Answers
=======================================================
Explanation:
Let C be the corner point.
x = distance from P to C
That makes segment AP to be 70-x feet long
Focus on the right triangle PBC. Use the pythagorean theorem to find the hypotenuse PB.
[tex]a^2 + b^2 = c^2\\\\c = \sqrt{a^2 + b^2}\\\\PB = \sqrt{(PC)^2 + (CB)^2}\\\\PB = \sqrt{x^2 + 90^2}\\\\PB = \sqrt{x^2 + 8100}\\\\[/tex]
If we knew what x was, then we could find a numeric value for PB.
---------------------
It costs $28 per foot to run cable along the ground. This is the portion from A to P. So it costs 28(70-x) dollars to run that portion of cable above ground. Simply multiply the cost per foot by the number of feet.
Similarly, the cost from P to B is [tex]53\sqrt{x^2+8100}[/tex] since it costs $53 per foot to have it run underground.
The total cost is therefore [tex]28(70-x) + 53\sqrt{x^2 + 8100}[/tex]
The derivative of this will help determine when the cost is minimized.
Type that function into GeoGebra and have it compute the derivative.
You should find that the x intercept of the derivative curve is exactly x = 56
If x = 56, then 70-x = 70-56 = 14
This means AP = 14 feet is the amount of cable to run along main street.
This also leads to [tex]PB = \sqrt{x^2 + 8100} = \sqrt{56^2 + 8100} = 106[/tex]
The total length of the wire is 14+106 = 120 feet
It costs $28 per foot along the 14 ft section, so 28*14 = 392 dollars is the cost for this section.
It costs $53 per foot along the 106 ft section, so 53*106 = 5618 dollars is the cost for this other section.
The total min cost is 392+5618 = 6010 dollars
------------------
Side note: You could do all this without a calculator to compute the derivative and use algebra to end up with x = 56. However, I think the use of technology is beneficial because it's fast/efficient. In real world settings, you won't be likely to pull out pencil/paper to get things done. The modern world relies on computers. It's refreshing to see that your teacher encourages the use of technology.
Let me know if you need me to go over the algebraic steps and I'll update my answer.
Related Questions
Write the equation of a line in the slope-intercept form that has a slope of 4 and contains the point (4, 12).
Answers
Answer:
y=4x-4
Step-by-step explanation:
Hi there!
we are given that a line has a slope of 4 and it contains the point (4, 12)
We want to write the equation of this line in slope-intercept form
Slope-intercept form is given as y=mx+b, where m is the slope and b is the y intercept
As we are already given the slope, we can immediately substitute it into the formula.
Replace m with 4 in y=mx+b:
y=4x+b
Now we need to find b
As the equation passes through the point (4, 12), we can use it to help solve for b
Substitute 4 as x and 12 as y:
12 = 4(4) + b
Multiply
12 = 16 + b
Subtract 16 from both sides
-4 = b
Substitute -4 as b
y = 4x - 4
Hope this helps!
Topic: Finding the equation of the line
See more on this topic here: https://brainly.com/question/27539102
Which function is the inverse of f(x)=-5x-4
Answers
Hello!
Let's solve this question with the information given to us in the question.
We were given the function, f(x) = -5x - 4, or also known as y = -5x - 4
With the function we need to find the inverse of it.
We can simply flip the "x" and "y" variables in the function and solve.
Solve:
y = -5x - 4
Flip the "x" and "y" variables.
x = -5y - 4
Now, solve for "y".
x = -5y - 4
Add 4 to both sides of the equation.
x + 4 = -5y
Divide everything by -5 to get "y" by itself.
-1/5x - 4/5 = y
Therefore, the inverse of the function would be [tex]-\frac{1}{5}x -\frac{4}{5}[/tex]
Answer:
Your answer would be A). [tex]-\frac{1}{5}x -\frac{4}{5}[/tex]
Hanson and his classmates placed colored blocks on a scale during a science lab. The blue block weighed 8.1 pounds and the green block weighed 3.758 pounds. How much more did the blue block weigh than the green block?
