Answer:
[tex]50\; {\rm ft} \times 50\; {\rm ft}[/tex] would maximize the area for a rectangle with the given circumference of [tex]200\; {\rm ft}[/tex]. (Note, that a circle of the same circumference would have an even larger area.)
Step-by-step explanation:
Assume that the base of the house is a rectangle. Let the length of the two sides be [tex]x\; {\rm ft}[/tex] and [tex]y\; {\rm ft}[/tex], respectively. The goal is to find the [tex]x[/tex] and [tex]y[/tex] that:
[tex]\begin{aligned} \text{maximize} \quad & x\, y \\ \text{subject to} \quad & 2\, (x + y) = 200 \\ & x > 0 \\ & y > 0 \end{aligned}[/tex].
Using the equality constraint [tex]2\, (x + y) = 200[/tex] (or [tex]x + y = 100[/tex]), the variable [tex]y[/tex] could be replaced with [tex](100 - x)[/tex] to obtain an equivalent problem of only one variable:
[tex]\begin{aligned} \text{maximize} \quad & x\, (100 - x) \\ \text{subject to} \quad & x > 0 \\ & (100 - x) > 0 \end{aligned}[/tex].
Simplify to obtain:
[tex]\begin{aligned} \text{maximize} \quad & -x^{2} + 100\, x \\ \text{subject to} \quad & x > 0 \\ & x < 100 \end{aligned}[/tex].
The objective function of this problem is [tex]f(x) = -x^{2} + 100\, x[/tex]. Derivatives of this function include
[tex]f^{\prime}(x) = -2\, x + 100[/tex] and[tex]f^{\prime\prime}(x) = -2[/tex].Since [tex]f^{\prime\prime}(x)[/tex] is constantly less than [tex]0[/tex], [tex]f(x)[/tex] is concave and would be maximized when [tex]f^{\prime}(x) = 0[/tex].
Setting [tex]f^{\prime}(x) = -2\, x + 100[/tex] to [tex]0[/tex] and solving for [tex]x[/tex] gives:
[tex]-2\, x + 100 = 0[/tex].
[tex]x = 50[/tex].
Notice that [tex]x = 50[/tex] satisfies both constraints: [tex]x > 0[/tex] and [tex]x < 100[/tex]. Therefore, [tex]x = 50[/tex] is indeed the solution that maximizes the area [tex]f(x) = -x^{2} + 100\, x[/tex] while at the same time meeting the requirements.
With the length of one side being [tex]x = 50[/tex] ([tex]50\; {\rm ft}[/tex],) the length of the other side would be [tex]100 - x = 50[/tex] ([tex]50\; {\rm ft}\![/tex].) Hence, a rectangular house of dimensions [tex]50\; {\rm ft} \times 50\; {\rm ft}[/tex] would maximize the area under the given requirements.
Carly needs $149 to buy a skateboard. She already has $52. She earns money washing cars for $20 a car.
Carly says that if she washes 5 cars she will have enough money to buy the skateboard.
Use the drop-down menus to explain how to solve this problem.
First, multiply
Choose...
× $20 to find how much money Carly will earn washing cars. Then add this amount to
Choose...
to find how much money Carly has in all. Finally,
Choose...
the total to the cost of the skateboard.
Answer:
Answer:
$149 - skateboard price
$52 - carly's money
$20 × 5 cars = $100
$100 + $52 = $152
$152 - $149 = $3 left
Step-by-step explanation:
f(x) = 1.1–4x when x = – √2
Answer:
f(x)=2x^2+4x+6
f(x)=2(x^2+2x)+6
f(x)+?=2(x^2+2x+?)+6
f(x)+?=2(x^2+2x+1)+6
f(x)+2x1=2(x^2+2x+?)+6
f(x)+2=2(x^2+2x+1)+6
f(x)=2(x+1)^2+6-2
f(x)=2(x+1)^2+4
Answer:
f(x)=2(x+1)^2+4
WORTH 75 POINTS WILL MARK BRAINLYEST HELP ME PLEASE 75 75 POINTS
Your answer is [tex]\frac{d^7}{c}[/tex]
Yw :D
Answer:
d⁷/c
Step-by-step explanation:
djsjdnsjjwndjaojc
In which type of circuit is the total current equal to the sum of all the branch currents?
