Answer: the intersection point is (2.4, -4.8)
Step-by-step explanation:
A) we have the function:
y = 0.5*x - 6.
First we want to know if this function intersects the line y´ = -1.5*x
Now, first we can recall that two lines are parallel only if the slope is the same for both lines, here we can see that the slopes are different, so the lines are not parallel, which means that the lines must intersect at some point.
Now, to find the intersection point we asumme y = y´ and want to find the value of x.
0.5*x - 6 = -1.5*x
(0.5 + 1.5)*x - 6 = 0
2.5*x = 6
x = 6/2.5 = 2.4
Now, we evaluate one of the functions in this value of x.
y = 0.5*2.4 - 6 = -4.8
So the intersection point is (2.4, -4.8)
Solve for X. pls help asap
Answer:
x=3
Step-by-step explanation:
Use the Pythagorean Theorem to write an equation.
x^2+y^2=z^2
Substitute values from the problem.
x^2 + 6^2 = 9^2
Solve for what you know.
x^2 + 36 = 81
Square root it.
x+6=9
Subtract 6 from both sides.
x=3
In the future, if you see a right triangle with an unknown side, and the other two sides are either 3, 6, or 9, you know that the other one is the missing value out of 3/6/9. This is called a 3/6/9 triangle.
Answer:
6.7Step-by-step explanation:
Hypotenuse (h) = 9
base (b) = X
Perpendicular (p) = 6
Now,
Using Pythagoras theorem:
[tex] {h}^{2} = {p}^{2} + {b}^{2} [/tex]
[tex] {b}^{2} = {h}^{2} - {p}^{2} [/tex]
[tex] {b}^{2} = {(9)}^{2} - {(6)}^{2} [/tex]
[tex] {b}^{2} = 81 - 36[/tex]
[tex] {b}^{2} = 45[/tex]
[tex]b = \sqrt{45} [/tex]
[tex]b = 6.7[/tex]
Hope this helps...
Good luck on your assignment..
After Keith picked 9 lemons, he wanted to share them with his fellow classmates. If Keith wants to give 1 1/8 lemons to each of his classmates, then how many classmates will get some lemon?
Answer:
8 classmates
Step-by-step explanation:
[tex]9/1\frac{1}{8}=\\9/\frac{9}{8}=\\9*\frac{8}{9}=\\\frac{72}{9}=\\8[/tex]
Solve for x. please help me its urgent
Answer:
x = 25
Step-by-step explanation:
The sum of the angles of a quadrilateral are 360 degrees
3x+x+10 + 4x+6x = 360
Combine like terms
14x+10 = 360
Subtract 10 from each side
14x +10-10 = 360-10
14x = 350
Divide each side by 14
14x/14 = 350/14
x = 25
Identify the value of the TEST STATISTIC used in a hypothesis test of the following claim and sample data:
Claim: "The average battery life (between charges) of this model of tablet is at least 12 hours."
A random sample of 80 of these tablets is selected, and it is found that their average battery life is 11.58 hours with a standard deviation of 1.93 hours. Test the claim at the 0.05 significance level.
a. -0.218
b. -1.645
c. -1.946
d. -1.667
Answer:
-1.946 ; C
Step-by-step explanation:
Here, we want to identify the value of the z-statistic
Mathematically;
z = (x -mean)/SD/√n
Thus we have ;
Z = (11.58-12)/1.93/√80
z = -1.946
Brainliest for the correct awnser!!! In general, when solving a radical equation with square roots, you should first isolate the radical and then _____ both sides.A.addB.squareC.multiplyD.subtract
Answer:
B
Step-by-step explanation:
Answer:
The answer for this Question is Elementary
It is B.
What’s this? I’m stuck!
Answer:
68 degrees
Step-by-step explanation:
Y=56,
56+56=112
180-112=68
Hope this helps, if you have any other questions, feel free to ask me to explain more
Have a good day! :)
URGENT)
In the figure, ABCDE is a regular pentagon and DEFG is a square. CD
produced and GF intersect at H. Find x.
