Answer:
-1.031 m/s or [tex]\frac{-\sqrt{17} }{4}[/tex]
Step-by-step explanation:
We take the length of the rope from the dock to the bow of the boat as y.
We take x be the horizontal distance from the dock to the boat.
We know that the rate of change of the rope length is [tex]\frac{dy}{dt}[/tex] = -1 m/s
We need to find the rate of change of the horizontal distance from the dock to the boat = [tex]\frac{dx}{dt}[/tex] = ?
for x = 4
Applying Pythagorean Theorem we have
[tex]1^{2} +x^{2} =y^{2}[/tex] .... equ 1
solving, where x = 4, we have
[tex]1^{2} +4^{2} =y^{2}[/tex]
[tex]y^{2} = 17[/tex]
[tex]y = \sqrt{17}[/tex]
Differentiating equ 1 implicitly with respect to t, we have
[tex]2x\frac{dx}{dt} = 2y\frac{dy}{dt}[/tex]
substituting values of
x = 4
y = [tex]\sqrt{17}[/tex]
[tex]\frac{dy}{dt}[/tex] = -1
into the equation, we get
[tex]2(4)\frac{dx}{dt} = 2(\sqrt{17} )(-1)[/tex]
[tex]\frac{dx}{dt} = \frac{-\sqrt{17} }{4}[/tex] = -1.031 m/s
can I get a step by step explanation Thnx
Answer:
( 2A - kn) /k = m
Step-by-step explanation:
A = k/2(m+n)
Multiply each side by 2/k
2/k *A =2/k * k/2(m+n)
2A /k = m+n
Subtract n from each side
2A /k - n = m+n -n
2A /k - n = m
Getting a common denominator
2A/k - kn/k = m
( 2A - kn) /k = m
Answer:
Step-by-step explanation:
[tex]A=\frac{k(m+n)}{2}\\2A=k(m+n)\\\frac{2A}{k} =m+n\\\frac{2A}{k}-n=m\\2A-kn=km\\\frac{(2A-kn)}{k}=m[/tex]
A person has a bag containing dimes and nickels. There are a total of 106 coins in the bag, and the total value of coins is $7.90. How many dimes and nickels are in the bag?
Answer:
52 dimes and 54 nickels
Step-by-step explanation: 52 dimes is $5.20 and 54 nickels is $2.70
Total coins 106 total $7.90
Identify the reference angle ∅ for each given angle, 0.
Answer:
When Ø = 300°, Ø = 60 degrees.
When Ø = 225°, Ø = 45 degrees.
When Ø = 480°, Ø = 60 degrees.
When Ø = -210°, Ø = 30 degrees.
Step-by-step explanation:
Reference angles are in Quadrant I (0° to 90°).
1. Find 300° (Quadrant IV) on the unit circle. Since it's in Quadrant IV, you use 360 - 300 = 60° to get your answer.
2. Find 225° (Quadrant III) on the unit circle. Since it's in Quadrant III, you use 225 - 180 = 45° to get your answer.
3. The angle 480° is not on the unit circle. To find its corresponding angle between 0° and 360°, use 480 - 360 = 120°. Then, find 120° (Quadrant II) on the unit circle. Since it's in Quadrant II, you use 180 - 120 = 60° to get your answer.
4. The angle -210° is not on the unit circle. To find its corresponding angle between 0° and 360°, use -210 + 360 = 150°. Then, find 150° (Quadrant II) on the unit circle. Since it's in Quadrant II, you use 180 - 150 = 30° to get your answer.
kamau is now 2 years older than Jane if James age is y now what will be the total age in 10 years
Answer:
(2y + 22) years
Step-by-step explanation:
kamau is now 2 years older than Jane if Janes age is y now what will be the total age in 10 years.
Answer: If Jane is y years old now and Kamau is 2 years older than Jane, therefore the age of Kamau now would be 2 + y years.
In ten years time Jane age would be y + 10 years while the age of Kamau would be y + 2 + 10 = y + 12 years.
To get their total age we just have to add their individual age. Therefore the total age in 10 years = Age of Kamau in ten years + age of Jane in ten years = (y + 12) + (y + 10) = y + 12 + y + 10 = y + y + 12 + 10 = 2y + 22 years
PLEASE HELP----- T.A. =
Answer:
vol = 96
Step-by-step explanation:
Area of a triangle = 1/2 * b * h
b = 4
h = 6
A = 0.5 * 4 * 6
A = 12
length = 8
vol = Area * length
vol = 12 * 8
vol = 96
Answer:
(104 + 16 sqrt 13)
Step-by-step explanation:
i did this on my school, it was correct
Jessica’s plane and Kayla’s plane take off at the same time. Lauren’s plane leaves 1 hour earlier than Maria’s plane. Maria’s plane leaves at least 2 hours after Kayla’s plane. Each person flight last 8 hours. Maria’s flight lands at 4:45pm. What is the true statement?
