010 using only the numbers 44 and 99, with at least one of each. This number must be divisible by both 44 and 9,9.
The last two digits of n must be divisible by 4 for n to be divisible by 4.
So last digits of n will be 44.
And for divisiblity by 9, sum of all digits of n has to be divisible by 9.
As two digits are fixed and their total is 8, next feasible total will be 45 so 9 can be atleast one time in n.
And as statement says n has to be smallest number n will be 4444444944
So last 4 digits of n are 4944.
Therefore, nn's last four numbers are 4944.
Learn more about positive integer :
brainly.com/question/28165413
#SPJ4
a die is rolled 2 times .what is the probability of getting a number 6 two times. what is the probability of not getting 6 at all?
The probability of not getting 6 at all is 11/36
Define probability.The term "probability" is most commonly used to refer to the likelihood that a specific event (or set of events) will occur, expressed as a linear scale from 0 (impossibility) to 1 (certainty), or as a percentage between 0 and 100%. Statistics is the study of events subject to probability.
Given,
A die is rolled 2 times
6 was on the first roll, but there was no 6 on the second,
6 came up on the second roll but not the first.
2 sixes
A) It is evident that 1/6 of the time you will roll a six.
B) There is a 5/6 chance of not getting a six on a single roll.
1/6x5/6 + 5/6x1/6 + 1/6x1/6
= 5/36 + 5/36 + 1/36
= 11/36
The probability of not getting 6 at all is 11/36
To learn more about probability, visit:
https://brainly.com/question/11234923
#SPJ4
A family buys a total of 32 tickets at a carnival. Ride tickets cost $1.50 each and
food tickets cost $3.25 each. The family pays a total of $90 for the tickets.
store.
The number of ride tickets that were sold are 8 and the number of food tickets that were sold are 24 .
In the question ,
it is given that
total number of tickets bought by the family at carnival = 32 tickets
total amount spent by the family of tickets = $90
let the number of ride tickets be [tex]=[/tex] x
let the number of food tickets be [tex]=[/tex] y
So , x + y = 32
x = 32 - y
cost of 1 ride ticket = $1.50
cost of 1 food ticket = $3.25
So the total cost is 1.25x + 3.25y = 90
Substituting x = 32 - y in the equation 1.5x + 3.25y = 90 ,
we get ,
1.5(32 - y) + 3.25y = 90
48 - 1.50y + 3.25y = 90
1.75y = 90 - 48
1.75y = 42
y = 24
So , x = 32 - 24 = 8
Therefore , The number of ride tickets that were sold are 8 and the number of food tickets that were sold are 24 .
The given question is incomplete , the complete question is
A family buys a total of 32 tickets at a carnival. Ride tickets cost $1.50 each and food tickets cost $3.25 each. The family pays a total of $90 for the tickets store. How many of each type of ticket were sold ?
Learn more about Equations here
https://brainly.com/question/25487722
#SPJ1