Answer:
Parallel circuit
Hope this one helps :)
Help me again! No one replied to my last one!
3. Amy Schorling is age 24 and is unmarried. She uses her vehicle
for business. Her driver-rating factor is 1.85. Her vehicle is
classified D-14. Her insurance consists of $25,000 property
damage, 25/50 bodily injury, $50-deductible comprehensive, an
no collision coverage.
a. What is her annual premium?
b. How much is her annual premium if she includes
$50-deductible collision coverage?
Based on Amy Schorling's driver rating factor, vehicle classification and bodily injury coverage, her annual premium is $576.46.
If she includes the $50-deductibel collision coverage, her insurance premium becomes $1,067.08.
How much is Amy Schorling's annual premium?At $25,000 property damage, her 25/50 bodily injury coverage premium is $206.40.
This should be added to her $50 comprehensive deductible D-14 vehicle classification of $105.20.
Annual base premium:
= 206.40 + 105.20
= $311.60
Annual premium:
= Annual base premium x Driver rating factor
= 311.60 x 1.85
= $576.46
How much is the annual premium including collision coverage?The annual base premium becomes:
= 311.60 + 265.20
= $576.80
Annual premium becomes:
= 576.80 x 1.85
= $1,067.08
Find out more on insurance coverage at https://brainly.com/question/25740123.
Is 32,000 millimeters = 3.2 liters?
Answer:
no
Step-by-step explanation:
Jake scored 9 out of 12 field goals during a basketball game. Reggie scored 3 out of 5. Who has the better average for this game?
Explain.
(I will give brainliest if you show your work)
Answer: jake
Step-by-step explanation:
no need to find avarage
9 to 12 is 0.75 or 75%
3 to 5 is 0.60 or 60%
step by step
9 divided by 12 is 0.75
3 divided by 5 is 0.60
to turn in to percentage just move two decimal places to the left .
Answer:
Jake
Step-by-step explanation:
When you compare them with fractions like on a fraction line Jake has more than Reggie
Marlene is going on a camping trip with a group of friends. She brings 3 boxes of granola bars, plus 3 extra bars. Robyn bring 2 boxes of granola bars and Wendy brings one box. They have a total of 57 granola bars. If each box contains the same number of bars, how many bars are in each box?
Answer:
19
Step-by-step explanation:
Please answer the attachment!
The perimeter of any shape is the length of all the sides added up:
1. For the rectangle
[tex]6 + (3x - 1) + (3x - 1) + 6 = 6x - 2 + 12 =6x + 10[/tex]
2. For hexagon
[tex]10.2 + (x+4)+(x+4)+10.2+(x+4)+(x+4)=4x + 16 + 20.4=4x + 36.4[/tex]
Hope that helps!
Solve the following equation for x. 10=2-4(ax-3)
Answer:
[tex]x=\frac{1}{a}[/tex]
Step-by-step explanation:
10 = 2 - 4 (ax - 3)
10 = 2 - 4ax + 12
10 = - 4ax + 14
-4 = -4ax
1/a = x
A number I divided by 3 is at most 5
What is the scale factor from ABC to DEF?
Answer:
C
Step-by-step explanation:
^
A six-sided die with sides labeled 1 through 6 will be rolled once. Each number is equally likely to be rolled. What is the probability of rolling a number greater than 2? Write your answer as a fraction in simplest form.
Answer:
4/6
Step-by-step explanation:
6 is the denominator as it's the total of the entire thing.
4 is the numerator because there's 4 numbers greater than 2
Angles A and C are supplementary. Find the measure of angle C.
A. List 2 pairs of angles in square CDFG that are complementary.
B. Name three angles that sum up to 180°
a. Two pairs complementary angles are: ∠DCM and ∠DMC; ∠MGF and ∠GMF
b. m∠GMF + m∠CMG + m∠DMC = 180°
What are Supplementary Angles and Complementary Angles?If the sum of two angles equal 90°, they are complementary angles.