Answer:
Step-by-step explanation:
From the given question, it can be concluded that Jessica and Kayla's planes took off an hour earlier than that of Lauren and at least two hours earlier than that of Maria. This implies that Maria's plane took off last among them.
Since each person's flight last 8 hours and Maria's plane lands at 4:45 pm, then Jessica and Kayla's planes land simultaneously at least at 2:45 pm. And that of Lauren lands exactly at 3:45 pm.
What is ∛2197? Explain how you got your answer.
Answer:
13
Step-by-step explanation:
We need to write our answer in exponential form. Ask yourself the question, "What times itself 3 times will give you 2197?" Your answer is [tex]13^{3}[/tex]. This will go inside of your cube root. You now have [tex]\sqrt[3]{13^{3} }[/tex]. Since there's a power of 3 and a cube root, those cancel each other out, and your answer is 13.
Answer:
[tex]\boxed{13}[/tex]
Step-by-step explanation:
=> [tex]\sqrt[3]{2197}[/tex]
Factorizing 2197 gives 13 * 13 * 13
=> [tex]\sqrt[3]{13*13*13}[/tex]
=> [tex]\sqrt[3]{13^3}[/tex]
We know that [tex]\sqrt[3]{} = ^{1/3}[/tex]
=> [tex]13^{3 * 1/3}[/tex]
=> [tex]13^1[/tex]
=> 13
A loudspeaker converts electrical energy into the kinetic energy of the speaker. This kinetic energy is transferred to air, and the motion of the air is the sound that people hear. An illustration of speaker with a wide arrow away from it labeled electrical energy 100 J and it splits into 3 arrows labeled sound energy 80 J, thermal energy ? J, and friction 5 J. How much thermal energy is put out by the speaker? 5 J 15 J 80 J 100 J
Answer:
15 J
Step-by-step explanation:
There is a total of 100 J of energy being used which is then converted into sound energy, thermal energy, and friction. This means the total amount must equal 100 J.
1. Set up the equation
80 + x + 5 = 100
2. Simplify
x + 85 = 100
3. Solve for x by subtracting 85 from both sides
x = 15
Answer:
The correct answer is 15J which is B.
Help ASAP!!!
A recursive sequence is a sequence where each term is found by adding a common difference
True or false
Answer:
True
Step-by-step explanation:
Given a rectangle with an area of 20 square units, if the width is x units and the length is x + 1 units, what is the difference between the length and the width?
Answer: 1unit.
Step-by-step explanation:
Area of the rectangle
A = length × width
Since the area = 20 and the width is x and the length is x + 1.
We now substitute for the values in the above formula and solve for x
20 = x × x + 1
20 = x( x + 1 ), we now open
20 = x² + x , then re arrange.
x² + x - 20 = 0, this is a quadratic equation.we solve for x using quadratic means
Here, I am going to solve using factorization by grouping
x² + x - 20 = 0
x² + 5x - 4x - 20 = 0
x( x + 5 ) - 4( x + 5 ) = 0
( x + 5 )( x - 4 ). = 0
Therefore, the solution for x will be
x = -5 or 4, but x can not be -5 ( negative), so x = 4.
Now the difference between width and the length can easily be calculated from the above,
Width = 4 (x) , and length = 5 (4 + 1),
Now difference will be
5 - 4 = 1unit.
What is x? The angle x
Answer:
x=60
Step-by-step explanation:
This is an equilateral triangle which means all the sides are equal.
