Answer:
L(min) = 560 m
Step-by-step explanation:
Dimensions of rectangular area are: "x" and "y"
Then x*y = 9800 m²
If this area have to be divided into three parallel pens total length of fencing material would be:
L = 2*x + 4*y
And L as a function of x is
x*y = 9800 ⇒ y = 9800/x
L(x) = 2*x + 4 * 9800/x ⇒ L(x) = 2*x + 39200/x
Taking derivatives on both sides of the equation we get
L´(x) = 2 - 39200/x²
L´(x) = 0 ⇒ 2 - 39200/x² = 0
2*x² - 39200 = 0
x² = 39200 / 2 ⇒ x² = 19600
x = 140 m
And y = 39200/ 140
y = 70 m
Then minimum length of fence is:
L(min) = 2*140 + 4*70
L(min) = 280 + 280
L(min) = 560 m
Checking in the second derivative:
L´´(x) = 2*39200/x³ > 0 then we get a minimum of the function L at the point x = 140
One airplane is located 200 km north and 50 km east of an airport. A second plane at the same altitude is located 30 km north and 100 km north and 100 km west.
The distance between the planes is closest to:
A. 150 km
B. 200 km
C. 300 km
D. 350 km
E. 400 km
Answer: B
Step-by-step explanation:
We can define the North as our positive y-axis, and the East as the positive x-axis.
The position of the airport is the (0, 0)
Then the position of the first plane is: (200 km north and 50 km east)
(50km, 200km)
The position of the other plane is: (30 km north and 100 km west)
(-100km, 30km)
Now, if we have two points (a, b) and (c, d)
The distance between those points is:
D = √( (a - c)^2 + (b - d)^2)
Then the distance between the planes is:
D = √( (50km - (-100km))^2 + (200km - 30km)^2)
D = √( (150km)^2 + (170km)^2)
D = 226.7km
Then the distance is closest to 200km, the correct option is B.
On a coordinate plane, we have:
North represents the positive y-axisSouth represents the negative y-axisEast represents the positive x-axisWest represents the negative x-axisThe closest distance between the planes is 200km
The positions of the two planes is given as:
[tex]A = (50,200)[/tex] --- 50km east and 200km north
[tex]B = (-100,30)[/tex] --- 100km west and 30km north
The distance between the planes is calculated using the following distance formula:
[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]
So, we have:
[tex]d = \sqrt{(50--100)^2 + (200-30)^2}[/tex]
[tex]d = \sqrt{150^2 + 170^2}[/tex]
[tex]d = \sqrt{51400}[/tex]
[tex]d = 226.72km[/tex]
From the list of given options, 200km is the closest to 226.72km
Hence, the closest distance between the planes is 200km
See attachment for the positions of both planes
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Find the equation of the sphere if one of its diameters has endpoints (-8, -3, -10) and (-6, 1, -4) which has been normalized so that the coefficient of x2 is 1.
Answer:
The equation is [tex]x^2 + y^2 +z^2 + 14 x + 3y \ + 14z + 86.25=0[/tex]
Step-by-step explanation:
From the question we are told that
The diameter endpoints is (-8, -3, -10) and (-6, 1, -4)
Generally the equation of a sphere with center coordinates (a, b , c ) and radius r is mathematically represented as
[tex](x - a )^2 + (y -b )^2 + (z -c)^2 = r^2[/tex]
Now since we are given the endpoints of the diameter then we can obtain the center coordinates as follows
[tex](a, b , c) = [ \frac{ -8 +(-6)}{2} , \frac{-3 + (1)}{ 2} , \frac{ -10 + (-4)}{2} ][/tex]
[tex](a, b , c) = [ -7 , -1.5 , -7 ][/tex]
Now the length of the diameter is evaluated as
[tex]|d| = \sqrt{ (-8 - (-6 ))^2 + ( -3 - (1) )^2 + ( -10 - (-4))^2 }[/tex]
[tex]|d| = \sqrt{56 }[/tex]
[tex]|d| = \sqrt{4 * 14 }[/tex]
[tex]|d| = 2 \sqrt{ 14 }[/tex]
Now the radius is mathematically represented as
[tex]r = \frac{|d|}{2}[/tex]
[tex]r = \frac{ 2 \sqrt{14} }{2}[/tex]
[tex]r = \sqrt{14}[/tex]
So
[tex](x - -7 )^2 + (y --1.5 )^2 + (z --7)^2 = ( \sqrt{14} )^2[/tex]
[tex](x +7 )^2 + (y +1.5 )^2 + (z +7)^2 = 14[/tex]
[tex]x^2 + 14 x + 49 + y^2 + 3y + 2.25 +z^2 14z + 49 = 14[/tex]
[tex]x^2 + y^2 +z^2 + 14 x + 3y \ + 14z + 86.25=0[/tex]
5 less than a number is equivalent to 1 more than three times the number. what is the number
Answer:
X = -3
Step-by-step explanation:
x - 5 = 3x + 1
-6 = 2x
x = -3
Hope it helped u if yes mark me BRAINLIEST!