Answer:
108 degrees
Step-by-step explanation:
angle CDE is 108 degrees, which is supplementary to angle EDH, so EDH must be 72 degrees
then put it into an equation
90+90+72+x=360
solve
x=108
Answer:
The answer is 108
Find the area of the kite below. POSSIBLE ANSWERS: 168 mm 2 or 216 mm 2 or 195 mm 2 or 228 mm 2
Answer:
168 mm²
Step-by-step explanation:
Let A be the area of this shape
the kite is made of two triangles
Let A' and A" be the areas of the triangles
let's calculate A' and A" :
The area of a triangle is the product of the base and the height over 2
A' = [tex]\frac{(12+12)*5}{2}[/tex] = 60 mm² A"= [tex]\frac{(12+12)*9}{2}[/tex] = 108 mm²Let's calculate A
A = A' + A" A = 108+ 60 A = 168 mm²A sample of 26 offshore oil workers took part in a simulated escape exercise, resulting in the accompanying data on time (sec) to complete the escape.
389 357 359 364 375 424 326 395 402 373
374 371 365 367 365 326 339 393 392 369
374 359 357 403 335 397
A normal probability plot of the n 26 observations on escape time given above shows a substantial linear pattern; the sample mean and sample standard deviation are 371.08 and 24.45, respectively. (Round your answers to two decimal places.)
Required:
a. Calculate an upper confidence bound for population mean escape time using a confidence level of 95%.
b. Calculate an upper prediction bound for the escape time of a single additional worker using a prediction level of 95%.
Answer:
The upper confidence bound for population mean escape time is: 379.27
The upper prediction bound for the escape time of a single additional worker is 413.64
Step-by-step explanation:
Given that :
sample size n = 26
sample mean [tex]\bar x[/tex] = 371.08
standard deviation [tex]\sigma[/tex] = 24.45
The objective is to calculate an upper confidence bound for population mean escape time using a confidence level of 95%
We need to determine the standard error of these given data first;
So,
Standard Error S.E = [tex]\dfrac{\sigma }{\sqrt{n}}[/tex]
Standard Error S.E = [tex]\dfrac{24.45 }{\sqrt{26}}[/tex]
Standard Error S.E = [tex]\dfrac{24.45 }{4.898979486}[/tex]
Standard Error S.E = 4.7950
However;
Degree of freedom df= n - 1
Degree of freedom df= 26 - 1
Degree of freedom df= 25
At confidence level of 95% and Degree of freedom df of 25 ;
t-value = 1.7080
Similarly;
The Margin of error = t-value × S.E
The Margin of error = 1.7080 × 4.7950
The Margin of error = 8.18986
The upper confidence bound for population mean escape time is = Sample Mean + Margin of Error
The upper confidence bound for population mean escape time is = 371.08 + 8.18986
The upper confidence bound for population mean escape time is = 379.26986 [tex]\approx[/tex] 379.27
The upper confidence bound for population mean escape time is: 379.27
b. Calculate an upper prediction bound for the escape time of a single additional worker using a prediction level of 95%.
The standard error of the mean = [tex]\sigma \times \sqrt{1+ \dfrac{1}{n}}[/tex]
The standard error of the mean = [tex]24.45 \times \sqrt{1+ \dfrac{1}{26}}[/tex]
The standard error of the mean = [tex]24.45 \times \sqrt{1+0.03846153846}[/tex]
The standard error of the mean = [tex]24.45 \times \sqrt{1.03846153846}[/tex]
The standard error of the mean = [tex]24.45 \times 1.019049331[/tex]
The standard error of the mean = 24.91575614
Recall that : At confidence level of 95% and Degree of freedom df of 25 ;
t-value = 1.7080
∴
The Margin of error = t-value × S.E
The Margin of error = 1.7080 × 24.91575614
The Margin of error = 42.55611149
The upper prediction bound for the escape time of a single additional worker is calculate by the addition of
Sample Mean + Margin of Error
= 371.08 + 42.55611149
= 413.6361115
[tex]\approx[/tex] 413.64
The upper prediction bound for the escape time of a single additional worker is 413.64
Function f is shown on the graph below where two points are marked. If function f is horizontally compressed by a factor of 2, plot the two corresponding points that would lie on the transformed function.
