You want to get from a point A on the straight shore of the beach to a buoy which is 54 meters out in the water from a point B on the shore. B is 70 meters from you down the shore. If you can swim at a speed of 5 meters per second and run at a speed of 7 meters per second, at what point along the shore, x meters from B, should you stop running and start swimming if you want to reach the buoy in the least time possible
Answers
Answer:
[tex]x =\dfrac{45 \sqrt{6}}{ 2}[/tex]
Step-by-step explanation:
From the given information:
The diagrammatic interpretation of what the question is all about can be seen in the diagram attached below.
Now, let V(x) be the time needed for the runner to reach the buoy;
∴ We can say that,
[tex]\mathtt{V(x) = \dfrac{70-x}{7}+\dfrac{\sqrt{54^2+x^2}}{5}}[/tex]
In order to estimate the point along the shore, x meters from B, the runner should stop running and start swimming if he want to reach the buoy in the least time possible, then we need to differentiate the function of V(x) and relate it to zero.
i.e
The differential of V(x) = V'(x) =0
=[tex]\dfrac{d}{dx}\begin {bmatrix} \dfrac{70-x}{7} + \dfrac{\sqrt{54^2+x^2}}{5} \end {bmatrix}= 0[/tex]
[tex]-\dfrac{1}{7}+ \dfrac{1}{5}\times \dfrac{x}{\sqrt{54^2+x^2}}=0[/tex]
[tex]\dfrac{1}{5}\times \dfrac{x}{\sqrt{54^2+x^2}}= \dfrac{1}{7}[/tex]
[tex]\dfrac{5x}{\sqrt{54^2+x^2}}= \dfrac{1}{7}[/tex]
[tex]\dfrac{x}{\sqrt{54^2+x^2}}= \dfrac{1}{\dfrac{7}{5}}[/tex]
[tex]\dfrac{x}{\sqrt{54^2+x^2}}= \dfrac{5}{7}[/tex]
squaring both sides; we get
[tex]\dfrac{x^2}{54^2+x^2}= \dfrac{5^2}{7^2}[/tex]
[tex]\dfrac{x^2}{54^2+x^2}= \dfrac{25}{49}[/tex]
By cross multiplying; we get
[tex]49x^2 = 25(54^2+x^2)[/tex]
[tex]49x^2 = 25 \times 54^2+ 25x^2[/tex]
[tex]49x^2-25x^2 = 25 \times 54^2[/tex]
[tex]24x^2 = 25 \times 54^2[/tex]
[tex]x^2 = \dfrac{25 \times 54^2}{24}[/tex]
[tex]x =\sqrt{ \dfrac{25 \times 54^2}{24}}[/tex]
[tex]x =\dfrac{5 \times 54}{\sqrt{24}}[/tex]
[tex]x =\dfrac{270}{\sqrt{4 \times 6}}[/tex]
[tex]x =\dfrac{45 \times 6}{ 2 \sqrt{ 6}}[/tex]
[tex]x =\dfrac{45 \sqrt{6}}{ 2}[/tex]
Related Questions
What is the answer of this question I don’t know what it is
Answers
Calculate the principal if the maturity value is $4,500 and the simple interest is $350.
Answers
Answer:
The principal is $4,150.
Step-by-step explanation:
We have to find the principal if the maturity value is $4,500 and the simple interest is $350.
As we know that the formula for calculating the final amount or maturity amount is given by;
Amount = Principal + Interest
Here, Simple interest = $350
Amount or Maturity value = $4,500
So, the Principal = Amount - Interest
Principal = $4,500 - $350
= $4,150
Hence, the principal if the maturity value is $4,500 and the simple interest is $350 is $4150.
What happens to the value of the expression 35 + kas k decreases?
Choose 1 answer:
A
It increases.
B
It decreases.
It stays the same.
Answers
Answer:
a i think
Step-by-step explanation:
Answer:
(B) It decreases
Step-by-step explanation:
I figured this out with basic logic, but we can use proof to find it out.
If we have [tex]35+k[/tex], we can assume that k is around 10.
So [tex]35+10=45[/tex].
Now let's decrease k by 1, making k=9.
[tex]35+9=44[/tex]
We can see that the value is decreasing, but let's try one more.
