Answer:
The approximated length of the cables that stretch between the tops of the two towers is 1245.25 meters.
Step-by-step explanation:
The equation of the parabola is:
[tex]y=0.00035x^{2}[/tex]
Compute the first order derivative of y as follows:
[tex]y=0.00035x^{2}[/tex]
[tex]\frac{\text{d}y}{\text{dx}}=\frac{\text{d}}{\text{dx}}[0.00035x^{2}][/tex]
[tex]=2\cdot 0.00035x\\\\=0.0007x[/tex]
Now, it is provided that |x | ≤ 605.
⇒ -605 ≤ x ≤ 605
Compute the arc length as follows:
[tex]\text{Arc Length}=\int\limits^{x}_{-x} {1+(\frac{\text{dy}}{\text{dx}})^{2}} \, dx[/tex]
[tex]=\int\limits^{605}_{-605} {\sqrt{1+(0.0007x)^{2}}} \, dx \\\\={\displaystyle\int\limits^{605}_{-605}}\sqrt{\dfrac{49x^2}{100000000}+1}\,\mathrm{d}x\\\\={\dfrac{1}{10000}}}{\displaystyle\int\limits^{605}_{-605}}\sqrt{49x^2+100000000}\,\mathrm{d}x\\\\[/tex]
Now, let
[tex]x=\dfrac{10000\tan\left(u\right)}{7}\\\\\Rightarrow u=\arctan\left(\dfrac{7x}{10000}\right)\\\\\Rightarrow \mathrm{d}x=\dfrac{10000\sec^2\left(u\right)}{7}\,\mathrm{d}u[/tex]
[tex]\int dx={\displaystyle\int\limits}\dfrac{10000\sec^2\left(u\right)\sqrt{100000000\tan^2\left(u\right)+100000000}}{7}\,\mathrm{d}u[/tex]
[tex]={\dfrac{100000000}{7}}}{\displaystyle\int}\sec^3\left(u\right)\,\mathrm{d}u\\\\=\dfrac{50000000\ln\left(\tan\left(u\right)+\sec\left(u\right)\right)}{7}+\dfrac{50000000\sec\left(u\right)\tan\left(u\right)}{7}\\\\=\dfrac{50000000\ln\left(\sqrt{\frac{49x^2}{100000000}+1}+\frac{7x}{10000}\right)}{7}+5000x\sqrt{\dfrac{49x^2}{100000000}+1}[/tex]
Plug in the solved integrals in Arc Length and solve as follows:
[tex]\text{Arc Length}=\dfrac{5000\ln\left(\sqrt{\frac{49x^2}{100000000}+1}+\frac{7x}{10000}\right)}{7}+\dfrac{x\sqrt{\frac{49x^2}{100000000}+1}}{2}|_{limits^{605}_{-605}}\\\\[/tex]
[tex]=1245.253707795227\\\\\approx 1245.25[/tex]
Thus, the approximated length of the cables that stretch between the tops of the two towers is 1245.25 meters.
If 1 euro is 1.07 dollars and 1 pound is 1.25 dollars how many euro is to the pound
Step-by-step explanation:
1.07×1.25
=1.3375 euros
Find the surface area of a sphere with a diameter 12 cm. Round your answer to the nearest whole number
Answer:
SA = 144π or 452 cm
Step-by-step explanation:
Surface area of a sphere: SA = 4πr²
To find r radius, we simply divide diameter by 2 to get r = 6. Now we simply plug in 6:
SA = 4π(6)²
SA = 4π36
SA = 144π or 452.389
Answer:
144pi
Step-by-step explanation:
calculator
A rectangle or pyramid has a volume of 1296 in.³, a height of 24 inches, and a base length of 6 inches. What is the width of its base?
Answer: base width = 27 in
Step-by-step explanation:
Base width = 3 x (V / hl)
3 x (1296 / 24 x 6)
3 x (1296 / 144)
3 x 9 = 27
given a 60 month car loan at 4.71%, explain how much your monthly payments would be for a $18,400 car and what your TOTAL COST would be given that interest.