Answer:
If you have
[tex]f(x) = x^2[/tex]
The point (2,4) would be transformed to (1,1)
Step-by-step explanation:
If your compression is horizontal then the transformation you are making is the following
[tex]g(x) = f(x/2)[/tex]
Therefore, if you have
[tex]f(x) = x^2[/tex]
The point (2,4) would be transformed to (1,1)
What is the measure of ∠BCD?
Answer: 77 degrees
Step-by-step explanation:
interior angles on the same side of transversal are supplementary. Thus,
103+x=180
x = 77
Hope it helps <3
Answer:
Hey there!
This is a parallelogram, and we have the angles next to each other add to 180 degrees. Angle ABC+Angle BCD=180
103+x=180
x=77
BCD=77 degrees.
Let me know if this helps :)
If the wavelength of the violet color is 400 nm, what is the value of its frequency?
Hi there! Hopefully this helps!
-------------------------------------------------------------------------------------------------- The frequency is ~7.5*1014 Hz
Since visible light has a wavelength spectrum of ~400 nm to ~700 nm, Violet light has a wavelength of ~400 nm and a frequency of ~7.5*1014 Hz.
Step-by-step explanation:
Speed = wavelength × frequency
3×10⁸ m/s = (400×10⁻⁹ m) f
f = 7.5×10¹⁴
Ashley has 500 songs in his music player. Every week he adds 10 songs to his collection. How many songs will he have in his music player after 20 weeks ?
At the end of n weeks, the number of songs is given by the function
f(n) =500 +10n
Or
f(n) = 10 +20b
The output of the function is 700
or
600
when the input is 20.
Answer:
700
Step-by-step explanation:
500+10*20=700
it's f(n) = 500+10n
1. What are the formulas that help determine the equation of a circle? 2. How are the center, radius and a point on the circle expressed algebraically? 3. What do you need to know in order to use the ellipse equation formulas?
Answer: see below
Step-by-step explanation:
1) The equation of a circle is: (x - h)² + (y - k)² = r² where
(h, k) represents the center of the circler represents the radius of the circle.2) If you are given a point on the circle and the center (h, k)
you can input those points into the equation of a circle to find r².
Then input (h, k) and r² to identify the equation of that particular circle.
3) If you divide each term in the equation of a circle by r², you will get:
[tex]\dfrac{(x-h)^2}{r^2}+\dfrac{(y-k)^2}{r^2}=1[/tex]
(h, k) is the center of the circler is the x-radius and y-radiusThe difference between a circle and an ellipse is that an ellipse is in the shape of an oval. In other words, the x-radius and y-radius are different.
The equation of an ellipse is:
[tex]\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2}=1[/tex]
(h, k) is the center of the ellipsea is the x-radiusb is the y-radiusA pile of 55 coins consisting of nickels and dimes is worth $3.90 . Find the number of each. PLZ ANSWER IN 1 MIN
Answer:
23 dimes; 32 nickel
Step-by-step explanation:
Let n = number of nickels.
Let d = number of dimes.
A nickel is worth $0.05; n nickels are worth 0.05n.
A dime is worth $0.10; d dimes are worth 0.1d.
Number of coins:
d + n = 55
Value of the coins:
0.1d + 0.05n = 3.9
Solve d + n = 55 for d:
d = 55 - n
Substitute 55 - n for d in second equation.