This is for my younger brother
Answers
Answer:
4.342
Step-by-step explanation:
8.1 - 3.758 = 4.342
When you are trying to find the amount of difference between two values you subtract the value less than the other and there you go, the solution!
I hope it was as simple as that and that this helped!
Which line is a line of symmetry for the figure attached?
A.
Line B
B.
Line A
C.
Line C
D.
Line D
Answers
Answer:
The correct Answer is D.Line D.
Hope it helps you Czn.
Please Mark me Brainleast!!!!!!!!!
A paper weight is in the shape of a square pyramid. The dimensions are shown in the net.
Square pyramid net consisting of a square and four triangles. The square has length and width of ten centimeters. Each triangle has a base of ten centimeters and a height of fourteen centimeters.
What is the surface area of the paper weight, including the base?
Enter your answer in the box.
cm²
Answers
The surface area of the square pyramid net consisting of a square and four triangles is 380 sq. cm
How to find the surface area of a figure?The surface area of a square pyramid is equal to the sum of the ara of the base square and the four triangle.
Find the area of the square baseArea of the base = 10cm * 10cm
Base area = 100 sq,cm
Find the area of a triangle
Area of triangle = 0.5 * 10 * 14
Area of a triangle = 70 square cm
Area of 4 triangles = 4(70) = 280 sq.cm
Determine the surface areaSA = 100 + 280
SA = 380 sq. cm
Hence the surface area of the square pyramid net consisting of a square and four triangles is 380 sq. cm
Learn more on surface area here: https://brainly.com/question/16519513
I The following data set represents
the shoe size of a group of
kindergarteners.
12, 12, 9.5, 10.5, 11.5, 12
Answers
Answer:
12 because it is repeat which means multiple kindergarteners have a size 12 shoe
Step-by-step explanation:
Find the value of x.
120°
(5x)
x = [?]°
Enter
Answers
Answer:
x = 24°
Step-by-step explanation:
Here we can see that 120° with the right angle is equal to 180° :
120° + right angle = 180°
then:
right angle = 180° - 120° = 60°
The right angle with 5x angle is equal to 180° too ;
right angle + 5x = 180°
solve for x :
5x = 180° - 60°
x = 24°
That its.
You want to buy a new computer for $1500. You only have $500 right now, so you decide to deposit the money into an account yeilding 5% interest compounded monthly, how long until you have enough to buy the computer
Answers
Answer:
Twenty-two months (a year and ten months)
Step-by-step explanation:
First, we have to find how much is 5% of 500
500 x 0.05 = 25
Next, you add it to 500
so after the first month, you will have $525
Then, we have to find 5% of 525
525 x 0.05 = 26.25
meaning that after the second month, you'll have $551.25
We keep on repeating these steps until we reach the desired amount.
month three:
$551.25 x 0.05 = 27.5625
551. 25 + 27.5625 = 578.8125
month four:
578.8125 x 0.05 = 28.940625
578.8125 + 28.940625 = 607.753125
month five:
607.753125 x 0.05 = 30.38765625
607.753125 + 30.38765625 = 638.14
month six:
638.14 x 0.05 = 31.91
638.14 + 31.91 = 670.05
month seven:
670.05 x 0.05 = 33.51
670.05 + 33.51 = 703.55
month eight:
703.55 x 0.05 = 35.18
703.55 + 35.18 = 738.73
month nine:
738.73 x 0.05 = 36.94
738.73 + 36.94 = 775.67
month ten:
775.67 x 0.05 = 38.78
775.67 + 38.78 = 814.45
month eleven:
814.45 x 0.05 = 40.72
814.45 + 40.72 = 855.17
month twelve:
855.17 x 0.05 = 42.76
855.17 + 42.76 = 897.93
month thirteen:
897.93 x 0.05 = 44.90
897.93 + 44.90 = 942.83
month fourteen:
942.83 x 0.05 = 47.14
942.83 + 47.14 = 989.97
month fifteen:
989.97 x 0.05 = 49.50
989.97 + 49.50 = 1039.47
month sixteen:
1039.47 x 0.05 = 51.97
1039.47 + 51.97 = 1091.44
month seventeen:
1091.44 x 0.05 = 54.57
1091.44 + 54.57 = 1146.01
month eighteen:
1146.01 x 0.05 = 57.30
1146.01 + 57.30 = 1203.31
month nineteen:
1203.31 x 0.05 = 60.17
1203.31 + 60.17 = 1263.48
month twenty:
1263.48 x 0.05 = 63.17
1263.48 + 63.17 = 1326.65
month twenty-one:
1326.65 x 0.05 = 66.33
1326.65 + 66.33 = 1392.98
month twenty-two:
1392.98 x 0.05 = 69.65
1392.98 + 69.65 = 1462.63
month twenty-three:
1462.63 x 0.05 = 73.13
1462.63 + 73.13 = 1535.76
So your final answer would be that it would take twenty-two months (a year and ten months) to have enough money to buy the computer.