Answer:
$23161.10
Step-by-step explanation:
Assuming this is compounded annually, we use our simple interest rate formula: A = P(1 + r)^t
Step 1: Convert months to years
60 months/12 month/year = 5 years
Step 2: Plug in known variables
A = 18400(1 + 0.0471)^5
Step 3: Solve
When you plug step 2 into your calc you should get 23161.1 as your answer. I am assuming that this isn't compounded quarterly or monthly, but just yearly.
If log 5 = p and log 2=q then log 200 can be written in terms of p and q as?
Work Shown:
log(200) = log(2^3*5^2)
log(200) = log(2^3) + log(5^2)
log(200) = 3*log(2) + 2*log(5)
log(200) = 3*q + 2*p
log(200) = 2p + 3q
The log rules I used were
log(A*B) = log(A)+log(B)
log(A^B) = B*log(A)
The equivalent expression of log(200) is 2p + 3q
The logarithmic expression is given as:
[tex]\mathbf{log 200}[/tex]
Rewrite as:
[tex]\mathbf{log(200) = log (25 \times 8)}[/tex]
Express as exponents
[tex]\mathbf{log(200) = log (5^2 \times 2^3)}[/tex]
Split
[tex]\mathbf{log(200) = log (5^2) +log(2^3)}[/tex]
Apply law of logarithms
[tex]\mathbf{log(200) = 2log (5) +3log(2)}[/tex]
From the question;
log(5) = p and log(2) = q
So, we have:
[tex]\mathbf{log(200) = 2p +3q}[/tex]
Hence, the equivalent expression of log(200) is 2p + 3q
Read more about logarithmic expressions at:
https://brainly.com/question/9665281
Explain how to translate the statement into an equation. Use n for the variable. Thirteen less than a number is four EXPLAIN:
start here
Answer:
13-n=4
Subtract both sides by 13
-n=-9
n=9
Step-by-step explanation:
13 less means - and a number means n that you don’t know. is means = sign. And so we get the answer that I gave you. Thank you
The access code for a garage door consists of three digits. Each digit can be any number from 1 through 5, and each digit can be repeated. Complete parts (a) through (c). (a) Find the number of possible access codes. (b) What is the probability of randomly selecting the correct access code on the first try? (c) What is the probability of not selecting the correct access code on the first try? (a) Find the number of possible access codes. The number of different codes available is nothing.
Answer:
(a) 125
[tex](b) \dfrac{1}{125}[/tex]
[tex](c) \dfrac{124}{125}[/tex]
Step-by-step explanation:
We are given that access code consists of 3 digits.
Each digit can be any digit through 1 to 5 and can be repeated.
Now, this problem is equivalent to the problem that we have to find:
The number of 3 digit numbers that can be formed using the digits 1 to 5 with repetition allowed.
(a) We have 3 places here, unit's, ten's and hundred's places respectively and each of the 3 places have 5 possibilities (any digit allowed with repetition).
So, total number of access codes possible:
[tex]5\times 5 \times 5 = 125[/tex]
(b) Suppose, an access code is randomly selected, what is the probability that it will be correct.
Formula for probability of an event E can be observed as:
[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}[/tex]
Here, only 1 code is correct, so
Number of favorable cases = 1
Total number of cases = 125
So, required probability:
[tex]P(E) = \dfrac{1}{125}[/tex]
(c) Probability of not selecting the correct access code on first time:
[tex]P(\overline E) = 1-P(E)\\\Rightarrow P(\overline E) = 1-\dfrac{1}{125}\\\Rightarrow P(\overline E) = \dfrac{125-1}{125}\\\Rightarrow P(\overline E) = \dfrac{124}{125}[/tex]
So, the answers are:
(a) 125
[tex](b) \dfrac{1}{125}[/tex]
[tex](c) \dfrac{124}{125}[/tex]
Please answer this correctly without making mistakes
Answer:
7
Step-by-step explanation:
hh
ht
th
tt
so it's a 1/4 chance
1/4 * 28 = 7
Answer:
7
Step-by-step explanation:
The probability of both coins landing on heads is:
1/2 × 1/2 = 1/4
Multiply by 28.
1/4 × 28
= 7
Solve the following and
make sure to write your
answer in scientific
notation.