0.1(55 - n) + 0.05n = 3.9
5.5 - 0.1n + 0.05n = 3.9
-0.05n = -1.6
n = 32
Substitute 32 for n in d + n = 55 and solve for d.
d + 32 = 55
d = 23
Answer: 23 dimes; 32 nickel
Question 3
Which of the following best describes the solution to the system of equations below?
-6x + y=-3
7x-y=3
The system of equations has exactly one solution where x = 6 and y = 3.
The system of equations has no solution.
The system of equations has infinitely many solutions.
The system of equations has exactly one solution where x = 0 and y=
-3
Answer:
The system has exactly one solution where x = 0 and y = -3.
Step-by-step explanation:
-6x + y = -3
7x - y = 3
(7x - 6x) + (y - y) = 3 - 3
x + 0 = 0
x = 0
7(0) - y = 3
0 - y = 3
-y = 3
y = -3
-6(0) + y = -3
0 + y = -3
y = -3
So, the system has exactly one solution where x = 0 and y = -3.
Hope this helps!
RVLC2019] IC/Off
In AMNO, m = 20, n = 14, and mZM = 51°. How many distinct triangles can be formed given these measurements?
O There are no triangles possible.
VX
O There is only one distinct triangle possible, with m N= 33º.
O There is only one distinct triangle possible, with mZN 147º.
O There are two distinct triangles possible, with m2N 33° or mZN-147º.
Done
) Intro
DO
There is only one distinct triangle possible, with m N= 33º. Therefore, option B is the correct answer.
What is sine rule?Law of Sines In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of any triangle to the sines of its angles.
The formula for sine rule is sinA/a=sinB/b=sinC/c
Given that, in ΔMNO, m = 20, n = 14, and m∠M = 51°.
Now, sin51°/20=sinN/14
0.7771/20=sinN/14
0.038855=sinN/14
sinN=14×0.038855
sinN=0.54397
N=33°
Therefore, option B is the correct answer.
Learn more about the sine rule here:
https://brainly.com/question/22288720.
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Find the value(s) of c guaranteed by the Mean Value Theorem for Integrals for the function over the given interval. (Round your answer to four decimal places. Enter your answers as a comma-separated list.)
f(x)=5√x,[4,9]
Answer:
25/4Step-by-step explanation:
The mean value theorem for integrals for the function f(c) over a given interval [a, b] is expressed as g prime(c) = g(b) - g(a)/b-a. The idea is that there is a value c in between the interval [a, b] for the function given.
Given the function g(x) = 5√x within the interval [4,9]
g prime (c) = g(9) - g(4)/9-4
g(9) = 5√9
g(9) = 5*3 = 15
g(4) = 5√4
g(4) = 5*2 = 10
g prime c) = 15-10/9-4
g prime (c) = 5/5
g prime(c) = 1
So we are to find the number for which g prime (x) = g prime(c)
If g(x) = 5√x = [tex]5x^{1/2}[/tex]
g prime (x) = [tex]5/2 \ x^{-1/2}[/tex]
g prime (x) = 5/2√x
Since g prime (c) = 1 then;
5/2√x = 1
5 = 2√x
√x = 5/2
x = (5/2)²
x = 25/4
The value of c guaranteed by the mid value theorem is 25/4
The possible value of c for [tex]\mathbf{f(x) = 5\sqrt x\ [4,9]}[/tex] is 6.25
The function is given as:
[tex]\mathbf{f(x) = 5\sqrt x\ [4,9]}[/tex]
