Answer:
Multiply By Decimal
Step-by-step explanation:
If you multiply a number by a decimal you get the same outcome that you would if you would have divided it
Evaluate `int cosec^(2)(7-5x)dx
Answer:
∫ cosec²(7-5x) dx =[-cot(7-5x)]/-5 +c
=(1/5)cot(7-5x)+c
note: d/dx(cotx)=- cosecx
The base of an aquarium with given volume V is made of slate and the sides are made of glass. If slate costs five times as much (per unit area) as glass, find the dimensions of the aquarium that minimize the cost of the materials. (Let x, y, and z be the dimensions of the aquarium. Enter your answer in terms of V.)
Answer:
The dimensions of the aquarium that minimize the cost of the materials:
[tex]x=y=\sqrt[3]{\frac{2V}{5}}\\z=\sqrt[3]{\frac{25V}{4}}[/tex]
Step-by-step explanation:
Let x, y and z be the dimensions of aquarium .
Surface area of an aquarium = xy+2yz+2xz
Volume of aquarium V=[tex]Length \times Breadth \times Height=xyz[/tex] ----A
We are given that slate costs five times as much (per unit area) as glass
So, Cost function : C=5xy+2yz+2xz
Now we will use langrage multiplier to find the dimensions of the aquarium that minimize the cost of the materials.
[tex]\nabla C =\lambda \nabla V[/tex]
[tex](\frac{\partial C}{\partial x},\frac{\partial C}{\partial y},\frac{\partial C}{\partial z})= \lambda (\frac{\partial V}{\partial x},\frac{\partial V}{\partial y},\frac{\partial V}{\partial z})[/tex]
[tex](5y+2z,5x+2z,2y+2x)=\lambda(yz,xz,xy)[/tex]
So,
[tex]5y+2z=\lambda yz[/tex] ----1
[tex]5x+2z=\lambda xz[/tex] -----2
[tex]2y+2x=\lambda xy[/tex] ----3
Multiply 1 ,2 and 3 by x,y and z respectively.
[tex]5xy+2xz=\lambda xyz[/tex] ----4
[tex]5xy+2yz=\lambda xyz[/tex] -----5
[tex]2yz+2xz=\lambda xyz[/tex] ----6
Now equate 4 and 5
5xy+2xz=5xy+2yz
x=y
Substitute y=x in 5 and 6 and equate them
[tex]5x(x)+2(x)z=2(x)z+2xz\\5x^2=2xz\\5x=2z\\\frac{5}{2}x=z[/tex]
Substitute the values in A
[tex]V = xyz = x \times x \times \frac{5}{2}xV=\frac{5}{2}x^3\\\sqrt[3]{\frac{2}{5}V}=x\\x=y=\sqrt[3]{\frac{2}{5}V}\\z=\frac{5}{2}x=\frac{5}{2}(\sqrt[3]{\frac{2}{5}})=\sqrt[3]{\frac{25V}{4}}[/tex]
Hence,
The dimensions of the aquarium that minimize the cost of the materials:
[tex]x=y=\sqrt[3]{\frac{2V}{5}}\\z=\sqrt[3]{\frac{25V}{4}}[/tex]
A minor league baseball office sells admission tickets for $5.75 for Wednesday night games. The ticket
office can sell a maximum of 500 tickets. The function M(t) = 5.75t represents the amount of money
(M) the ticket office brings in on Wednesday nights, where t is the number of tickets sold. Which best
describes the domain of M(t) in this context?
Answer:
Its B because 500 tickets is the maximum amount
Step-by-step explanation:
Subtract 1 4/5 from 4 2/3 =?
Answer:
2.86666667
Step-by-step explanation:
Answer:
1 18/25
Step-by-step explanation:
4 2/3-1 4/5
=14/3-9/5
LCM is 15
=(70-27)/15
=43/25
hi, what is 1+1 and 2+3
Answer:
1+1 is 2 and 2+3 is 5
Step-by-step explanation:
I need help please it’s due today I forgot how to do this :(
Answer:
Samantha payed 12.71$ for her purchase.
Step-by-step explanation:
I may have misunderstood the question, but it looks like you can use a calculator for this!
6.19 + 2.85 + 2.29 + 1.38 =
12.71
slove the equation
7h-5(3h-8)=-72
Answer:
Step-by-step explanation:
You can break it down into steps if you'd like.