If all the sides are equal then all the angles are equal
180/3 = 60
x=60
Answer:
x= 60°
Step-by-step explanation:
We can tell that both of these triangles are equilateral. We can tell because all of their sides have little tick marks, meaning that they are all equal, meaning that the triangle is equilateral. In an equilateral triangle, we know that through definitions all of the angles are equal to 60°. Since y is an angle inside of an equilateral triangle, it is equal to 60°
Solve of the following equations for x: 2 − x = −3
Answer:
x=5
Step-by-step explanation:
2 − x = −3
Subtract 2 from each side
2-2 − x = −3-2
-x = -5
Multiply by -1
x = 5
Dan is helpin Hazard tape needs to be placed all around the edge of the stage. Calculate the perimeter of the stage.6m-300cm-3.5m-12m
The correct answer is 24.5 m. You're given four different values but if you notice closely, not all the units match. Before you can add the values together, you need to get the same units. Because cm (centimeters) is the only one that's out of place, it will be easier to change it to m (meters). I think of centimeters as a century (same prefix) which equals 100. Therefore, to convert 300 cm to m, we will divide 300 by 100 to get 3. After that, add all the values together (6m+3m+3.5m+12m) to get a grand total of 24.5 m. I hope this helps!
The tape required to apply on the edge of the tape is 21.8m.
What is Perimeter?Perimeter is the sum of the length of the outer edges of a two-dimensional object.
A quadrilateral is a two-dimensional shape that is a polygon of four sides, one of the opposite sides of a quadrilateral is parallel.
Dan needs to apply tape on the edges of the stage, the tape required will be calculated by determining the perimeter of the stage.
The stage is in the shape of a quadrilateral.
The sides of the quadrilateral are as follows:
Side 1 = 6m
Side 2 = 300cm
Side 3 = 3.5m
Side 4 = 12m
300 cm will be converted into m
100 cm = 1m
300 cm = 0.3 m
The perimeter = Side 1 + Side 2 + Side 3+ Side 4
Perimeter = 6 + 0.3 +3.5 + 12
Perimeter = 21.8 m
The perimeter of the stage is 21.8m.
To know more about Perimeter
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If f(x) = 2x2 + 2 and g(x) = x2 – 1, find (f – 9)(X).
Answer:
x^2 +3
Step-by-step explanation:
f(x) = 2x^2 + 2
g(x) = x2 – 1,
find (f – g)(X).
f(x) - g(x) = 2x^2 + 2 -( x^2 – 1)
Distribute the minus sign
= 2x^2 +2 -x^2 +1
= x^2 +3
Find the value of x.
Answer:
[tex]\huge\boxed{x=\sqrt{21}}[/tex]
Step-by-step explanation:
ΔABD and ΔBCD are similar (AAA).
Therefore the corresponding sides are in proportion:
[tex]\dfrac{BD}{CD}=\dfrac{AD}{BD}[/tex]
Substitute
[tex]BD=x;\ CD=3;\ AD=7[/tex]
[tex]\dfrac{x}{3}=\dfrac{7}{x}[/tex] cross multiply
[tex](x)(x)=(3)(7)\\\\x^2=21\to x=\sqrt{21}[/tex]
perform the division...please!
Answer:
-7/3x + 3
Step-by-step explanation:
Answer:
(9x-7)/3x or (3-7/3x)
Step-by-step explanation:
Divide each term of numerator by denominator.
-28x^5/12x^6 +36x^6/12x^6
-7/3x +3
The Customer Service Center in a large New York department store has determined that the amount of time spent with a customer about a complaint is normally distributed, with a mean of 8.9 minutes and a standard deviation of 2.5 minutes. What is the probability that for a randomly chosen customer with a complaint, the amount of time spent resolving the complaint will be as follows. (Round your answers to four decimal places.)
The complete question is;
The Customer Service Center in a large New York department store has determined that the amount of time spent with a customer about a complaint is normally distributed, with a mean of 8.9 minutes and a standard deviation of 2.5 minutes. What is the probability that for a randomly chosen customer with a complaint, the amount of time spent resolving the complaint will be as follows. (Round your answers to four decimal places.)
(a) less than 10 minutes
(b) longer than 5 minutes
(c) between 8 and 15 minutes
Answer:
A) P (x < 10) = 0.6700
B) P (x > 5 ) = 0.9406
C) P (8.0000 < x < 15.0000) = 0.6332
Step-by-step explanation:
A) we are given;
Mean;μ = 8.9 minutes
Standard deviation;σ = 2.5 minutes
Normal random variable;x = 10
So to find;P(x < 10) we will use the Z-score formula;
z = (x - μ)/σ
z = (10 - 8.9)/2.5 = 0.44
From z-distribution table and Z-score calculator as attached, we have;
P (x < 10) = P (z < 0.44) = 0.6700
B) similarly;
z = (x - μ)/σ =
z = (5 - 8.9)/2.5
z = -1.56
From z-distribution table and Z-score calculator as attached, we have;
P (x > 5 ) = P (z > -1.56) = 0.9406
C)between 8 and 15 minutes
For 8 minutes;
z = (8 - 8.9)/2.5 = -0.36
For 15 minutes;
z = (15 - 8.9)/2.5 = 2.44
From z-distribution table and Z-score calculator as attached, we have;
P (8.0000 < x < 15.0000) = P (-0.36 < z < 2.44) = 0.6332
ian invested an amount of money at 3% per annum compound interest. At the end of 2 years the value of the investment was £2652.25 Work out the amount of money Ian invested.