Calculate f(4) and f(9)
[tex]\mathbf{f(4) = 5\sqrt 4 = 10}[/tex]
[tex]\mathbf{f(9) = 5\sqrt 9 = 15}[/tex]
Substitute c for x in f(x)
[tex]\mathbf{f(c) = 5\sqrt c }[/tex]
Calculate f'(c)
[tex]\mathbf{f'(c) = \frac{f(b) - f(a)}{b - a}}[/tex]
So, we have:
[tex]\mathbf{f'(c) = \frac{f(9) - f(4)}{9 - 4}}[/tex]
[tex]\mathbf{f'(c) = \frac{f(9) - f(4)}{5}}[/tex]
This gives
[tex]\mathbf{f'(c) = \frac{15 -10 }{5}}[/tex]
[tex]\mathbf{f'(c) = \frac{5 }{5}}[/tex]
[tex]\mathbf{f'(c) = 1}[/tex]
Also, we have:
[tex]\mathbf{f'(x) = \frac 52x^{-1/2}}[/tex]
Substitute c for x
[tex]\mathbf{f'(c) = \frac 52c^{-1/2}}[/tex]
Substitute 1 for f'(c)
[tex]\mathbf{\frac 52c^{-1/2} = 1}[/tex]
Multiply through by 2/5
[tex]\mathbf{c^{-1/2} = \frac 25}[/tex]
This gives
[tex]\mathbf{c^{1/2} = \frac 52}[/tex]
Square both sides
[tex]\mathbf{c = \frac{25}4}[/tex]
[tex]\mathbf{c = 6.25}[/tex]
Hence, the possible value of c is 6.25
Read more about mean value theorem at:
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Write these numbers in standard form 0.000 04
Answer:
4/ 100000
hope it was useful for you
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Select the equation that could represent the relationship between f(x) and g(x).
Answer:
Option C.
Step-by-step explanation:
We have to see the common things we have in both graphs and express them:
1. There is a value x=a≠0, where g(a)=f(a)=0
2. The slope of g(x) is of opposite sign of the slope of f(x). Then f(x)=m*g(cx) with m<0.
3. The slope of f(x) seems to be higher than the slope of g(x)
A. As the slopes are different, this is not adequate.
B. As the slopes are different, this is not adequate.
C. This can be adequate, as it applies to all the observations we have made.
D. This is not adequate because f(0)≠g(-2*0).
The only adequate option then is C.
Bart bought a digital camera with a list price of $219 from an online store offering a 6 percent discount. He needs to pay $7.50 for shipping. What was Bart's total cost? A. $205.86 B. $211.50 C. $213.36
Answer:
Barts total cost is (c)213.36
Step-by-step explanation:
First, you subtract 6% from $219
=204.92
add shipping,
+7.50
=213.36
Hope this helps <3
Answer:
C. $213.36
Step-by-step explanation:
The original price is $219 and the discount is 6% which is equal to $13.14
$219 - $13.14 + $7.50 (shipping cost) = $213.36
An open-top rectangular box is being constructed to hold a volume of 350 in3. The base of the box is made from a material costing 8 cents/in2. The front of the box must be decorated, and will cost 10 cents/in2. The remainder of the sides will cost 4 cents/in2. Find the dimensions that will minimize the cost of constructing this box.
Answer:
the dimensions that will minimize the cost of constructing the box is:
a = 5.8481 in ; b = 5.848 in ; c = 10.234 in
Step-by-step explanation:
From the information given :
Let a be the base if the rectangular box
b to be the height and c to be the other side of the rectangular box.