Tysm!
;)
The equation formed by the information, 5 less than a number is equivalent to 1 more than three times the number is x - 5 = 3x + 1. And the number is x = -3.
What are linear equations in one variable?The simplest equation used to express and solve for an unknown quantity is a linear equation in one variable. It's simple to depict graphically since it's always a straight line. A linear equation is a simple technique to convey a mathematical proposition. Unknown quantities can be represented by any variable or symbol, however, in most cases, the unknown quantity in a linear equation in one variable is represented by the variable 'x'. A collection of basic strategies are used to solve a linear equation. To determine the final value of the unknown quantity, the variables are isolated on one side of the equation and the constants are isolated on the other side of the equation.
How do we solve the given question?We are given that 5 less than a number is equivalent to 1 more than three times the number. We are asked to determine the number.
To determine the number, we will let the unknown number be x.
We will now try to make the two equal expressions, equate them to get a linear equation in one variable, and then solve the equation to find x.
First expression: 5 less than the number, that is, x - 5
Second expression: 1 more than three times the number, that is, 3x + 1.
Both the expressions are equal, so we equate them to get our equation:
x - 5 = 3x + 1
To solve for x, we do the following steps.
1. Subtract 3x from both sides of the equation:
x - 5 - 3x = 3x + 1 - 3x
or, -2x -5 = 1 (Simplifying)
2. Add 5 to both sides of the equation:
-2x - 5 + 5 = 1 + 5
or, -2x = 6 (Simplifying)
3. Divide both sides of the equation by (-2):
-2x/(-2) = 6/(-2)
or, x = -3 (Simplifying).
∴ The equation formed by the information, 5 less than a number is equivalent to 1 more than three times the number is x - 5 = 3x + 1. And the number is x = -3.
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4x+12 is greater than or equal to 4x-4
Answer:
20/:&&:/$/686th
Step-by-step explanation:
ggbnk
I tried different ways of doing the equation but I still didn't get a correct answer
Answer:
[tex]\huge \boxed{\mathrm{0.65 \ in^2}}[/tex]
Step-by-step explanation:
Area of square = [tex]s^2[/tex]
[tex]0.5^2 = 0.25[/tex]
Area of triangle = [tex]\frac{bh}{2}[/tex]
[tex]\frac{0.5 \times 0.4}{2}=0.1[/tex]
The surface area of the net = area of square + 4(area of triangle)
[tex]0.25+4(0.1)=0.65[/tex]
Regular airfare to Boston is $125 one way, but as a special discount, the fare was lowered to $105 one way. How much money will four people save altogether one way using the lower rate? ill make brainest
Answer:
$80
Step-by-step explanation:
So for this we need the cost of 4 regular tickets minus the cost of 4 discount tickets.
4(125$) = 500$
4(105$) = 420$
From here, we can find out how much is saved by the four people.
500$ - 420$ = 80$
So 80 dollars are saved by the four people.