p.s. sorry for the super long answer, I wanted to make sure you had the complete process. hope this helped!
Stacy performed an experiment in which she rolled a six-sided die multiple times. The results are shown below
Based on the results above, predict the number of times a 3 would be rolled if Stacy performs the experiment a total of 480 times.
Answers
Answer:
5/9
Step-by-step explanation:
Let the probability of getting a multiple of 3 is "A"
Let the probability of getting an even number is "B"
Total number of outcomes=36
Total number of favourable outcomes of either a multiple of 3 or an even number are
(1,1) ,(1,2) ,(2,1) ,(1,3) ,(3,1) ,(2,2) ,(1,5) (5,1) ,(3,3) ,(2,4) ,(4,2) ,(2,6) ,(6,2) ,(3,5) ,(5,3) ,(4,4) ,(6,4) ,(4,6) ,(5,5) ,(6,6)
That is we have 20 favourable outcomes
Hence, Probability=\frac{\text{favourable outcomes}}{\text{total number of outcomes}}Probability=
total number of outcomes
favourable outcomes
Therefore, after substituting the values we get
probability=\frac{20}{36}probability=
36
20
After simplification we will get
probability=\frac{5}{9}probability=
9
5
what is the area of a square whose diagonal is 8?
Answers
Answer:
A=32
Step-by-step explanation:
A=[tex]a^{2}[/tex]
d=[tex]\sqrt{2[/tex] a
A= [tex]\frac{1}{2}[/tex] [tex]d^{2}[/tex] = [tex]\frac{1}{2}[/tex]=·[tex]8^{2}[/tex]=32
Answer:
Step-by-step explanation:
Situation: Holly wants to save money for an emergency. Holly invests $800 in an account that pays an interest rate of 4%. A = P(1 + r)¹ P = amount of money invested r = interest rate percentage in decimal form How many years will it take for the account to reach $1,600? Round your answer to the nearest hundredth. Enter the correct answer. DONE
Answers
Answer:
t = 74.897 years
(about 74 years 11 months)
Step-by-step explanation:
First, convert R as a percent to r as a decimal
r = R/100
r = 4/100
r = 0.04 per year,
Then, solve the equation for t
t = ln(A/P) / n[ln(1 + r/n)]
t = ln(16,000.00/800.00) / ( 365 × [ln(1 + 0.04/365)] )
t = ln(16,000.00/800.00) / ( 365 × [ln(1 + 0.00010958904109589)] )
t = 74.897 years
Summary:
The time required to get a total amount of $16,000.00 with compoundeded interest on a principal of $800.00 at an interest rate of 4% per year and compounded 365 times per year is 74.897 years.
(about 74 years 11 months)
Since it wasn't stated howmany times the interest is compunded I took the value of once a year.
In an examination,33 1/3 percentage of the examinees passed.If 240 examinees failed,find the total number of the examinees!!