Then ;
the area of the base is ac
area for the front of the box is ab
area for the remaining other sides ab + 2cb
The base of the box is made from a material costing 8 ac
The front of the box must be decorated, and will cost 10 ab
The remainder of the sides will cost 4 (ab + 2cb)
Thus ; the total cost C is:
C = 8 ac + 10 ab + 4(ab + 2cb)
C = 8 ac + 10 ab + 4ab + 8cb
C = 8 ac + 14 ab + 8cb ---- (1)
However; the volume of the rectangular box is V = abc = 350 in³
If abc = 350
Then b = [tex]\dfrac{350}{ac}[/tex]
replacing the value for c in the above equation (1); we have :
[tex]C = 8 ac + 14 a(\dfrac{350}{ac}) + 8c(\dfrac{350}{ac})[/tex]
[tex]C = 8 ac + \dfrac{4900}{c}+\dfrac{2800}{a}[/tex]
Differentiating C with respect to a and c; we have:
[tex]C_a = 8c - \dfrac{2800}{a^2}[/tex]
[tex]C_c = 8a - \dfrac{4900}{c^2}[/tex]
[tex]8c - \dfrac{2800}{a^2}=0[/tex] --- (2)
[tex]8a - \dfrac{4900}{c^2}=0[/tex] ---(3)
From (2)
[tex]8c =\dfrac{2800}{a^2}[/tex]
[tex]c =\dfrac{2800}{8a^2}[/tex] ----- (4)
From (3)
[tex]8a =\dfrac{4900}{c^2}[/tex]
[tex]a =\dfrac{4900}{8c^2}[/tex] -----(5)
Replacing the value of a in 5 into equation (4)
[tex]c = \dfrac{2800}{8*(\dfrac{4900}{8c^2})^2} \\ \\ \\ c = \dfrac{2800}{\dfrac{8*24010000}{64c^4}} \\ \\ \\ c = \dfrac{2800}{\dfrac{24010000}{8c^4}} \\ \\ \\ c = \dfrac{2800*8c^4}{24010000} \\ \\ c = 0.000933c^4 \\ \\ \dfrac{c}{c^4}= 0.000933 \\ \\ \dfrac{1}{c^3} = 0.000933 \\ \\ \dfrac{1}{0.000933} = c^3 \\ \\ 1071.81 = c^3\\ \\ c= \sqrt[3]{1071.81} \\ \\ c = 10.234[/tex]
From (5)
[tex]a =\dfrac{4900}{8c^2}[/tex] -----(5)
[tex]a =\dfrac{4900}{8* 10.234^2}[/tex]
a = 5.8481
Recall that :
b = [tex]\dfrac{350}{ac}[/tex]
b = [tex]\dfrac{350}{5.8481*10.234}[/tex]
b =5.848
Therefore ; the dimensions that will minimize the cost of constructing the box is:
a = 5.8481 in ; b = 5.848 in ; c = 10.234 in
The dimensions that will minimize the cost of constructing this box are: a = 5.8481 inches, b = 5.848 inches, and c = 10.234 inches and this can be determined by using the given data.
Given :
An open-top rectangular box is being constructed to hold a volume of 350 inches cube.The base of the box is made from a material costing 8 cents/inch square.The front of the box must be decorated and will cost 10 cents/inch square. The remainder of the sides will cost 4 cents/inch square.According to the given data the total cost is given by:
C = 8ac + 14ab + 8cb --- (1)
The volume of the rectangular box is (V = abc = 350 inch cube). So, the value of b is given by:
[tex]\rm b = \dfrac{350}{ac}[/tex]
Now, substitute the value of 'b' in the equation (1).
[tex]\rm C = 8ac + \dfrac{4900}{c}+\dfrac{2800}{a}[/tex]
First differentiating the above equation with respect to c.
[tex]\rm C_c = 8a-\dfrac{4900}{c^2}[/tex] --- (2)
Now, differentiating the above equation with respect to a.
[tex]\rm C_a = 8c-\dfrac{2800}{a^2}[/tex] --- (3)
Now, equate equation (2) and equation (3) to zero.
From equation (2):
[tex]\rm a=\dfrac{4900}{8c^2}[/tex] ----- (4)
From equation (3):
[tex]\rm c=\dfrac{2800}{8a^2}[/tex] ----- (5)
Now, from equations (4) and (5).
[tex]\rm c = \dfrac{2800}{8\left(\dfrac{4900}{8c^2}\right)^2}[/tex]
Now, simplifying the above expression in order to get the value of c.
c = 10.234
Now, put the value of 'c' in equation (5) in order to get the value of 'a'.
a = 5.8481
The value of 'b' is given by:
[tex]\rm b = \dfrac{350}{5.8481\times 10.234}[/tex]
b = 5.848
So, the dimensions that will minimize the cost of constructing this box are: a = 5.8481 inches, b = 5.848 inches, and c = 10.234 inches.