Cheers.
what OneEnginer said
Step-by-step explanation:
use PEMDAS: please excuse my dear aunt sally
Simplify these expressions:
1) 8y + 5 - 10y - 2
Answer:
here I think
Step-by-step explanation:
8y + 5 - 10y - 2 = (8y-10y)+(5-2)=-2y+3
Pulse rates of women are normally distributed with a mean of 77.5 beats per minute and a standard deviation of 11.6 beats per minute. Answer the following questions. What are the values of the mean and standard deviation after converting all pulse rates of women to z scores using z = ? (x − μ) σ μ = σ = The original pulse rates are
Answer:
So we need to find the P (Z< 1.0776) which is equal to 0.86 from z- tables.
Step-by-step explanation:
Given that mean = 77.5 beats per minute
Standard deviation= s= 11.6 beats per minute
We need to find the pulse rate of randomly selected women.
Suppose randomly selected women X= 90
The test statistic used here is
z = (x − μ) /σ
Putting the values we get
z= 90- 77.5/ 11.6
z= 1.0776
So we need to find the P (Z< 1.0776) which is equal to 0.86
This is a supposed values of randomly selected women. Any other value can be solved in the same way.
Which of the following is a cash transaction? Calculating interest charges Making change Making time payments Using a credit card
Answer:
Making change
Step-by-step explanation:
Making change is a cash transaction. Change is cash, bills or coin, that refunds the difference between the amount due and the amount paid.
Answer:
Step-by-step explanation:
Making change: you work entirely with cash (coins), exchanging the money in one form for the same amount of money in another form (e. g., coins to dollar bills).
Evaluate 8 2/9 - 7 1/6
Answer:
19/18
Step-by-step explanation:
convert to an improper fraction
8 2/9 = 74/9
7 1/6 = 43/6
= 74/9 - 43/6
convert so denominators are equal -- multiply by 2
= 148/18 - 129/18
subtract
19/18
On subtracting two mixed numbers 8 2/9 and 7 1/6 we will get 1 1/18.
Given is subtraction operation involving two mixed numbers 8 2/9 and 7 1/6.
We need to evaluate 8 2/9 - 7 1/6.
To evaluate the expression 8 2/9 - 7 1/6, we first need to convert the mixed numbers to improper fractions, then perform the subtraction.
Step 1: Convert mixed numbers to improper fractions.
To convert a mixed number to an improper fraction, multiply the whole number by the denominator of the fractional part and add the numerator. Keep the denominator the same.
Let's do this for both numbers:
8 2/9 = (8 × 9 + 2) / 9 = 74 / 9
7 1/6 = (7 × 6 + 1) / 6 = 43 / 6
Step 2: Perform the subtraction.
Now that both numbers are in the form of improper fractions, we can subtract them:
(74 / 9) - (43 / 6)
To subtract fractions, they must have the same denominator. To achieve this, we find the least common multiple (LCM) of 9 and 6, which is 18. Now, we'll rewrite the fractions with a common denominator of 18:
(74 / 9) = (74 / 9) × (2 / 2) = 148 / 18
(43 / 6) = (43 / 6) × (3 / 3) = 129 / 18
Now, the expression becomes:
(148 / 18) - (129 / 18)
Step 3: Subtract the fractions.
Subtract the numerators while keeping the common denominator:
(148 - 129) / 18 = 19 / 18
Step 4: Simplify (if necessary).
The result, 19/18, is an improper fraction. To convert it back to a mixed number, we find the whole number and the proper fraction part:
19 / 18 = 1 (1/18)
So, the final result is: 8 2/9 - 7 1/6 = 1 1/18.
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Find the anhle measure x in the figure
Answer:
x=25°
Step-by-step explanation:
Sum of angles of a triangle equals 180°
x + 10° + 2x + 15° + 3x + 5° = 180°6x + 30° = 180°6x = 180° - 30°6x = 150°x = 150°/6x = 25°If f ' is continuous, f(5) = 0, and f '(5) = 7, evaluate
lim x→0
f(5 + 5x) + f(5 + 6x)
x
Correct question is;
If f ' is continuous, f(5) = 0, and f '(5) = 7, evaluate;
lim x→0 [f(5 + 5x) + f(5 + 6x)]/x
Answer:
The limit is 77
Step-by-step explanation:
Since we want to evaluate;
lim x→0 [f(5 + 5x) + f(5 + 6x)]/x
Thus, let's plug in 0 for x to get;
lim x→0 [f(5 + 5x) + f(5 + 6x)]/x = [f(5) + f(5)]/0
Since we are told that f(5) = 0, thus we now have;
[f(5) + f(5)]/0 = 0/0
Since, we have a limit of both numerator and denominator as 0,thus let's apply L'Hospital's Rule which states that: if we have an indeterminate form of 0/0 or ∞/∞, we will differentiate the numerator and differentiate the denominator and then take the limit.