(1.5 x 105)(5 x 103)
Answer:
7.5* 10^8
Step-by-step explanation:
(1.5 x 10^5)(5 x 10^3)
Multiply the numbers
1.5*5=7.5
Add the exponents
10 ^(5+3) = 10^8
Put back together
7.5* 10^8
This is in scientific notation
PLEASE I NEED HELP ASAP
Find the substance's half-life, in days.
Round your answer to the nearest tenth.
A 11 gram sample of a substance that's
used to treat thyroid disorders has a k-
value of 0.1247.
Enter the correct answer.
N = Noekt
DONE
No = initial mass (at time t = 0)
ĐOO
t?
N = mass at time t.
k = a positive constant that depends on
the substance itself and on the units
used to measure time
t = time, in days
Answer: 55.6 days
Step-by-step explanation:
[tex]P=P_oe^{kt}\\\\\bullet \quad P=\dfrac{1}{2}P_0\\\bullet \quad k=-0.1247\\\bullet \quad t = unknown\\\\\\\dfrac{1}{2}P_o=P_oe^{-0.1247t}\\\\\\\dfrac{1}{2}=e^{-0.1247t}\\\\\\ln\bigg(\dfrac{1}{2}\bigg)=-0.1247t\\\\\\\dfrac{ln\dfrac{1}{2}}{-0.1247}= t\\\\\\\large\boxed{55.6=t}[/tex]
The amount of energy it takes to lift a box might be a function of which of the
following?
A. The weight of the objects inside the box
OB. The shape of the box
C. The time of day that you are lifting it
Answer:
A. The weight of the objects inside the box
Step-by-step explanation:
The energy required to lift a box is a function of the weight of it and of the distance it is lifted.
_____
In physics terms, the energy is the product of force and distance. The applicable force when lifting the box is the weight of the box (the box itself and any objects inside).
4. The dimensions of a triangular pyramid are shown below. The height of
the pyramid is 6 inches. What is the volume in cubic inches?
Answer:
5in³Step-by-step explanation:
The question is in complete. Here is the complete question.
"The dimensions of a triangular pyramid are shown below. The height of
the pyramid is 6 inches. What is the volume in cubic inches?
Base of triangle = 1in
height of triangle = 5in"
Given the dimension of the triangular base of base 1 inch and height 5inches with the height of the pyramid to be 6inches, the volume of the triangular pyramid is expressed as [tex]V = \frac{1}{3}BH[/tex] where;\
B = Base area
H = Height of the pyramid
Base area B = area of the triangular base = [tex]\frac{1}{2}bh[/tex]
b = base of the triangle
h = height of the triangle
B = [tex]\frac{1}{2} * 5 * 1\\[/tex]
[tex]B = 2.5in^{2}[/tex]
Since H = 6inches
Volume of the triangular pyramid = [tex]\frac{1}{3} * 2.5 * 6\\[/tex]
[tex]V = 2.5*2\\V =5in^{3}[/tex]
The checking accounts of USF Credit Union are categorized by age of account and balance in account. We are going to select an account at random from this group of 2000 accounts.What is the conditional probability that the account has a balance at least $500, given that it is at least 3 years old, that is P(>=$500 | >=3 years)?
a. 1/2
b. 1/10
c. 1/4
d. None of these
Missing details to question is attached
Answer:
c) [tex] \frac{1}{4} [/tex]
Step-by-step explanation:
S
Required:
Find the probability that the account has a balance at least $500, given that it is at least 3 years old.
Which means: P(≥$500 | ≥3 years)
To find the probability, use the formula below:
P(≥$500 | ≥3 years) = (No. of accounts with balance≥ 500 and age ≥3 years) / (No. of accounts with age≥3 years)
Where from th given information:
Number of accounts with balance≥ 500 and age ≥3 years = 200
Number of accounts with age≥3 years = 600 + 200 = 800
Therefore,
P(≥$500 | ≥3 years) [tex] = \frac{200}{800} = \frac{1}{4} [/tex]
The probability that the account has a balance at least $500, given that it is at least 3 years old = [tex] \frac{1}{4} [/tex]
What is the greatest number that can be divided evenly into 78 and 104 without leaving a remainder?
