Answer:
a. A = 50x - x² b. length = 25 inches and width = 25 inches and the maximum area is 625 in²
Step-by-step explanation:
a. The perimeter of a rectangle P = 2(L + W) where L = length and W = width. Now, given that P = 100 inches and W = x, substituting these into the equation, we have
P = 2(L + W)
100 = 2(L + x)
dividing both sides by 2, we have
100/2 = L + x
50 = L + x
making L subject of the formula, we have
L = 50 - x
Now, the are of a rectangle A = LW. Substituting the values of L and W, we have
A = LW
A = (50 - x)x
A = 50x - x²
b. To find the largest possible area of rectangle with perimeter 100 inches, we differentiate A and equate it to zero to find the value of x that maximizes A.
So, dA/dx = d(50x - x²)/dx
dA/dx = d50x/dx - dx²/dx
dA/dx = 50 - 2x
dA/dx = 0 ⇒ 50 - 2x = 0
50 = 2x
dividing both sides by 2, we have
x = 50/2
x = 25
To find it this gives maximum value for A, we differentiate A twice.
d²A/dx² = d(50 - 2x)/dx
d²A/dx² = d50/dx - d2x/dx
d²A/dx² = -2
Since d²A/dx² = -2 < 0, so x = 25 gives maximum value for the area, A.
Since W = x = 25 in and L = 50 - x. So, L = 50 - 25 = 25 in
So, the maximum area A = LW = Lx = 25 in × 25 in = 625 in²
The dimension with perimeter 100 inches that give maximum area are length = 25 inches and width = 25 inches and the maximum area is 625 in²
Which graph represents a function?
Simplify(6^5/7^3)^2 .................help please
Answer:
513.95402 I think lol
4.1 7776 = 25•35
(7776)2 = (25•35)2 = 210 • 310 4.2 343 = 73 (343)2 = (73)2 = 76
I have no idea how to do this, any clues?
Answer:
(2x-5)+(x+25)+x
4x+20
Step-by-step explanation:
Simplify the expression.
Click below for question!
THANKS FOR ALL YOUR HELP GUYS!
Answer:
B= -7/5
Step-by-step explanation:
Subtract the 2nd y from the first (2-9)
Subtract the 2nd x from the first (11-6)
-7/5
Find the surface area of the prism
Answer:
the answer is 29
Step-by-step explanation:
For a party, Samantha bought eight half gallon bottles of soda. About how many cups of soda did Samantha buy?
Help please!!!! thank you sm!!
Answer:
64 cups
Step-by-step explanation:
Question 2
The cell membrane controls what enters and exits the cell to maintain
A.energy
B. Photosynthesis
C.respiration
D.homeostasis
HELP ME OUT IM DUMB
Answer:
around 15.3
Step-by-step explanation:
3^2 + 15^2=c^2
Answer:
Step-by-step explanation:
Formula:
a^2 + b^2 + c^2
3^2 + 15^2 + c^2 = To find hypotenuse
3 • 3 + 15 • 15 = -c^2
9 + 225 = -c^2
234 = c^2
square root of 234 = 15.2970585408
c = 15.2970585408
The roof is 15.2970585408
Devin paid $30 to be a member of the Fox Lake Gym. When he takes the boxing
class, it costs him $2. How many classes can he take if spent $42?
Answer:
30 + 2x = 5x i hope this helps
Solve the system using a method of your choice
Answer:
(4, 1)
Step-by-step explanation:
Method elimination would be good for this system
2x - y = 7 ........ (1)
x + y = 5 ......... (2)
(1) + (2)
3x = 12 ⇒ x = 4
4 + y = 5 ⇒ y = 1
(4, 1)
In RST, if m
than seven times x, find x and the measure of each angle.
Answer:
RST
Step-by-step explanation:
scientific notation for 1.0 ×10^6
Answer:
1000000
Step-by-step explanation:
I'm not sure what you meant by "scientific notation". So uhh, I only solved the 1.0 times 10^6,
10^6=10×10×10×10×10×10
10^6=1000000
(Fun fact. If you ever see a power of 10, you don't actually need to solve it. Look at the power, and add the same amount of 0's. For example 10^2. Power sign is 2. 2 trailing 0's.)
2y + 14x - 7x + 9y
Answer:
1, - 2
Step-by-step explanation:
Answer:
7x + 11y
Explanation:
1. Subtract 7x from 14x. 2y + 7x + 9y
2. Add 2y and 9y together. 11y + 7x
Noah pays $7.65 for a cappuccino on days he's running late to work. One week, he was late on Monday, Wednesday, and Friday. How much did he spend (in $) on cappuccinos that week? $
Answer:
Amount Noah spent on cappuccino for that week = $22.95
Step-by-step explanation:
Noah pays $7.65 for a cappuccino on days he's running late to work
Cost of cappuccino per day = $7.65
One week, he was late on Monday, Wednesday, and Friday.
That is 3 days in a week
How much did he spend (in $) on cappuccinos that week? $
Amount Noah spent on cappuccino = cost of cappuccino per day × 3 days
= $7.65 × 3
= $22.95
Amount spent on cappuccino for that week = $22.95
Lines m and n are drawn in the coordinate plane. The equation of line m is y=-3x+8 and line n goes through point (-4,-11). When a transversal of the two lines is constructed the alternate interior angles formed by the transversal are congruent. What is the equation of line n?