Thus, applying L'Hospital's rule and using chain rule in differentiating, we have;
lim x→0 [5f'(5 + 5x) + 6f'(5 + 6x)]/1 = 5f'(5) + 6f'(5) = 11f'(5)
We are given f'(5) = 7
Thus,we now have;
11 × 7 = 77
An indeterminate form is an expression involving two functions whose limit cannot be determined solely from the limits of the individual functions.
After evaluation, [tex]\lim_{x \to 0} \frac{f(5+5x)+f(5+6x)}{x} =77[/tex]
Here, given that, f(5) = 0, and f '(5) = 7
We have to find,
[tex]\lim_{x \to 0} \frac{f(5+5x)+f(5+6x)}{x}[/tex]
When substituting the limit x=0. We get 0/0 form which is indeterminate form.
So, Here we use L'Hospital's rule, because direct substitution of a limit yields an indeterminate form.
[tex]\lim_{x \to 0} \frac{5*f'(5+5x)+6*f'(5+6x)}{1} =\frac{5f'(5)+6f'(5)}{1}[/tex]
Substituting the value of f '(5) = 7 in above equation.
[tex]=\frac{5f'(5)+6f'(5)}{1}=\frac{(5*7)+(6*7)}{1}[/tex]
= [tex]35+42=77[/tex]
Thus, [tex]\lim_{x \to 0} \frac{f(5+5x)+f(5+6x)}{x} =77[/tex]
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Consider the partial construction of a line parallel to line r through point Q. What would be the final step in the construction? Question 1 options: Draw a line through T and S Draw a line through W and S Draw a line through P and S Draw a line through Q and S
Answer:
Draw a line through Q and S
Step-by-step explanation:
I took the quiz. I hope this helps :)
A new television set was recently purchased for the commons room in a residence hall for $469.20 including tax. If the tax rate is 2% find the price of the television set before taxes
Answer:
459.81
Step-by-step explanation:
So if the TV is 469.20 take that number and subtract 2% away from it and boom you got your answer.
Deandre buys candy that costs $6 per pound. He will spend at least $42 on candy. What are the possible numbers of pounds he will buy? Use p for the number of pounds Deandre will buy.
At a concert, floor tickets are $20 each, and
balcony seats are $10 each. 324 floor tickets were
sold & the box office collected $10,000. How many
balcony tickets were sold?
Answer: 352 tickets
Step-by-step explanation:
because multiplying $20 floor tickets by 324 (how many were sold) gives you 6480
subtract from 10000
gives you 3520 (amount made from balcony)
divide by $10
Step-by-step explanation:
Let No. of balcony ticket sold be x
Rate of floor ticket = $20
Rate of balcony ticket = $10
Total Box Office collection :
324 * 20 + 10 * x = $ 10,000
X = 352 tickets
A weather forecasting website indicated that there was a 60% chance of rain in a certain region. Based on that report, which of the following is the most reasonable interpretation? Choose the correct answer below.
A. 60% of the region will get rain today.
B. In the region, it will rain for 60% of the day.
C. There is a 0.60 probability that it will rain somewhere in the region at some point during the day.
D. None of the above interpretations are reasonable.
Answer:
C. There is a 0.60 probability that it will rain somewhere in the region at some point during the day.
Step-by-step explanation:
The probability that it will rain is given by =p= 60% = 0.6
60% chance of rain in a certain region means that the probability of rain in the given region is 0.6 at any time of the day in any part of the region.
So Choice C is the best option.