Answers
Answer:
[tex]SOLUTION:-[/tex]
[tex] \rm{passed \: percent = { \displaystyle{33 \frac{1}{3} \%} = \frac{100}{3}\% }}[/tex]
[tex]{ \displaystyle{ \rm{failed \: percent = \left( 100 - \frac{100}{3} \right)}\%}}[/tex]
[tex]\displaystyle{ \frac{3 \times 100 - 100}{3}\% }[/tex]
[tex]\displaystyle{ \frac{200}{3}\% }[/tex]
Let,x be the total number of examinees:-
We have,
[tex]\displaystyle{ \frac{200}{3}\% \: \rm{of \: x = 240} }[/tex]
[tex]\displaystyle{ \frac{200}{3} \times \frac{1}{100} \rm \: x = 240}[/tex]
[tex]\displaystyle{ \rm{x = \frac{240 \times 3 \times 100}{200} }}[/tex]
[tex]\displaystyle{ \rm{x = 360}}[/tex]
Hence,required number of examinees = 360 .
Simone is four years older than her sister Olivia. Their combined ages is 28. What are their ages
Answers
Answer:
Simone is 16 and Olivia is 12
Step-by-step explanation:
The hypotenuse of a right triangle measures 15 cm and one of its legs measures 13 cm. Find the measure of the other leg
Answers
Hi!
We can solve this using the Pythagorean Theorem.
[tex]a^2+b^2=c^2[/tex] where [tex]a[/tex] and [tex]b[/tex] are the legs and [tex]c[/tex] is the hypotenuse.
Given:
1 leg = 13
2 leg = ???
hypotenuse = 15
Plug the values into the equation above:
[tex]13^2+b^2=15^2[/tex]
Multiply using exponents:
[tex]169+b^2=225[/tex]
Subtract 169 from both sides:
[tex]b^2=56[/tex]
Take the square root of both sides:
[tex]b=[/tex][tex]\sqrt{56}[/tex]
what conclusoin can be drawn based on the expirement
Answers
Answer:
Drawing a conclusion means making a state- ment summing up what you have learned from an experiment.
Step-by-step explanation:
this makes you understand the context or concept better and you may recall that a hypothesis is a possible explanation for a set of observations or answer to a scientific question.
Answer:
Drawing a conclusion means making a state- ment summing up what you have learned from an experiment. The conclusion of an experiment is usually related to the hypothesis. You may recall that a hypothesis is a possible explanation for a set of observations or answer to a scientific question.
Step-by-step explanation:
please consider as brainlest if useful
Now, you will consider Option 1, setting a maximum shower time of 10 minutes.
rer
Assume all students who showered longer than 10 minutes will now shower for
exactly 10 minutes. Assume the rest of the students will shower for the same amount
of time as they did yesterday.
Blake claims Option 1 would result in the class mean going below 8 minutes, but the
class median would not change.
Explain whether you agree or disagree with Blake's claim. Include the class mean and
median that would result from Option 1 in your explanation.
BI
Answers
The maximum shower time is an illustration of mean and median, and the conclusion is to disagree with Blake's claim
How to interpret the shower time?The question is incomplete, as the dataset (and the data elements) are not given.
So, I will answer this question using the following (assumed) dataset:
Shower time (in minutes): 6, 7, 7, 8, 8, 9, 9, 9, 12, 12, 12, 13, 15,
Calculate the mean:
Mean = Sum/Count
So, we have:
Mean = (6+ 7+ 7+ 8+ 8+ 9+ 9+ 9+ 12+ 12+ 12+ 13+ 15)/13
Mean = 9.8
The median is the middle element.
So, we have:
Median = 9
From the question, we have the following assumptions:
The shower time of students whose shower times are above 10 minutes, is 10 minutesOther shower time remains unchanged.So, the dataset becomes: 6, 7, 7, 8, 8, 9, 9, 9, 10, 10, 10, 10, 10
The mean is:
Mean = (6+ 7+ 7+ 8+ 8+ 9+ 9+ 9+ 10+ 10+ 10+ 10+ 10)/13
Mean = 8.7
The median is the middle element.
So, we have:
Median = 9
From the above computation, we have the following table:
Initial Final
Mean 9.8 8.7
Median 9 9
Notice that the mean value changed, but it did not go below 8 as claimed by Blake; while the median remains unchanged.
Hence, the conclusion is to disagree with Blake's claim
Read more about mean and median at:
https://brainly.com/question/14532771
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Which of the following is a solution of the inequality?
-3 < 2x + 1 < 5
Answers
Answer:
-2<x<2
Step-by-step explanation:
HELP HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Answers
The answer is C. A fraction is basically another way of writing division, and six divided by three is two.