For more information, refer to the link given below:
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Express the following ratio in the simplest form vii) 4.5km: 450m
Answer:
4.5 ×1000 =4500m
Step-by-step explanation:
450/1000=0.45km
Answer: 10 : 1
Step-by-step explanation: Now first let’s convert this to the same units, for instance, the SI unit for length meters. 4.5 x 1000 = 4500m. Then put the ratio 4500m : 450m. You can divide 4500 by 450 as it is divisible so you get 10 as the answer.
Even if you have converted them to kilometers before, nevermind, still 4.5 divide by 0.45 is 10 and there the answer is 10 : 1 or shortly the ratio is just 10.
PLEASE HELP I DO NOT UNDERSTAND AT ALL ITS PRECALC PLEASE SERIOUS ANSWERS
You want to end up with [tex]A\sin(\omega t+\phi)[/tex]. Expand this using the angle sum identity for sine:
[tex]A\sin(\omega t+\phi)=A\sin(\omega t)\cos\phi+A\cos(\omega t)\sin\phi[/tex]
We want this to line up with [tex]2\sin(4\pi t)+5\cos(4\pi t)[/tex]. Right away, we know [tex]\omega=4\pi[/tex].
We also need to have
[tex]\begin{cases}A\cos\phi=2\\A\sin\phi=5\end{cases}[/tex]
Recall that [tex]\sin^2x+\cos^2x=1[/tex] for all [tex]x[/tex]; this means
[tex](A\cos\phi)^2+(A\sin\phi)^2=2^2+5^2\implies A^2=29\implies A=\sqrt{29}[/tex]
Then
[tex]\begin{cases}\cos\phi=\frac2{\sqrt{29}}\\\sin\phi=\frac5{\sqrt{29}}\end{cases}\implies\tan\phi=\dfrac{\sin\phi}{\cos\phi}=\dfrac52\implies\phi=\tan^{-1}\left(\dfrac52\right)[/tex]
So we end up with
[tex]2\sin(4\pi t)+5\cos(4\pi t)=\sqrt{29}\sin\left(4\pi t+\tan^{-1}\left(\dfrac52\right)\right)[/tex]
Answer:
y(t) = √29·sin(4πt +1.1903)amplitude: √29angular frequency: 4πphase shift: 1.1903 radiansStep-by-step explanation:
In the form ...
y(t) = Asin(ωt +φ)
you have ...
Amplitude = Aangular frequency = ωphase shift = φThe translation from ...
y(t) = 2sin(4πt) +5cos(4πt)
is ...
A = √(2² +5²) = √29 . . . . the amplitude
ω = 4π . . . . the angular frequency in radians per second
φ = arctan(5/2) ≈ 1.1903 . . . . radians phase shift
Then, ...
y(t) = √29·sin(4πt +1.1903)
_____
Comment on the conversion
You will notice we used "2" and "5" to find the amplitude and phase shift. In the generic case, these are "coefficient of sin( )" and "coefficient of cos( )". When determining phase shift, pay attention to whether your calculator is giving you degrees or radians. (Set the mode to what you want.)
If you have a negative coefficient for sin( ), you will need to add 180° (π radians) to the phase shift value given by the arctan( ) function.
Wina drove 282 miles on 10 gallons of gas. At this same rate, how many miles could she drive on 12 gallons of gas?
Hey there! I'm happy to help!
Let's set this up a proportion (two equal ratios) to find out how many miles Wina can drive on 12 gallons gas.
[tex]\frac{miles}{gallons} =\frac{282}{10} =\frac{m}{12}[/tex]
What do we multiply the bottom 10 by to get to 12? Well, to find out, we can divide 12 by 10 below.
12÷10=1.2
This means that we multiply the numbers in the first fraction by 1.2 to have the same numerator and denominator as the second fraction.