-5 ( 3h - 8) = -15h + 40
So,
7h - 5 ( 3h -8 ) = -72
7h - 15h + 40 = -72
Now you can combine the like terms
-8h + 40 = -72
Add 8h to both sides
40 = -72 + 8h
Add 72 to both sides
40 + 72 = 8h
112 = 8h
Divide both sides by 8 to find h.
h = 112/8 = 14
please help me solve this problem.. Piecewise Functions
Answer:
There is No solution to the question above.
Answer:
103
Step-by-step explanation:
Since x= 10, we need to use the second piece of the function x^2+3
f(x) = x^2 +3
Let x=10
f(10) = 10^2 +3
= 100 +3
= 103
A store plans to sell two different game consoles, the YuuMi and the ZBox. The store’s wholesale cost for a YuuMi is $250, and the store can sell one for $295. The ZBox’s wholesale price is $400, and the store can sell it for $450. The store’s marketing research indicates that the total monthly demand for game consoles will not exceed 250 units sold. The store’s financial manager does not want to invest more than $70,000 in inventory costs for game consoles. How many of each game console should the store stock in order to maximize their profits, and what is their maximum monthly profit?
Constraints:
Objective formula:
9514 1404 393
Answer:
Constraints: x + y ≤ 250; 250x +400y ≤ 70000; x ≥ 0; y ≥ 0Objective formula: p = 45x +50y200 YuuMi and 50 ZBox should be stockedmaximum profit is $11,500Step-by-step explanation:
Let x and y represent the numbers of YuuMi and ZBox consoles, respectively. The inventory cost must be at most 70,000, so that constraint is ...
250x +400y ≤ 70000
The number sold will be at most 250 units, so that constraint is ...
x + y ≤ 250
Additionally, we require x ≥ 0 and y ≥ 0.
__
A profit of 295-250 = 45 is made on each YuuMi, and a profit of 450-400 = 50 is made on each ZBox. So, if we want to maximize profit, our objective function is ...
profit = 45x +50y
__
A graph is shown in the attachment. The vertex of the feasible region that maximizes profit is (x, y) = (200, 50).
200 YuuMi and 50 ZBox consoles should be stocked to maximize profit. The maximum monthly profit is $11,500.
A biker rides for h hours at a speed of s miles per hour and travels d miles. Which equation models the relationship?
Answer:
hs=d
Step-by-step explanation:
Answer:
hs= d
Step-by-step explanation:
order the numbers from least to greatest please help
Answer:
-2,-7/4, 1/2, square root of 5, 2.4
Step-by-step explanation:
Answer:
-2, -1.75, 1/2, [tex]\sqrt{5}[/tex], 2.4
Step-by-step explanation:
1/2
-2
√5≈2.24
-1.75
2.4
-2, -1.75, 1/2, [tex]\sqrt{5}[/tex], 2.4
Compute 49/24 of 15/24. Give your answer as a fraction in simplest form (not a mixed number).
Answer: 35/16
Step-by-step explanation:
Answer:
35/16
Step-by-step explanation:
49x15=735
Denominator will stay the same because both are same (24)
Then you simplify 735/24
Which will give you 35/16
Find m
a. 90
b. 31
c. 59
Answer:
i think its B
sorry if its wrong im not really sure by my answer
What is the midpoint of the segment shown below?
10
A. (10,1)
B.(5,1)
c.(5,1/2)
d. (10,1/2)
please help thank you so much
Answer:
no solution
Step-by-step explanation:
Solve by taking the square too of both sides.
3(c+3)^2-81=0
Answer:
x = -3 ±3sqrt(3)
Step-by-step explanation:
3(x+3)^2-81=0
Add 81 to each side
3(x+3)^2=81
Divide each side by 3
3/3(x+3)^2=81/3
(x+3)^2=27
Take the square root of each side
sqrt ((x+3)^2)=±sqrt(27)
x+3 =±sqrt(9*3)
x+3 =±sqrt(9)*sqrt(3)
x+3 =±3sqrt(3)
Subtract 3 from each side
x = -3 ±3sqrt(3)
Does anybody know this one as well plz I really need it I have a test and it ends in 20 thank you so much
Answer:
0.6 of a serving is 225
3.85 servings are 1350
What is the solution to j + (-3) = 9?