Let's make k=8.
[tex]35+8=43[/tex]
So we can see the general pattern here is that it's decreasing.
Hope this helped!
A family lives in a large tower apartment building, 10 floors high. Every day their son takes the elevator from the family’s apartment on the 10th floor to the ground floor and goes to school. When he returns in the afternoon, he uses the elevator to get to the fifth floor, and then uses the stairs for the remaining five floors. Why?
Answers
Answer:
Step-by-step explanation:
Considering that the question is a fun riddle, I will give a suitable fun answer.
The question says that the son goes to school, so we can assume that the boy is a young child. So, he is probably short.
So, while getting down the stairs, it is easy for him to press the button in the elevator to reach the ground floor as the button for ground floor is the on the bottom of the switch panel.
However, since he is short he cannot reach the button for the 10th floor after returning from school. He can only reach up to the button for the 5th floor. So, he travels up to the 5th floor by the elevator and from there he takes the stairs to reach the 10th floor.
If 4x – 3 = 2x + 9, then x = ?
Answers
Answer:
x=6
Step-by-step explanation:
subtract the 2x from 4x and add 3 to 9. we would get 2x=12. divide by 2 on both sides and you get x=6!
What is the slope of the line that goes through the points (1,-5) and (4,1)?
Answers
Answer:
D. 2
Step-by-step explanation:
(1 - -5)/(4 - 1) = 6/3 = 2
Answer: 2
Step-by-step explanation:
The slope of a line through two points (x₁, y₁) and (x₂, y₂) is given by (y₂ - y₁)/(x₂ - x₁). In this case, x₁ = 1, y₁ = -5, x₂ = 4, and y₂ = 1. So the slope is:
(1 - (-5))/(4 - 1) = 6/3 = 2
Which undefined geometric term is described as a two-dimensional set of points that has no beginning or end? a;line b;distance c;plane
Answers
Answer:
I believe that it is a line, since a line is infinite
Step-by-step explanation:
he highest elevation in a country is a mountain, with an altitude of 14,309feet. The lowest elevation in the country is a valley, with an altitude of 288 feet below sea level.
Answers
Answer:
Diffrent between altitude = 14,021 ft
Step-by-step explanation:
Given:
Heighest altitude = 14,309 ft
Lowest altitude = 288 ft
Find:
Diffrent between altitude
Computation:
Diffrent between altitude = Heighest altitude - Lowest altitude
Diffrent between altitude = 14,309 - 288
Diffrent between altitude = 14,021 ft
John buys a new set of golf clubs for $757.75, including tax. If the sales tax rate is 8.25%, then what is the cost of the set of golf clubs? How much did he pay in tax?
Answers
Answer: Total cost: $820.26 Paid in tax: $62.51
Step-by-step explanation:
First you have to get the Tax. Since the Tax is 8.25% MOVE the decimal 2 spots to the right so now it is 0.0825.
Multiply 0.0825 by 757.75 you will get 62.514375.
Dont get scared of the big number simply simplify and you get the tax.
if you want the total he paid add tax and original cost.
Question 1
H
Write the slope intercept form for the equation of the line.
Do not leave spaces in your equation and do not use the WIRIS editor to enter you
Answers
Answer:
x=3
Step-by-step explanation:
slope: (y² - y¹) / (x² - x¹)
(3, 0) & (3, 1)
(1 - 0) / (3 - 3) = 1 / 0
undefined = vertical line
The equation for the line of best fit relating the weight of a child in kilograms y in relation to the child's age in years x. Which of the following
statements is true?y = 3x +3.25
O A The average weight in kilograms is 3 times the age.
OB. The average weight in kilograms is 3 times the height
O C. The average child is 3 years old.
D. The average child weighed 3.25 kg at birth.
Answers
Answer: D
Step-by-step explanation:
It is D because using the equation y=3x +3.25 you can see that the y intercept is 3.25 which means in zero years the child will weigh 3.25 or weighs 3.25 kg at birth.
(20 points) A statistics practitioner calculated the mean and the standard deviation from a sample of 400. They are x = 98 and s = 20: (a) Compute the p-value in order to test H0 : = 100 against H1 : 6= 100: (b) Compute the p-value in order to test H0 : = 100 against H1 : > 100:
Answers
Answer:
The P-value is 0.0234.