Answer:
26 can be divides evenly into 78 and 104 without leaving a remainder
Step-by-step explanation:
Answer:
26
Step-by-step explanation:
78= 2 × 3 × 13
104= 2 × 2 × 2 × 13
The required number is: 2 × 13= 26
If a coin is tossed 5 times, and then a standard six-sided die is rolled 4 times, and finally a group of three cards are drawn from a standard deck of 52 cards without replacement, how many different outcomes are possible?
Answer: 5,499,187,200
Step-by-step explanation:
A coin is tossed 5 times.
There are two options (heads or tails) so the possible outcomes are: 2⁵
A six-sided die is rolled 4 times.
There are six options so the possible outcomes are: 6⁴
A group of 3 cards are drawn (without replacement).
The first outcome has 52 options, the second has 51 options, and the third has 50 options: 52 x 51 x 50
Now if we want the coin AND the die AND the cards, we have to multiply all of their possible outcomes:
2⁵ x 6⁴ x 52 x 51 x 50
= 32 x 1296 x 132,600
= 5,499,187,200
Rhea obtained a CO-OP credit working at a computer store. They have now hired her for a summer job with the store. She makes $8/hour, plus a 5% commission on sales.
Which expression best describes Rhea's total earnings? Explain.
a) E = 8h + 5s b) E = 8h + .50s
c) E = 8h + .005s d) E = 8h + 0.05s
Rhea worked 15 hours last week and made $260 in total. What were her total sales in computers for the week?
Why do you think employers offer commissions to their employees? Do you think there are any potential problems with this form of earnings?
Answer:
d) E = 8h + 0.05s
Her total sales in computers for the week is $2800.
Step-by-step explanation:
Let Rhea's hourly pay =h
She makes $8/hour, therefore sales for h hours =$8h
Let the volume of sales = s
She also earns 5% commission on sales = 5% of s = 0.05s
Therefore, the expression which best describes Rhea's total earnings:
(D) E=8h+0.05s
Rhea worked 15 hours last week and made $260 in total.
h=$15
From the formula
260=8(15)+0.05s
0.05s=260-8(15)
0.05s=140
s=2800
Her total sales in computers for the week is $2800.
Employers offer commissions to their employees to motivate them to seek to make sales rather than just passing time.
In so far as the sales commission do not eat up the profit of the business, there are no potential problems with this form of earnings
What is the solution of √1-3x = x+3 ?
Answer:
{-1, -8}
Step-by-step explanation:
Please enclose "1 - 3x" inside parentheses so the reader will know that you want the square root of all of "1 - 3x".
Squaring both sides of the given equation, we get:
1 - 3x = x^2 + 6x + 9, or x^2 + 6x + 8 + 3x, or
x^2 + 9x + 8 = 0. Factoring, we get: (x + 8)(x + 1) = 0, so that the solutions are {-1, -8}.
Answer:
I hope the given equation is :
{-1, -8}
First step to solve this equation to remove square root from the left side. So, take square on each sides of the equation. Therefore,
1 - 3x = (x + 3)²
1 - 3x = (x + 3)*(x + 3) Since a² = a * a
1 - 3x = x² + 3x + 3x + 3² By multiplication.
1 - 3x = x² + 6x + 9 Combine the like terms.
x² + 6x + 9 - 1 + 3x = 0 Subtract 1 and add 3x from each sides of equation
x² + 9x + 8 = 0 Combine the like terms.
Next step is to factor the trinomial to solve the above equation for x.
For that break downn the constant 8 into two multiples so that the addition of the multiples will result the coefficient of x = 9.
So, 8 = 1 * 8
Addition of 1 and 8 will give 9. So, next step is to replace 9x with 1x + 8x. So,
x² + 1x + 8x + 8 = 0
(x² + 1x) + (8x + 8) = 0 Group the terms.
x ( x + 1) + 8 (x + 1 ) = 0 Take out the common factor from each group.
(x +1 ) ( x + 8 ) = 0 Take out the common factor (x + 1).
So, x + 1 = 0 and x + 8 = 0 Set up each factor equal to 0.
Hence, x = -1 and - 8.
Next step is to plug in -1 and -8 in the original equation to cross check the solutions.