Answer:
j = 12
Step-by-step explanation:
j + (-3) = 9
j = 12
melonie is 3 times older than her cousin their total of there ages are 36 how old is melonies cousin
Answer:
Her cousin is 12
Step-by-step explanation:
Use division
The 7th grade team went out for lunch. Their server brought the bill that totaled $72. The team wanted to tip the server 20% and there is also a 9% sales tax. How much will the 7th grade team spend after the tip and tax are added? Round your answer to the nearest cent if necessary.
Answer:
I think it's 92.88
Step-by-step explanation:
add up 20 and 9 to get a total of 29%
then multiply .29 and 72 to get 20.88
then add 20.88 and 72 to get the total cost including tips and tax
A store owner paid $15 for a book. She marked up the price of the book by 20% to determine its selling price. What is the selling price, in dollars, of the
books?
Answer:
18
Step-by-step explanation:
.2x15=3
3+15=18
Answer:
18$
Step-by-step explanation:
(4 to the 4th power)to the 3rd power
ayuda nose ayudaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa
timed question need help
Step-by-step explanation:
m-7/3 = m+2
= m-7 = 3(m+2)
= m-7 = 3m+6
= -7-6 = 3m-m
= 2m = -13
= m = -13/2
What is the domain of the function
f(x)=1x-3
-3 when the range is {-6. 0, 9}?
Answer:
D : { -3, 3, 12}
Step-by-step explanation:
I would suggest substituting the range for the function and solving for x like so.
i.e -6 = 1x-3, -6 + 3 = 1x -3 + 3, -3 = x, x = -3.
0 = 1x - 3, 0 + 3 = 1x - 3 + 3, 3 = x, x = 3.
9 = 1x - 3, 9 + 3 = 1x -3 + 3, 12 = x, x = 12
Charlie bought hamburgers and drinks for his coworkers. Each hamburger cost $3.75 and each drink cost 50 cents. In total, Charlie paid $25.50 for his order. Write an equation that represents the relationship between the number of hamburgers he bought, h, and the number of drinks he bought, d.
Answer:
25.50=3.75h+0.50d
Step-by-step explanation:
Angles of triangles I need help with homework
Answer:
150 degrees
Step-by-step explanation:
A triangle adds to 180 degrees.
48 + 102= 150
180-150 = 30
Then the angle x in total adds to 180
180-30= 150 degrees
me pueden explicar las sumas y restas con punto decimal por favor
Answer:
Para sumar o restar decimales se colocan los números decimales uno debajo del otro, haciendo que coincidan las unidades en la misma columna. De esta manera, también tienen que coincidir las décimas, las centésimas… y la coma.
Step-by-step explanation:
A recipe calls for 3 3/4 cups of flour. How many cups will you need if you are preparing 5 batches of the recipe?
Answer:
18.75 cups of flour
Step-by-step explanation:
The answer is 18.75 cups of flour as you have to multiply 5 by 3 3/4. The result will be 18.75. Hope it helps!
You need 18 3/4 cups of flour, to make 5 batches of the recipe.
What is a fraction?An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.
If one batch of the recipe calls for 3 3/4 cups of flour, then 5 batches of the recipe will require:
5 × 3 3/4 cups
To multiply a whole number by a mixed number, we first convert the mixed number to an improper fraction:
3 3/4 = (4 × 3 + 3) / 4 = 15/4
Now we can multiply:
5 × 15/4 = (5 × 15) / 4 = 75/4
To convert this fraction to a mixed number, we divide the numerator by the denominator and write the remainder as a fraction:
75 ÷ 4 = 18 remainder 3
So, 75/4 is equal to 18 3/4.
Therefore, 5 batches of the recipe will require:
18 3/4 cups of flour.
To learn more about fractions;
https://brainly.com/question/10354322
#SPJ2
Graph the line with slope – 7 and y-intercept 6.
Answer:
(✿◠‿◠)
I put the link in the comments!
A graph of the line with a slope of -7 and y-intercept of 6 is shown in the image below.
What is the slope-intercept form?In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;
y = mx + b
Where:
m is the slope or rate of change.x and y are the points.b is the y-intercept or initial value.Based on the information provided about this line, the y-intercept is 6 and the slope is -7.
In this context, we can logically deduce that a linear equation that models the line is given by;
y = mx + b
y = -7x + 6
Read more on slope-intercept here: brainly.com/question/7889446
#SPJ6