Answer:
True.
Step-by-step explanation:
If you multiply the length value, you'd get 880 yd. Which basically answers it, the answer is true.
Answer:
True
Step-by-step explanation:
I did this before it kind of complicated but trust me it true
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]
Emma is building a scale model of a jet airplane. The real airplane has a wingspan of 200 feet and a length of 240 feet. If Emma’s model has a wingspan of 30 centimeters, what is the length of the model ?
Answer:
Since it is a to-scale model,
the ratio of the wingspan to the length of both the airplanes must be equal
wingspan1 = 200 ft wingspan2 = 30 cm
length1 = 240 ft length2 = x cm
wingspan1 / length1 = wingspan2/length2
replacing the variables
200 / 240 = 30 / x
x = 30 * 240/200
x = 36 cm
Therefore, the length of Emma's airplane is 36 cm
Answer:
Step-by-step explanation:
Homer sold cupcakes and cookies yesterday. Each cupcake sold for $2.25 and each cookie sold for $0.25. At the end of the day, Homer has sold $55.50 worth of cookies and cupcakes. If he sold 54 cupcakes and cookies combined, how many cupcakes were sold and how many cookies were sold
Answer: 21 cupcakes and 33 cookies were sold.
Step-by-step explanation:
Let x= Number of cupcakes
y = Number of cookies
As per given,
x+y= 54 (i)
Cost: 2.25x+0.25y=55.50 (ii)
Multiply 0.25 to (i0, we get
0.25x+0.25y = 0.25(54)
⇒0.25x+0.25y = 13.5 (iii)
subtract (iii) from (ii), we get
2x=42
Divide both sides by 2, we get x= 21
Put this in (i) , we get 21+y =54 ⇒ y= 54-21= 33
Hence, 21 cupcakes and 33 cookies were sold.
2(x-5)=4x+7
solve for x
Answer:
x=-6
Step-by-step explanation:
The distance (d) in meters that an ant can travel varies directly with the amount of time (t) in hours it spends walking. assume that an ants constant off proportionality is 18.write the equation to the represent the proportional relationship between d and t using the information given. What does the constant of proportionality represent in this problem?
The constant is 18
To find distance (d) you would multiply the constant by the time(t).
D = 18t
Distance is speed x time, so the given constant would be the speed of the ant.
Find the value of x
(6x+7) (8x-17)
Answer:
x=12
Step-by-step explanation:
6x+7=8x-17
-6x -6x
7=2x-17
+17 +17
24=2x
÷2 ÷2
12=x
x=12
What is-1 5/6 times 6 1/2
Answer:
-11.9166666667
Step-by-step explanation:
Answer:
-11.9166666667
Step-by-step explanation: I just seached it up
what is the product of 2(-4)
Answer:
-8
Step-by-step explanation:
First, write it out in standard form:
2 x (-4)
Then multiply!
Answer:
-8
Step-by-step explanation:
it is basically 2 x -4 and a negative times a positive is a negative which makes it -8
Snow is falling steadily in Syracuse, New York. After 2 hours, 4 inches of snow has fallen.
Write an equation that gives the amount of snow that has fallen after x hours at this rate.
Answer:
y = 2x
Step-by-step explanation:
y-int = 0
slope = 2
5. (01.07A MC)
Which number line best shows the position of ? (5 points)
J7
HHHH +
-4 -3
-1 0 1 2
+
4
-2
3
3
7
HHH H
-4 -3 -2 -1 0 1 2 3
+
4
7
HH
-4
-3 -2
-1 0 1 2
3
4
-
OL
7
t. +
3 4 5
-5 -4
-3 -2
-1 0 1 2
Answer:
if u could include a photo it may help more ..thanks
Expression for divide the difference between 1200 and 700 by 5
Step-by-step explanation:
(1200-700)/5
=500/5
=
The expression results to 100.
What is Expression?Mathematical statements are called expressions if they have at least two terms that are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.
A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation.
Given:
divide the difference between 1200 and 700 by 5
so, mathematically
(1200- 700)/5
= 500 /5
= 100
Hence, the expression results to 100.
Learn more about expression here:
https://brainly.com/question/14083225
#SPJ5
Edgar made an initial deposit of $3200 into a deposit account, and plans to contribute an additional $175 every month. The account does not pay any interest. After how many months will he have a total of $6000?
Answer:
16
Step-by-step explanation:
Do you think that students should be proficient in addition before learning multiplication?
answer in 175 words! thank you so much :)
Answer:
Yes students should be confident in addition before they proceed to mulplication.This is because addition is the base of multiplication and requires mastery before you start,so It would be much easier to solve
How much does 4 7/5 kg of candy cost if 5/6 of candy costs $7.50?