Step-by-step explanation:
We are given that a statistics practitioner calculated the mean and the standard deviation from a sample of 400. They are x = 98 and s = 20.
Let [tex]\mu[/tex] = population mean.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 100 {means that the population mean is equal to 100}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > 100 {means that the population mean is more than 100}
The test statistics that will be used here is One-sample t-test statistics because we don't know about population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean = 98
s = sample standard deviation = 20
n = sample size = 400
So, the test statistics = [tex]\frac{98-100}{\frac{20}{\sqrt{400} } }[/tex] ~ [tex]t_3_9_9[/tex]
= -2
The value of t-test statistics is -2.
Now, the P-value of the test statistics is given by;
P([tex]t_3_9_9[/tex] < -2) = 0.0234 {using the t-table}
The surface area of a sphere is 4πr^2 A sphere has a radius (r) that measures 3cm
Use π= 3.142 or 22/7 . Work out the surface area of the sphere to the nearest cm^2
Answers
Answer:
113cm²
Step-by-step explanation:
Area = 4 π r²
= 4 * 3.142 * 3²
= 113.112 cm²
The triangular figures shown below are constructed with toothpicks. The pattern shows what happens with 1 triangle, with 2 triangles, and with 3 triangles. Describe a possible pattern. Assuming the pattern continues, answer the following questions. How many toothpicks would be needed for the 10th figure? How many toothpicks are needed for the nth figure? In which figure are exactly 102 toothpicks used?
Answers
Answer:
(a) 51
(b) [tex]T_{n}=a+(n-1)d[/tex]
(c) 20th figure
Step-by-step explanation:
The diagram is attached below.
The first triangle is formed using 6 toothpicks.
The second triangle is formed using 11 toothpicks.
The third triangle is formed using 16 toothpicks.
So, there is an increases of 5 toothpicks every time.
We can say that the number of toothpicks used to form n triangles are following an arithmetic progression with the first term as 6 and the common difference as 5.
The nth term will be:
[tex]T_{n}=a+(n-1)d[/tex]
(a)
Compute the number of toothpicks required for the 10th figure as follows:
[tex]T_{n}=a+(n-1)d[/tex]
[tex]T_{10}=6+(10-1)\times5[/tex]
[tex]=6+(9\times5)\\=6+45\\=51[/tex]
Thus, the number of toothpicks required for the 10th figure is 51.
(b)
Compute the number of toothpicks required for the nth figure as follows:
[tex]T_{n}=a+(n-1)d[/tex]
(c)
Compute the value of n for [tex]T_{n}=102[/tex] as follows:
[tex]T_{n}=102[/tex]
[tex]a+(n-1)d=102\\\\[/tex]
[tex]6+(n-1)\times 5=102[/tex]
[tex]5(n-1)=96[/tex]
[tex]n-1=19.2[/tex]
[tex]n=20.2\\n\approx 20[/tex]
Thus, the 20th figure will require exactly 102 toothpicks.
Evaluate 2x+(x−y2) when x=8 and y=2
Answers
Answer:
20.
Step-by-step explanation:
2x + x - y^2; x = 8 and y = 2.
2(8) + 8 - (2)^2
= 16 + 8 - 4
= 24 - 4
= 20.
Hope this helps!
Answer:
= 20
Step-by-step explanation:
2x + (x - y²)
x = 8
y = 2
then:
2*8 + (8 - 2²)
= 16 + (8 - 4)
= 16 + 4
= 20
Help! need the answer
Answers
Answer:
D. (f - g)(x) = 4x^3 + 7x^2 - 6x + 1
Step-by-step explanation:
You need to subtract g(x) from f(x).
(f - g)(x) = f(x) - g(x) =
= 4x^3 + 7x^2 - 2x - 1 - (4x - 2)
Distribute the negative sign at the left of the parentheses as you would distribute a -1. Every sign inside the parentheses changes.
= 4x^3 + 7x^2 - 2x - 1 - 4x + 2
Combine like terms.