If the sum of two angles equal 180°, they are supplementary angles.
Given square CDFG:
a. Two pairs of angles that are complementary are: ∠DCM and ∠DMC; ∠MGF and ∠GMF
b. m∠GMF + m∠CMG + m∠DMC = 180° (angles on a straight line)
Therefore, three angles that sum up to 180° are: ∠GMF, ∠CMG, and ∠DMC.
Learn more about complementary angles on:
https://brainly.com/question/16281260
Help help help help help
Answer:
4
Step-by-step explanation:
5x/2 - 1 = 9
add 1 to each side
5x/2 = 10
multiply both sides by 2
5x = 20
divide both sides by 5
x=4
Answer:
x=4
Step-by-step explanation:
5x-2=18 (multiply 9 with 2=18)
5x=18+2 (move 2 to the other side)
5x=20 (add 18 and 2=20)
X=4 (divide 20 and 5 =4)
what is the value of 0 in the number 9,603,450,503
Answer:
0
Step-by-step explanation:
0 x 10
0 x 1000
0 x 10 000 000 they all equal 0
Hey there!
9,603,450,503
“Nine billion six hundred three million four hundred fifty thousand five hundred three”
9,000,000,000
+ 600,000,000
+ 00
+ 3,000,000
+400,000
+ 50,000
+ 00
+ 500
+ 00
+ 03
9 = billions (9 billion)
,
6 = Hundred Millions (600 million)
0 = Ten Millions
3 = Millions (3 million)
,
4 = Hundred Thousands (400 thousand)
5 = TenThousands (50 thousand)
0 = Thousands
,
5 = Hundreds (5 hundreds)
0 = Tens
3 = ones (3)
So, therefore your answer(s) is/are:
• ten millions
• thousands
• tens
Good luck on your assignment & enjoy your enjoy your day!
~Amphitrite1040:)
Q. Solve using the quadratic formula x2 + 4x – 16 = 0 ?
-
answer choices
2 + 25
A
B 2 + 4V5
C -2 + 275
D -2 + 4V5
Answer:
Step-by-step explanation:
ax² + bx + c = 0
[tex]x_{1}[/tex] = [tex]\frac{-b - \sqrt{b^2 -4ac} }{2a}[/tex]
[tex]x_{2}[/tex] = [tex]\frac{-b+\sqrt{b^2 -4ac} }{2a}[/tex]
~~~~~~~~~~~~~~~~~~~
x² + 4x - 16 = 0
a = 1 , b = 4 , c = - 16
[tex]x_{1}[/tex] = ( - 4 - [tex]\sqrt{16+64}[/tex] ) ÷ 2 = - 2 - 4√5
[tex]x_{2}[/tex] = - 2 + 4√5
Which expression represents a negative number? A.-4.5x-22.1 B.4.5x22.1 C.-45x2.21 D.-45x-2.21
Hey there!
-4.5 * (-22.1)
= -4.5(-22.1)
= 99.45
4.5 * 22.1
= 99.45
-45 * 2.21
= -99.45
-45(2.21)
= -99
Therefore, your answer is:
Option C.
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Answer:
C.-45 x 2.21Step-by-step explanation:
When you multiply two negative or two positive numbers you get a positive result and when you multiply one positive and one negative number you get a negative result.
Looking at answer choices, we see
A) negative x negative = positiveB) positive x positive = positiveC) negative x positive = negativeD) negative x negative = positiveSo the correct one is C
HELP my mom said if i get caught up with my school work they will take me to the beach so help me with this test pls
Answer:
If i give you the answers, it will not help you, because you need to learn these things...I will however give you something that will help you .
Step-by-step explanation:
Hope this helps! Have a good day! :)
Determine the finance charge on a $6,800 car loan if monthly payments were $158.50 for 48 months.
Answer:
808
Step-by-step explanation:
Plan
You make 48 payments of 158.50. That gives you the total of what you have paid back.