Answer:
It costs $42.43
Step-by-step explanation:
Answer:
$1.35
Step-by-step explanation:
7.5÷ 5/6=0.25
0.25x4 7/5=1.35
Help please.............
Please answer this math questions ASAP thanks the picture is attached !!
Answer:
The answer is C
Step-by-step explanation:
Both f(x) and g(x) have a domain of [0,infinite). and a range of [0, infinite).
Is 4:5 equivalent to 8:10 as radios?
0.02 divided by 924.3
Answer: 0.00002163799
Step-by-step explanation:
Answer:
46,215
Step-by-step explanation:
you just have to divide the bigger number first and then the smallest
solve for brainliestA keem measured the capacity of a glass as
2 7 0 mL and the capacity of a Th e rm o s® a s
1 L. He said that the ratio 270 :1 compare s
the capacity of the glass with the cap a c i t y
of the Th e rm o s®. Is his reasoning corre c t ?
E x p l a i n .
Answer:
[tex]his \: reasoning \: is \: correct.[/tex]
Step-by-step explanation:
[tex]since \: the \: ratio \: of \: the \: glass \: to \:that \\ \: of \: the \: thermos \: is \: in \: the \: fraction : \\ \frac{2 7 0 mL }{1mL} \: which \: is \:270 mL : 1mL \\ then \: the \: keem \: is \: right.[/tex]
what is 1000000000000x0??????
Answer:
0
Step-by-step explanation:
Everything multiplied by 0 is 0.
The basketball team scored a total
of 80 points, all off of 2-point
baskets and 3-point baskets (no
they didn't make any free throws). If
six 3-point baskets were made, find
the number of 2-point baskets
made.
Answer:
31 2-point baskets were made
Step-by-step explanation:
We can find how many of the 80 points were made with 2-point baskets by subtracting all the points gained through 3-point baskets. Since there are six 3-point baskets:
# of points through 2-point baskets = 80 - 6(3) = 80 - 18 = 62
To find the number of 2-point baskets that were made, divide the points by the worth of the basket:
# of 2-point baskets made = 62/2 = 31
9514 1404 393
Answer:
31
Step-by-step explanation:
6×3 = 18 of the 80 points were from 3-point baskets, so the remaining 62 points were 2-point baskets.
62 = 2b
62/2 = b = 31
31 2-point baskets were made.
What is the quotient of : 4.652/.3
Answer:
15.51
Step-by-step explanation:
Will give brain if correct segment addition
Answer:
13) 28
14) 22
15) 24
16)13
Step-by-step explanation:
13) Because they all lie on the same line, AC would be AB+BC, or 16+12, or 28.
14) Same thing as 13, 13+9=22
15) Same thing as others but make an equation
-1+2x+11=3x+3
Simplifying the equation, we get x=7. Now, we plug in x=7 to 3x+3 to get AC.
3(7)+3=21+3=24
16) build the equation:
x+14+x+10=22
2x+24=22
2x=-2
x=-1
Now plug in x=-1 to x+14.
-1+14=13
1 1/2 x 3/4 pls full aswer
Answer:
1.125 or 9/8
Step-by-step explanation:
What number is 30 percent of 50
Answer:
15 (50*0.3)
Step-by-step explanation:
Answer:
15
Step-by-step explanation:
0.3*50 = 15
Can someone help me with Number 7 i’ll give the brainly thingy
Answer:
$9.50
Step-by-step explanation:
1 gallon = 4 quarts
1 quart = 2 pints
1 pint = 2 cups
1 cup = 8 ounces
How many ounces are in 4 gallons?
Answer:
512 ounces
Step-by-step explanation:
Answer:
512
Step-by-step explanation:
multiply the volume value by 128
Can someone please help, ty!!
Answer:
B i think
Step-by-step explanation:
The Gators football team gained 4 yards on its first play, but lost 9 yards on the
second play. Which of the following best represents the result of these two
plays?
Answer:
-5 yards
Step-by-step explanation:
4 - 9
= -5
in that two plays:
loss 5 yards
PLSSS HELPPPPP ASSAAAPPPP
Answer:
∡BEN=122
x=17
Step-by-step explanation:
Since you know that when two sides are congruent like this then the to angles are congruent then you know that angle BNE equals 29.
Once you know that since we know that 180 is the sum of all three angles set an equation like this:
180=29+29+(11x-65)
Take off parentheses since you can't simplify in them.
180=29+29+11x-65
Combine like terms.
180=11x-7
Solve for x.
187=11x
x=17
Plug that in to (11x-65) to find angle BEN
angle BEN = 11(17)-65
angle BEN=122