= 4x^3 + 7x^2 - 6x + 1
Answer: D. (f - g)(x) = 4x^3 + 7x^2 - 6x + 1
Answer:
4x^3+7x^2-6x+1
Step-by-step explanation:
f(x) = 4x^3 +7x^2 -2x-1
g(x) = 4x-2
f(x) - g(x) = 4x^3 +7x^2 -2x-1 - ( 4x-2)
Distribute the minus sign
4x^3 +7x^2 -2x-1 - 4x+2
Combine like terms
4x^3+7x^2-6x+1
If CB=2x+5 and DE=10, find the value of x
Answers
Step-by-step explanation:
see the attachment......
Answer:
[tex]x=4[/tex]
Step-by-step explanation:
We are given that:
[tex]CB=2x+5[/tex]
And that DE = 10. We want to determine the value of x.
Note that CB is the sum of CD and DB. In other words:
[tex]CB=CD+DB[/tex]
Similarly, DE is the sum of DB and BE. Thus:
[tex]DE=DB+BE[/tex]
From the second equation, we can subtract BE from both sides:
[tex]DE-BE=DB[/tex]
Substitute this into the first equation:
[tex]CB=CD+(DE-BE)[/tex]
We are given that CB is 2x + 5 and DE is 10.
From the diagram, we can also see that CD is 3x - 1 and BE is 8.
Substitute:
[tex](2x+5)=(3x-1)+((10)-(8))[/tex]
Solve for x:
[tex]\displaystyle \begin{aligned}(2x+5) & = (3x-1) + (2) \\ \\ 2x + 5 & = 3x + 1 \\ \\ -x + 5 & = 1 \\ \\ - x & = -4 \\ \\ x & = 4 \end{aligned}[/tex]
In conclusion, the value of x is 4.
The Bessel function or order zero of the first kind may be defined by. Find the radius of convergence of J0(x).
Answers
Answer:
Step-by-step explanation:
The Bessel function or order zero of the first kind may be defined by the solution - to Bessel's differential equation - which is a finite value at the origin X=0 for positive or negative whole numbers (integers) or positive alpha (α) values.
the value of all things needed to create the product
Answers
Answer:
All of the functions required to transform inputs into outputs (goods and ... provide all of the materials and supplies required to create finished products and deliver ... System for determining the right quantity of various items to have on hand
Step-by-step explanation:
find pricipal when amount is rupee 4624 at6% and two yrs time ....
Answers
Answer:
Rs. 4128.57
Step-by-step explanation:
Given:
Principal = xAmount after 2 yrs = Rs. 4624Rate = 6% PASolving for x:
x + 2*6% of x = 4624x + x*12%/100 = 4624x*1.12 = 4624x= 4624/1.12x≈ 4128.57Ms. Maitner and Mr. Grote play each other in FIFA on Xbox 360. They score a total of 74 points. If Ms. Maitner scores 16 more points than Mr. Grote, what is the final score?
Answers
Answer:
Mr. Grote: 29, Ms. Maitner: 45
Step-by-step explanation:
x = number of points Mr. Grote scored
x + 16 = number of points Ms. Maitner scored
x + x + 16 = 74
x + x = 58
2x = 58
x = 29
29 + 16 = 45
The grade point averages for 10 randomly selected students in an algebra class with 125 students are listed below. What is the effect on the width of the confidence interval if the sample size is increased to 20?
Answers
Answer:
width of the confidence interval decreases if the sample size is increased to 20.
Step-by-step explanation:
There are some factors which affect the width of the confidence interval such as:
The decrease in the sample standard deviation decreases the width of the interval .
The decrease the confidence level decreases the width of the interval .
The increase in the sample size decreases the width of the interval .
In the given question the previous sample size was 10 which was then increased to 20. So this increase in sample size causes the confidence interval to decrease. This is because when sample size increases, it decreases the standard error. This interprets that the sample size is getting closer to true population size.
Write two related division statements for : -6 x (-7) = 42
Answers
Answer:
42÷(-6). 42÷(-7).
Step-by-step explanation:
Is this what you want?
The following table shows the number of snow days each school district in Mill County had last winter. School District District 200200200 District 211211211 District 221221221 District 231231231 District 241241241 Number of snow days 666 888 333 222 666 Find the mean absolute deviation (MAD) of the data set. snow days
Answers
Answer:
DIstrict 241 had 4 snow days.