Equation
Total payment = months * monthly payments
Solution
Total Payment = 48 * 158.50
Total Payment = 7608
Cost of the loan
Finance charge = amount paid - amount loaned
Finance charge = ?
amount paid = 7608
amount loaned = 6800
Finance charge = 7608 - 6800
Answer: Finance charge = 808
Satellite
Mass
(kg)
An engineer is collecting data on
four different satellites orbiting
Earth. The engineer records the
satellites' distances from Earth in
kilometers (km) and their forces
due to gravity in Newtons (N).
Distance
(km)
4000
Force due to gravity
(N)
17000
1
700
2.
700
36000
3
1000
11000
4
1000
7000
8100
Estimate the values for the two
missing quantities. Enter your
estimates into the blank boxes in
the table.
The first missing quantity is force due to gravity, and it is 215.1 N.
The second missing quantity is distance between the statellite and the Earth, determined as 6,000 km.
Force between two massesThe force between two masses is determined by applying Newton's law of universal gravitation as shown below;
[tex]F = \frac{GMm}{R^2}[/tex]
where;
M is mass of Earth = 5.97 x 10²⁴ kgm is mass of the satelliteR is the distance between the satellite and the EarthG is universal gravitation constantFirst missing quantityThe first missing quantity is force due to gravity, and it is calculated as follows;
[tex]F = \frac{(6.67 \times 10^{-11} ) \times (5.97 \times 10^{24}) \times (700)}{(36,000 \times 10^3)^2} \\\\F = 215.1 \ N[/tex]
Second missing quantityThe second missing quantity is distance between the statellite and the Earth,
[tex]R^2 = \frac{GMm}{F} \\\\R^2 = \frac{(6.67 \times 10^{-11})(5.97 \times 10^{24})(1000)}{11,000} \\\\R^2 = 3.62 \times 10^{13}\\\\R = 6,000 \ km[/tex]
Learn more about Newton's law here: https://brainly.com/question/3999427
Pls help I will give brainliest.
Answer:
50 yards
Step-by-step explanation:
This is a 3-4-5 triangle. You can use this shortcut to find the hypotenuse. (Multiply the3, 4, 5 by 10) OR
You could also use Pythagorean Theorem.
30^2 + 40^2 = h^2
900+1600=h^2
2500 = h^2
Squareroot.
50 = h
A store can buy 8 cartons of milk for 24 dollars or 7 cartons of milk for $28.
How much less does each carton of milk cost if the store buys 8 cartons instead of 7 cartons?
A.
$1 less
B.
$2 less
C.
$3 less
D.
$4 less
Answer:
a
Step-by-step explanation:
28/7=4
24/8=3
pleasee help I would appreciate very!
Answer:
D
Step-by-step explanation:
We can visually see the line going down so the slope is negative. (-30)
The y-intercept must be 120, because it does not intersect 90.
My math teacher randomly assigned this but it’s something far outta my range, I need some help!!!!!
If d=26 then r = d/2 = 13
...........................................
Which graph represents the parametric equations x(t) = t – 4 and y(t) = t2 + 5 for –1 ≤ t ≤ 2?
Which graph indeed?
Eliminate the parameter:
x = t - 4 ⇒ t = x + 4
⇒ y = t² + 5 = (x + 4)² + 5
which is the equation of a parabola with vertex at (-4, 5) and opening upwards, plotted with domain
-1 ≤ t ≤ 2 ⇒ -1 ≤ x + 4 ≤ 2 ⇒ -5 ≤ x ≤ -2
Answer:
it is c
Step-by-step explanation:
WHAT IS THE ANSWER TO THIS QUESTION
A car can travel 580 miles on a full tank of gas. With four new eco-tyres it
can travel 620 miles. Find the percentage increase in miles the tyres have
made.
Please help you don't have to do 11 please help
Answer:
Step-by-step explanation:
for number 8 we have to use the equation πr^2, so plugging 9 into the equation would give us π(9^2). squaring the 9 gives us 81, and 81 times π equals ~25.
for number 9 we need to use the same equation, πr^2 to find the area, but since we are given the diameter we do not need to use r^2. Instead, we can use π(106) which gives us 333.