Answer:
the amount of money Ian invested is P = £2,500
Step-by-step explanation:
The standard formula for compound interest is given as;
[tex]A = P(1+r/n)^{nt} \\P = \frac{A}{(1+r/n)^{nt}} ...........1\\[/tex]
Where;
A = final amount/value
P = initial amount/value (principal)
r = rate yearly
n = number of times compounded yearly.
t = time of investment in years
For this case, Given that;
A = £2652.25
t = 2 years
n = 1 (semiannually)
r = 3% = 0.03
substituting the given values into equation 1;
[tex]P = \frac{A}{(1+r/n)^{nt}} ...........1\\P = \frac{2652.25}{(1+0.03)^{2}} \\P = \frac{2652.25}{(1.03)^{2}} \\[/tex]
P = £2,500
the amount of money Ian invested is P = £2,500
Grace Kelley earns $2,000 per week. She is married and claims 2 exemptions. What is Grace’s income tax?
Answer:
$153
Step-by-step explanation:
Since she claimed two exemptions, Grace Kelly income's tax will only be $153, and $1847 being the yearly take home.
Effective tax rate is set at 7.65%
Solve the quadratic equation 4x2 – x = 8 using the quadratic formula.
Answer:
[tex]1x=\frac{1\sqrt{129} }{8}[/tex]
Step-by-step explanation:
In between the 1 and the [tex]\sqrt{129}[/tex] goes this symbol: ±
hope this helps!
please answer asap. there are two pics :)
Answer:
[tex]\boxed{\sf A. \ 0.34}[/tex]
Step-by-step explanation:
The first triangle is a right triangle and it has one acute angle of 70 degrees.
We can approximate [tex]\sf \frac{WY}{WX}[/tex] from right triangle 1.
The side adjacent to 70 degrees is WY. The side or hypotenuse is WX.
The side adjacent to 70 degrees in right triangle 1 is 3.4. The side or hypotenuse is 10.
[tex]\sf \frac{3.4}{10} =0.34[/tex]
Find the probability of each event. A gambler places a bet on a horse race. To win, he must pick the top three finishers in any order. Eight horses of equal ability are entered in the race. Assuming the horses finish in a random order, what is the probability that the gambler will win his bet?
Answer: [tex]\dfrac{1}{56}[/tex]
Step-by-step explanation:
Total horses = 6
Number of ways to choose top 3 finishers in order = 3! = 6
Number ways to select 3 horses out of 8 in order = [tex]^8P_3[/tex] [By permutations]
[tex]=\dfrac{8!}{(8-3)!}=\dfrac{8!}{5!}=8\times7\times6=336[/tex]
Now, the probability that the gambler will win his bet =
[tex]\dfrac{\text{Number of ways to choose top 3 finishers }}{\text{Number ways to select 3 horses out of 8 in order}}[/tex]
[tex]=\dfrac{6}{336}\\\\=\dfrac{1}{56}[/tex]
Hence, the required probability = [tex]\dfrac{1}{56}[/tex]
iv)
6x+3y=6xy
2x + 4y= 5xy
Answer:
Ok, we have a system of equations:
6*x + 3*y = 6*x*y
2*x + 4*y = 5*x*y
First, we want to isolate one of the variables,
As we have almost the same expression (x*y) in the right side of both equations, we can see the quotient between the two equations:
(6*x + 3*y)/(2*x + 4*y) = 6/5
now we isolate one off the variables:
6*x + 3*y = (6/5)*(2*x + 4*y) = (12/5)*x + (24/5)*y
x*(6 - 12/5) = y*(24/5 - 3)
x = y*(24/5 - 3)/(6 - 12/5) = 0.5*y
Now we can replace it in the first equation:
6*x + 3*y = 6*x*y
6*(0.5*y) + 3*y = 6*(0.5*y)*y
3*y + 3*y = 3*y^2
3*y^2 - 6*y = 0
Now we can find the solutions of that quadratic equation as:
[tex]y = \frac{6 +- \sqrt{(-6)^2 - 4*3*0} }{2*3} = \frac{6 +- 6}{6}[/tex]
So we have two solutions
y = 0
y = 2.