For x = -1,
Simplify each sides separately.
2 = 2
2 = 2 is correct. So, x = -1 satisfy the equation.
Hence, x = -1 is the real solution of the given equation.
Similarly let's plug in x = -8 now. So,
Simplify each sides separately.
5 = 2
5 = 2 is not true. So, x = -8 is the extraneous solution.
Therefore, the only solution is x = -1.
Hence, the correct choice is C.
Hope this helps you!
Step-by-step explanation:
mark brainlies plssssssssss
Emily worked only 4/5 of her normal 40-hr work week. If she makes $18 per hour, how much money did she earn for the week? Use the equation
Answer:
576 for the week
Step-by-step explanation:
First determine how many hours she worked
4/5 * 40 = 32 hours
32 hours times the hourly rate of 18
32*18 =576
After a 4% reduction, you purchase a new suit for $288. What was the original price of the suit?
Answer:
$300
Step-by-step explanation:
Let [tex]x[/tex] be the original price.
[tex]x \times (1-0.04)=288[/tex]
[tex]0.96x=288[/tex]
[tex]x=\frac{288}{0.96}[/tex]
[tex]x=300[/tex]
Answer:
$300
Step-by-step explanation:
If it was a 4% reduction then we get:
[tex]x*0.96=288\\[/tex]
Divide both sides by 0.96
[tex]x=300[/tex]
The original suit price was $300
Please help me....I need it
Answer:
Volume: 3x2x4=24 so the volume is 24 Meter3
Surface area:
52 Square meter
Need help please :) thanks
Brian set a goal to horseback ride more than 6 miles. The horse he rode averaged a speed of 4.6 miles per hour. A 2-column table with 4 rows titled Brian's Activity time (hours). Column 1 has entries hiking, mountain biking, horseback riding, cross-country skiing. Column 2 has entries 3, 1.45, 1.2, 0.75. Brian rode miles. Did he reach his goal?
Answer:
BRIAN DID NOT REACH HIS GOAL! Brian rode 5.52 miles!
Step-by-step explanation:
Answer:
he didn't reach his goal. he rode 5.52 miles
Step-by-step explanation:
Which are true of the function f(x)=49(1/7)?select three options. A)The domain is the set of all real numbers. B) the range is the set of all real numbers. C) the domain is x >0. D)the range is y>0. E)as increases by 1, each y value is one -seventh of the previous y-value.
Answer:
A,D and E
Step-by-step explanation:
We are given that a function
[tex]f(x)=49(\frac{1}{7})^x[/tex]
The given function is exponential function .
The exponential function is defined for all real values of x.
Therefore, domain of f=Set of all real numbers
Substitute x=0
[tex]y=f(0)=49>0[/tex]
Range of f is greater than 0.
x=1
[tex]y(1)=\frac{49}{7}[/tex]
x=2
[tex]y=49(\frac{1}{7})^2=\frac{1}{7}y(1)[/tex]
As x increases by 1, each value of y is one-seventh of the previous y-value.
Therefore, option A,D and E are true.
Answer:
A D E
Step-by-step explanation:
Edge2020 quiz
A marketing team is targeting people who might buy a hybrid car. In their city, with a population of 30,000 people, 3,170 people either drive a hybrid car or have indicated on a recent survey that they would be interested in driving one. Find the population proportion, as well as the mean and standard deviation of the sampling distribution for samples of size n
Answer:
The population proportion is 0.1057.
For samples of size n: Mean = 0.1057, Standard deviation [tex]s = \frac{0.3075}{\sqrt{n}}[/tex]
Step-by-step explanation:
Central Limit Theorem for Proportions:
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Population proportion:
Of 30,000 people, 3,170 people either drive a hybrid car or have indicated on a recent survey that they would be interested in driving one.
This means that [tex]p = \frac{3170}{30000} = 0.1057[/tex]
The population proportion is 0.1057.