Step-by-step explanation:
5 * 5 = 25
Add the ones you know
4 + 8 + 3 + 6 = 21
Then
25 - 21 = 4
So District 241 had 4 snow days.
I know this answer is 100% correct. I answered it correctly. This problem wasn't that hard. Let me know if you need help with anything else.
The number of snow days of District 241 are 4.
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
We have to find the number of snow days of District 241
School District District201 District211 District221 District231 District 241
Number of 4 8 3 6 ?
snow days
Mean of snow days is 5.
Mean =Sum of observations/Number of observations
5=4+8+3+6+x/5
25=21+x
Subtract 21 from both sides
x=4
Hence, the number of snow days of District 241 are 4.
To learn more on Statistics click:
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Find the missing probability. P(A)=25,P(B|A)=920,P(A∩B)=?
Answers
Assuming you meant to say P(A) = 2/5 and P(B|A) = 9/20, then,
P(A∩B) = P(A)*P(B|A)
P(A∩B) = (2/5)*(9/20)
P(A∩B) = (2*9)/(5*20)
P(A∩B) = (2*9)/(5*2*10)
P(A∩B) = 9/(5*10)
P(A∩B) = 9/50 is the answerThe required probability P( A ∩ B ) = 2300.
To find the missing probability. P( A ) = 25, P( B | A ) = 920, P( A∩ B) = ?
What is probability?Probability can be defined as the ratio of favorable outcomes to the total number of events.
From properties of probability
P( A ∩ B ) / P(A) = P( B | A )
P( A ∩ B) = P( B | A ) . P(A)
From given
P( A ) = 25, P( B | A ) = 920
P( A ∩ B ) = P( B | A ) . P(A)
P( A ∩ B ) = 920 . 25
P( A ∩ B ) = 2300
Thus, the required probability P( A ∩ B ) = 2300 for P( A ) = 25, P( B | A ) = 920.
Learn more about probability here:
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What is the value of the slope of a line with the equation: 20-5x?
Answers
Answer:
-5
Step-by-step explanation:
the slope is the variable in front of the x
If EF = 4x + 15 and FG = 39 and EG = 110. Find the value of EF.
Answers
Answer:
EF + FG = EG Plug in the given values
4x + 15 + 39 = 110 Combine like terms (15 and 39)
4x + 54 = 110 Subtract 54 from both sides
4x = 56 Divide both sides by 4
x = 14
the equation of a circle whose center is at (1, 2) and radius is 5 is
Answers
Answer:
(x − 1)² + (y − 2)² = 25
Step-by-step explanation:
Equation of a circle is (x − h)² + (y − k)² = r², where (h, k) is the center and r is the radius.
PLEASE HELP AND PLEASE MAKE IT BE CORRECT!!!!
5.5 Scaling a
Rectangle
A rectangle that is 2 inches by 3 inches has been scaled by a
factor of 7.
1. What are the side lengths of the scaled
copy?
2.Suppose you want to scale the copy back to it’s original size.What scale factor should you use?
Answers
Answer:
1) 14 by 21
2)7
Step-by-step explanation:
i Dint do the complete work i am not sure.
The side lengths of the scaled copy would be 14 by 21 and If you want to scale the copy back to its original size then you should use a scale factor that would be 1/7.
What is a scale image?Scale image is defined as a ratio that represents the relationship between the shape and size of a figure and the corresponding dimensions of the actual figure or object.
A rectangle that is 2 inches by 3 inches has been scaled by a factor of 7 which is given in the question.
As we know scale factor is the ratio of sides in the original image and the image after dilation.
So the side lengths of the scaled copy would be 14 by 21
If you want to scale the copy back to its original size
Therefore, you should use a scale factor that would be 1/7.
Learn more about the Scale images here:
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what is the difference between a repeating decimal and a terminating decimal
Answers
Step-by-step explanation:
Terminating decimals: these have a finite number of digits after the decimal point.
Example: 9.5
Recurring decimals: these have one or more repeating numbers or sequences of numbers after the decimal point, which continue infinitely.
Example: 0.333333...