Melissa is building
a skateboarding ramp by propping the end of a piece of wood on a cinder
block. If the ramp begins 24 inches from the block and the block is 7 inches tall, how long is
the piece of wood?
inches
Answers
a skateboarding ramp by propping the end of a piece of wood on a cinder
block. If the ramp begins 24 inches from the block and the block is 7 inches tall, how long is
the piece of wood?
inches
The total amount you earn as a salary or hourly wage is called ___ income.
A. Net
B. Surplus
C. Residual
D. Gross
Answers
Answer:
Gross income
Step-by-step explanation:
the gross income is whatever you earn in total, so that must be it
15
Janice had a total of 156 red and yellow beads in the ratio 6:7.
After she gave away an equal number of each type of beads, the
number of red and yellow beads left was in the ratio 3:7.
(a)Did the fraction of red beads that Janice had left increase,
decrease or remain the same?
B)How many yellow beads were given away?
Answers
Answer:
decrease because the ratio number is Less so multiply by 156 to each ratio to find your relationship between. hope this helps.
39-42 Differentiate [tex]f[/tex] and find the domain of [tex]f\text{.}[/tex]
40. [tex]f(x)=\ln \left(x^{2}-2 x\right)[/tex]
Answers
[tex]\text{Given that,}\\\\f(x) = \ln (x^2 - 2x)\\\\f'(x) = \dfrac 1{x^2 -2x} \cdot (2x - 2) = \dfrac{2(x-1)}{x(x-2)}\\\\\\\text{domain f(x): } \{x| x < 0, x > 2 \}[/tex]
Find the limit of the function by using direct substitution. limit as x approaches zero of quantity x squared minus eight.
Answers
Answer:
-8
Step-by-step explanation:
lim x⇒0 (x²-8) = 0-8 = -8
what three numbers give you 206 when multiplied
Answers
Answer:
1, 1, 206.Step-by-step explanation:
There are nothing else that can multiply to get to 206, so this is the answer.
Solve:
1 * 1 * 206= 1 * 206= 206.This is the only equation that can make 206 with 3 numbers.
Solve for x:
AD bisects ZBAC
A
Answers
Answer: 3
Step-by-step explanation:
Male and female high school students reported how many hours they worked each week in summer jobs. The data is represented in the following box plots.
Identify any values of data that may affect the statistical measures of center and spread. (1 point)
A)The males worked less than the females, and the male median is close to Q1.
B)There are significant outliers at the high ends of both the males and females.
C)Both graphs are symmetrical, so IQR and median are appropriate measures of spread and center for both males and females.
D)There is a high data value that causes the data set for the or females to be asymmetrical.
Answers
Answer:
Males have a significantly high outlier
Step-by-step explanation:
answer asap!
A bag of chips weighs 8 ounces. How many pounds do 20 bags of chips weigh?
How many bags would you need to equal a ton?
Answers
Answer:
160 ounces
Which is 10 pounds
And 4410 chip packets will equal about a ton
Step-by-step explanation:
because 20 x 8 =160
35274/8 = 4409.25
*note 35274 ounces is equal to a ton
Answer:
4000 bags
Step-by-step explanation:
8 x 20 = 160 oz = 10 lb
2,000 lb = 1 ton
16 oz = 1b
2,000 x 16 = 32,000 oz = 1 ton
32,000/8 = 4,000 bags
Write a two-digit number ...
a
that has 9 tens and 1 ones;
.
Answers
Answer: 91
Step-by-step explanation:
9 tens= 90
1 ones= 1
90+1=91
Find the volume of the cone. Either enter an exact answer in terms of π or use 3.14 for π. radius is 10 height is 6
Answers
200pi (in terms of pi)
OR
628 (when pi equals 3.14)
Explanation:
I’ve attached my work below
Hope it helps, Let me know if you have any questions!
Have a nice rest of your day :)
if you invest $421 for 9 years at an interest rate of 4%, how much interest will you earn?
Answers
Step-by-step explanation:
421×9=3789 it is easy when you know your multiple choice