Choice A is wrong because 60% of the region does not mean 60% of the rain.
Choice B is also wrong because 60% of the day does not mean 60% of the rain.
The weather report tells about the rain , not the region or part of the day. So choice C is the best option
Solve for the indicated variable 3x - y = 10; y
Answer:
y = 3x - 10
Step-by-step explanation:
Starting with 3x - y = 10, add y to both sides:
3x = 10 + y
Then subtract 10 from both sides:
3x - 10 = y
If you switch the sides of the equation, it can also be written as:
y = 3x - 10
If (x - 3) 2 = 5, then
Answer:
Step-by-step explanation:
2(x-3) = 5
Distribute.
2x - 6 = 5
Eliminate the 6.
2x = 11
Divide by 2.
x = 11/2
Answer:
[tex]\frac{11}{2}[/tex]
Step-by-step explanation:
We can use distributive property to simplify the equation, [tex]2x-6=5[/tex]. Now, we can move -6 to the right hand side. [tex]2x=11[/tex]. Finally, we can divide 2, [tex]x=\frac{11}{2}[/tex] or [tex]x = 5\frac{1}{2}[/tex]
to make his special drink, jerome uses 8 cups of water and 3 cups of drink mix. what is the ratio of water to drink mix?
Answer:
8:3
Step-by-step explanation:
read the question carefully
Answer:
8/3 or 8:3
Step-by-step explanation:
It says WATER to DRINK MIX. Therefore, It can't be 3:8 or 3/8. The only thing to make sense is 8/3 or 8:3
Write 34/9 as a decimal
Answer:
3.777...
Step-by-step explanation:
You would divide the 2 and once you get the remainder put a decimal after the divisor and keep bringing down 0 until you can divide anymore 3.777...
Ms. Ironperson and Mr. Thoro are making Avenger posters to give children when they visit Avenger Academy. Ms. Ironperson has completed 12 posters and will complete 6 more per day. Mr. Thoro has not started yet but can make 12 per day. At some point Mr. Thoro will catch up and both will have finished the same number of posters. When this does happen, how many posters will each Avenger have completed? If x denotes the number of days and y denotes the number of posters, what are the equations needed to solve this problem?
Answer:
The equations needed to solve this problem are:
y = 12 + 6x
y = 12x
The number of posters completed by each Avenger will be 24.
Step-by-step explanation:
The information provided are:
Ms. Ironperson has completed 12 posters and will complete 6 more per day.Mr. Thoro has not started yet but can make 12 per day. The variable x denotes the number of days and y denotes the number of posters.So, after x day the number of poster completed by Ms. Ironperson will be:
y = 12 + 6x
And after x day the number of poster completed by Mr. Thoro will be:
y = 12x
Thus, the equations needed to solve this problem are:
y = 12 + 6x
y = 12x
Compute the value of x as follows:
12x = 12 + 6x
6x = 12
x = 2
The number of posters completed by each Avenger is:
y = 12x = 12 × 2 = 24
Thus, the number of posters completed by each Avenger will be 24.
what is the length of the hypotenuse triangle if both sides are 36
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{36 \sqrt{2} \: \: units}}}}}[/tex]Step-by-step explanation:
Given,
Perpendicular ( P ) = 36
Base ( b ) = 36
Hypotenuse ( h ) = ?
Finding the hypotenuse :
Using the Pythagoras theorem :
[tex] \sf{ {h}^{2} = {p}^{2} + {b}^{2} }[/tex]
plug the values
⇒[tex] \sf{ {h}^{2} = {36}^{2} + {36}^{2} }[/tex]
Evaluate the power
⇒[tex] \sf{ {h}^{2} = 1296 + 1296}[/tex]
Add the numbers
⇒[tex] \sf{ {h}^{2} = 2592}[/tex]
Squaring on both sides
⇒[tex] \sf{h = 36 \sqrt{2} }[/tex] units
Hope I helped!
Best regards!!