Mean and standard deviation of the sampling distribution for samples of size n
By the Central Limit Theorem, the mean is [tex]\mu = p = 0.1057[/tex]
Standard deviation:
[tex]s = \sqrt{\frac{0.1057*0.8943}{n}} = \frac{0.3075}{\sqrt{n}}[/tex]
Jillian’s school is selling tickets for a play. The tickets cost $10.50 for adults and $3.75 for students. The ticket sales for opening night totaled $2071.50. The equation 10.50 a plus 3.75 b equals 2071.50, where a is the number of adult tickets sold and b is the number of student tickets sold, can be used to find the number of adult and student tickets. If 82 students attended, how may adult tickets were sold? Answer: 168 adult tickets
Answer:
Step-by-step explanation:
10.5a + 3.75b = 2071.50
b = 82 students
Substitute 'b' value in the equation
10.5a + 3.75 * 82 = 2071.50
10.5a + 307.5 = 2071.50
10.5a = 2071.50 - 307.5
10.5a = 1764
Divide both sides by 10.5
a = 1764/10.5
a =17640/105
a= 168
168 adult tickets were sold
Dylan paid a plumber $120 for 4 hours of labor. How much does the plumber charge per hour of labor? A. $15 per hour B. $30 per hour C. $116 per hour D. $480 per hour stay safe!
Answer:
Brainleist :)
Step-by-step explanation:
120 dollars for 4 hours of labor
120/4 dollars for 1 hour of labor
B) 30 dollars for 1 hour of labor
answe:
B) 30 dollars for 1 hour of labor
Step-by-step explanation:
120 dollars for 4 hours of labor
120/4 dollars for 1 hour of labor
important messagee:
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There are 1,596 fans at a football match. 3/7 of them are children. How many adults attended the football match?
Solve for x in the equation x squared minus 4 x minus 9 = 29. x = 2 plus-or-minus StartRoot 42 EndRoot x = 2 plus-or-minus StartRoot 33 EndRoot x = 2 plus-or-minus StartRoot 34 EndRoot x = 4 plus-or-minus StartRoot 42 EndRoot
Answer:
[tex]x=2$\pm$\sqrt{42}[/tex]
Step-by-step explanation:
The given equation is:
[tex]x^{2} -4x-9=29\\\Rightarrow x^{2} -4x-9-29=0\\\Rightarrow x^{2} -4x-38=0[/tex]
Formula:
A quadratic equation [tex]ax^{2} +bx+c=0[/tex] has the following roots:
[tex]x=\dfrac{-b+\sqrt D}{2a}\ and\\x=\dfrac{-b-\sqrt D}{2a}[/tex]
Where [tex]D= b^{2} -4ac[/tex]
Comparing the equation with [tex]ax^{2} +bx+c=0[/tex]
a = 1
b = -4
c= -38
Calculating D,
[tex]D= (-4)^{2} -4(1)(-38)\\\Rightarrow D = 16+152 = 168[/tex]
Now, finding the roots:
[tex]x=\dfrac{-(-4)+\sqrt {168}}{2\times 1}\\\Rightarrow x=\dfrac{4+2\sqrt {42}}{2}\\\Rightarrow x=2+\sqrt {42}\\and\\x=\dfrac{-(-4)-\sqrt {168}}{2\times 1}\\\Rightarrow x=\dfrac{4-2\sqrt {42}}{2}\\\Rightarrow x=2-\sqrt {42}[/tex]
So, the solution is:
[tex]x=2$\pm$\sqrt{42}[/tex]
Answer is A or the first one
Which of the x-values are solutions to the following inequality? 17 > x Choose all answers that apply: (A) x = 7 (B) x = 12 (C) x = 17
Answer:
7 and 12
Step-by-step explanation:
7 and 12 are ok
17 is not
hope this helps
The solution of the inequality x < 17 will be all the real numbers less than 17. Then the correct options are A and B.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The inequality is given below.
x < 17
The solution of the inequality x < 17 will be all the real numbers less than 17. Then the correct options are A and B.
More about the inequality link is given below.
https://brainly.com/question/19491153
#SPJ2
A chemist mixes 175 millilters of solution that is 62% acid with 75 milliliters of pure acid. What percentage of the resulting Mixture is acid
Answer:
73.4%
Step-by-step explanation:
The ratio of acid to mixture volume is ...
(0.62·175 +1.00·75)/(175 +75) = 183.5/250 = 0.734 = 73.4%
73.4% of the resulting mixture is acid.