Answer:
The equation of line n is;
y = -3x - 23
Step-by-step explanation:
Here, we want to find the equation of line n
For the alternate interior angles to be congruent after drawing the transversal, then both lines must be parallel
If the two lines are parallel, then their slopes are equal
To get the slope of line m, we compare the equation of line m to the standard form
The equation of line m is y = -3x + 8
if we compare this with the standard form which is y = mx + c
Then the slope of line m is -3 and since they are parallel lines, the slope of line n is -3 too
So now, we need to get the equation of line n
It passes through (-4,-11)
What we have already is;
y = -3x + c
we need to get the y-intercept to write the complete equation
To get the y-intercept we simply substitute for (-4,-11)
Thus, we have
-11 = -3(-4) + c
-11 = 12 + c
c = -11-12 = -23
The equation of line n is;
y = -3x - 23
A grocery store clerk can scan 1 product every
1/2
of a second. At what rate can she scan products?
Tara plans to put wallpaper on the walls of her room. She will not put the wallpaper across the doorway, which is 3 feet wide and 7 feet tall. Tara decides to get the same wallpaper for both rooms. Write the expression for the total amount of wallpaper she needs.
Answer: $28x^-63$ or $16^2-42$
Step-by-step explanation:
hope this helps
16/21 decimal rounded to the nearest hundreth
Answer:
0.76
Step-by-step explanation:
Hundredth is just the 2nd decimal point
i need help i will mark brainliest!! look at the pictures
Answer:
yes
Step-by-step explanation:
the picture is not clear
You are Miguel Cervantes de Navas y Colon, captain in the Royal Spanish
Army in Sevilla in the year 1842. Outside your barracks window is a stack of
cannonballs, as shown in the illustration. On an idle afternoon you decide to
calculate the number of cannonballs in the stack. What is the number of
cannonballs?
Answer: The correct answer would be 164(c)
Step-by-step explanation:
You are Miguel Cervantes de Navas y Colon, captain in the Royal Spanish
Army in Sevilla in the year 1842. Outside your barracks window is a stack of
cannonballs, as shown in the illustration. On an idle afternoon you decide to
calculate the number of cannonballs in the stack. What is the number of
cannonballs?
650 is the number of cannonballs. It typically fires a projectile propelled by an explosive chemical.
What is cannonballs?A cannon constitutes a large-caliber gun that belongs to the artillery category. It typically fires a projectile propelled by an explosive chemical. Prior to the development of smokeless powder in the late 19th century, gunpowder (sometimes known as "black powder") served as the main propellant.
Depending on their intended purpose on the battlefield, different types of gun combine and balance these characteristics to differing degrees. Cannons differ in gauge, effective range, mobility, rate of fire, angle of fire, and firepower. A large artillery weapon is a cannon.
By utilizing the formula of a square pyramid,
n(n+1)(2n+1)/6
12(12+1)(2(12)+1)/6
12(13)(25)/6
2*13*25
=650
Therefore, 650 is the number of cannonballs.
To know more about cannonballs, here:
https://brainly.com/question/14330897
#SPJ7
The formula for the volume of a cylinder is V = gran.
Solve V = 872) for h, the height of the cylinder.
O A. =
nar
B. n =
O c. h =
Vr2
O D. h=
372
Answer:
B . n
Step-by-step explanation:
Find the value of X and Y in this triangle.
Step-by-step explanation:
if leg a is the missing side, then transform the equation to the form when a is on one side, and take a square root: a = √(c² - b²)
if leg b is unknown, then. b = √(c² - a²)
for hypotenuse c missing, the formula is. c = √(a² + b²)
Answer:
[tex] \sin(60) = \frac{45}{x} \\ [/tex]
[tex] x = \frac{45}{ \sin(60) } [/tex]
x=5 1.96
Step-by-step explanation:
[tex] \tan(30) = \frac{y}{45} [/tex]
[tex]y = 45 \tan(30) [/tex]
y=25.98
Question is attached!
Answer:
what are the answer
Step-by-step explanation:
If an oxygen atom gains 2 electrons what is it's overall charge?
(Remember: electrons have a negative charge)
Answer:
I think it would be -2 if it has a negative charge
Step-by-step explanation:
A person invests 5500 dollars in a bank. The bank pays 5.75% interest compounded annually. To the nearest tenth of a year, how long must the person leave the money in the bank until it reaches 14700 dollars?
Answer:
It’s 17.6
Step-by-step explanation:
Calcula la relación entre los volúmenes de estos dos cilindros, si el radio de uno de ellos es el doble que del otro
Answer:
calfdmf mjd fmjs wsmc wsjmc jesd jms
Step-by-step explanation:
A student has some $1 bills and $5 bills in his wallet. He has a total of 13 bills that are worth $45. How many of each type of bill does he have?
Answer:
8 $5 bills and 5 $1 bills
Step-by-step explanation:
5x8=40, which would be $40
1x5=5, which would be $5
$40+$5=$45
hope this helps! :)
Answer:
it's not possible. I've tried every way, r these the right amounts?
I’ll mark brainliest please help!
Answer:
4x + 2 = 30
Step-by-step explanation:
To find the perimeter of a triangle, add up the length of all three sides of the triangle.
Here, the sides of the triangle are "x+6", "x+6", and "2x-10". When you add up all three sides of the triangle, it should be equal to the perimeter, 30. So:
(x+6) + (x+6) + (2x-10) = 30
We can simplify this equation:
(2 * (x+6)) + (2x-10) = 30
2x + 12 + 2x - 10 = 30
4x + 2 = 30
Answer D: 4x + 2 = 30
What is the square root function?
Answer:
f(x) = [tex]\sqrt{x}[/tex]
Step-by-step explanation:
hope this helped :-)
identify the type of represented f(x)=3/8(4)^x
Answer:
Exponetial Growth