Shota is a dangerous fellow who likes to go rock climbing in active volcanoes. One time, when he was 303030 meters below the edge of a volcano, he heard some rumbling, so he decided to climb up out of there as quickly as he could. He climbed up at a constant rate. After 4.54.54, point, 5 seconds, he was 7.57.57, point, 5 meters below the edge of the volcano How fast did Shota climb? In total, how long did it take Shota to reach the edge of the volcano?
Answer:
Speed = 5m/s
Total time taken = 6 seconds
Step-by-step explanation:
Shota's initial position = 30 metres below the edge of a volcano
If Shota climbed at a constant rate:
Shota's position after 4.5 seconds = 7.5meters below the edge of the volcano
Shota's climbing speed :
Distance covered / time taken
Distance covered = (30 - 7.5) = 22.5 meters
Hence, speed = (22.5 / 4.5) = 5m/s
Time taken to reach edge of volcano:
Time left to reach edge = (distance left to cover / speed)
Time left to reach edge = (7.5 / 5) = 1.5 seconds
Total time taken: (4.5 + 1.5) = 6 seconds
A local electronics store is offering a $200.00 rebate along with a 20% discount. Let x represent the original price of an item in the store. Find the composite function (D ° R)(x) Group of answer choices 200 – 0.8x 0.8x (0.8x – 80) 0.8x – 200 0.8x - 80
Answer:
0.8(x - 200)
Step-by-step explanation:
The rebate function is subtracting 200 from the price.
R(x) = x - 200
The discount function is to take 20% off the original price which means to pay for 80% of the original price.
D(x) = 0.8x
(D ° R)(x) =
= D(R(x))
= D(x - 200)
= 0.8(x - 200)
The sprocket on the crankshaft of an engine power the camshaft by a chain assembly. If the engine crankshaft is turning 3250 revolutions per minute and the sprocket has a radius of 1.5 inches, to the nearest inch how many inches of chain travel past the sprocket in one minute? To the nearest foot how many feet of chain travel past the sprocket in one minute?
Answer:
30,631 inches2553 feetStep-by-step explanation:
The length of one revolution of the sprocket is ...
C = 2πr = 2π(1.5 in) = 3π in
Then the length of 3250 revolutions is ...
3250(3π in) = 30,630.53 in
About 30,631 inches of chain travel past the sprocket in one minute.
__
There are 12 inches in a foot, so the number of feet is ...
30,630.53 in/(12 in/ft) = 2552.54 ft
About 2553 feet of chain travel past in one minute.
can someone please help me
Answer:
Mark answer C and D as correct
Step-by-step explanation:
Recall that a bisector cuts the side in two equal segments, then KH has to be half of 136 that is KH = 68
Also KHZ and HLZ are right angle triangles that share the same hypotenuse, so they are congruent triangles, which means that HL must equal KH and therefore the full side HJ must be 68 times 2 = 136
Which of the following is the rational exponent expression of fourth root of f?
f to the one fourth power
f4
4f
f over four
Answer:
[tex] \sqrt[4]{f} = f^{\frac{1}{4}} [/tex]
Step-by-step explanation:
Rule:
[tex] \sqrt[n]{a} = a^{\frac{1}{n}} [/tex]
This question:
[tex] \sqrt[4]{f} = f^{\frac{1}{4}} [/tex]
Whats 1+2+3+4+5 add them together pls
Answer:
15
*ignore this answers have to be a minimum of 20 characters.
Answer:
15
Step-by-step explanation:
1+2=3
3+3=6
6+4=10
10+5=15.
uber has faced a host of ethics and financial challenges ever since it started in 2011. which of mintzberg's roles is most closely related to uber's senior leadership's responsibility to fix problems the company is facing?
Answer: C. disturbance handler
Step-by-step explanation:
According to Henry Mintzberg, a manager has 10 roles which can be organized into three categories being; Decisional, Interpersonal and Informational roles.
The relevant role is that of a Disturbance handler and it falls under Decisional roles.
As the Disturbance handler, a manager should take the responsibility of resolving any problems that the company runs into that is under their authority to manage. They are to mediate in the issue to resolve the problem so that it does not disrupt the operations of the business.
The senior managers of Uber should take charge and guide Uber through the financial and ethical issues they are facing as this is their responsibility as disturbance handlers.