Suppose that we select the solution y = 0
Then, using one of the equations we can find the value of x:
2*x + 4*0 = 5*x*0
2*x = 0
x = 0
(0, 0) is a solution
if we select the other solution, y = 2.
2*x + 4*2 = 5*x*2
2*x + 8 = 10*x
8 = (10 - 2)*x = 8x
x = 1.
(1, 2) is other solution
Explain the relationship between variance and standard deviation. Can either of these measures be negative? Explain. Choose the correct answer below. A. The variance is the positive square root of the standard deviation. The standard deviation and variance can never be negative. Squared deviations can never be negative. B. The standard deviation is the positive square root of the variance. The standard deviation and variance can never be negative. Squared deviations can never be negative. C. The variance is the negative square root of the standard deviation. The variance can be negative but the standard deviation can never be negative. D. The standard deviation is the negative square root of the variance. The standard deviation can be negative but the variance can never be negative.
Answer:
A. The variance is the positive square root of the standard deviation. The standard deviation and variance can never be negative. Squared deviations can never be negative.
Step-by-step explanation:
As we know that
The standard deviation is the square root of the variance and on the other side the variance is the square of the standard deviation
In mathematically
[tex]\sigma = \sqrt{variance}[/tex]
And,
[tex]variance = \sigma^2[/tex]
Moreover, the standard deviation and the variance could never by negative neither the squared deviation is negative. All three are always positive
Hence, the correct option is a.
Answer:
B. The standard deviation is the positive square root of the variance. The standard deviation and variance can never be negative. Squared deviations can never be negative.
assume that the salaries of elementary school teachers in the united states are normally distributed with a mean of
mark wants to invest $10,000 for his daughter’s wedding. Some will go into a short term CD that pays 12% and the rest in a money market savings account that pays 5% interest. How much should he invest at Each rate if he wants to earn $1095.00 in interest in one year.
Which of the following is the correct name for below?
A.
Midsegment
B.
Perpendicular Bisector
C.
Angle Bisector
D.
Midpoint
Answer: B. Perpindicular Bisector.
Step-by-step explanation:
BD is a perpindicular bisector because it splits CE into 2 equal segments via a right angle.
Answer:
midsegement
Step-by-step explanation:
a survey was done Of 600 shoppers at a grocery store to determine if they like a new flavor Of potato chip. Of the 600 shoppers, 376 of them liked the new flavor. a) What percentage of the 600 shoppers liked the new flavor? Round your answer to the nearest percent. b) If 37.5% of the. 600 shoppers stated they would buy the new flavor, how many of the 600 would buy it?
Answer:
63%
225 buyers
Step-by-step explanation:
To find the percent take the number that liked it over the total
376/600
Change to decimal form
.62666666
Change to percent by multiplying by 100
62.66666666%
The nearest percent is 63%
37.5 % would but it then multiply by the number of shoppers
37.5 % ( 600)
Change to decimal form
.375 * 600
225
the value of 4^-1+8^-1÷1/2/3^3
Answer:
1.9375.
Step-by-step explanation:
To solve this, we must use PEMDAS.
The first things we take care of are parentheses and exponents.
Since there are no parentheses, we do exponents.
4^-1+8^-1÷1/2/3^3
= [tex]\frac{1}{4} +\frac{1}{8} / 1/ 2/ 27[/tex]
= 1/4 + (1/8) / 1 * (27 / 2)
= 1/4 + (27 / 8) / 2
= 1/4 + (27 / 8) * (1 / 2)
= 1/4 + (27 / 16)
= 4 / 16 + 27 / 16
= 31 / 16
= 1.9375.
Hope this helps!
College Calculus - hyperbolic functions (see attachment)
Answer:
g(x) = sinh^-1 ( ln(7x^6 +3) / sqrt( 8+cot( x^( 3+x))))
Step-by-step explanation:
Using the fundamental theorem of calculus
Taking the derivative of the integral gives back the function
Since the lower limit is a constant when we take the derivative it is zero
d/dx [tex]\int\limits^x_4 {g(t)} \, dt = g(x)[/tex]
g(t) = sinh^-1 ( ln(7t^6 +3) / sqrt( 8+cot( t^( 3+t))))
Replacing t with x
g(x) = sinh^-1 ( ln(7x^6 +3) / sqrt( 8+cot( x^( 3+x))))