If we multiplied our 10 b y 1.2 to get the denominator in the second fraction, we should be able to multiply 282 by 1.2 to get the numerator in the second fraction!
282×1.2=338.4
If you use 338.4 in this proportion, the ratios will be equal.
Therefore, Wina could drive 338.4 miles on 12 miles of gas at this same rate.
Have a wonderful day!
An ecologist wishes to mark off a circular sampling region having radius 10 m. However, the radius of the resulting region is actually a random variable R with the following pdf.
f(r)={34(1−(14−r)2)13≤r≤150 otherwise
What is the expected area of the resulting circular region?
Answer:
the expected area of the resulting circular region is 616.38 m²
Step-by-step explanation:
Given that:
[tex]f(r) = \left \{ {{\dfrac{3}{4}(1-(14-r)^2)} \atop {0 }} \right. \ \ 13 \leq r \leq 15[/tex] otherwise
The expected area of the resulting circular region is:
= [tex]E(\pi r^2)[/tex]
= [tex]\pi E (r^2)[/tex]
To calculate [tex]E(r^2)[/tex]
[tex]E(r^2) = \int\limits^{15}_{13} {r^2} \ f(r) \ dr[/tex]
[tex]E(r^2) = \int\limits^{15}_{13} \ \dfrac{3r^2}{4}(1-(14-r)^2)dr[/tex]
[tex]E(r^2) = \dfrac{3}{4} \int\limits^{15}_{13} \ r^2 (1-196-r^2+28r) dr[/tex]
[tex]E(r^2) = \dfrac{3}{4} \int\limits^{15}_{13} \ r^2 (28r^3-r^4-195r^2)dr[/tex]
[tex]E(r^2) = \dfrac{3}{4}[\dfrac{28 r^4}{4}-\dfrac{r^5}{5}-\dfrac{195r^3}{3}]^{^{15}}}__{13}[/tex]
[tex]E(r^2) = \dfrac{3}{4} [ \dfrac{28 \times 50625}{4} - \dfrac{759375}{5} - \dfrac{195 \times 3375}{3} ]-[ \dfrac{28 \times 28561}{4} - \dfrac{371293}{5} - \dfrac{195 \times 2197}{3} ][/tex]
[tex]E(r^2) = \dfrac{3}{4} [ 354375-151875-219375-199927+74258.6+142805][/tex]
[tex]E(r^2) = \dfrac{3}{4} [261.6][/tex]
[tex]E(r^2) = 196.2[/tex]
Recall:
The expected area of the resulting circular region is:
= [tex]E(\pi r^2)[/tex]
= [tex]\pi E (r^2)[/tex]
where;
[tex]E(r^2) = 196.2[/tex]
Then
The expected area of the resulting circular region is:
= [tex]\pi \times 196.2[/tex]
= 616.38 m²
A bag contains balls colored in 7 different colors. What is the minimum no of balls one need to pick in order to get three balls of same color
Answer:
twenty one balls.
Step-by-step explanation:
there would be three of each colour.
Answer:
the real answer is 15
Step-by-step explanation:
HELP:How many ways can four
students be seated in a row of
four seats? (answer is not 4 or 16)
Answer:
24 ways.
Step-by-step explanation:
In this case, you just need a factorial.
For the first seat, you have 4 students you can place.
For the second seat, you have 3 students.
For the third, you have 2.
For the fourth, you have 1.
So, you can arrange the students by doing 4 * 3 * 2 * 1 = 12 * 2 = 24 ways.
Hope this helps!
Answer:
There are 24 ways you can seat the people.Explantation:
First seat: 4 seats
Second seat: 3 seats
Third: 2 seats
Fourth seat: 1 seat remaining
4 * 3 * 2 * 1 = 12 * 2 * 1 = 24 * 1 = 24
There are 24 ways you can seat the people.Find X. Please help.
Answer:
x = 18.08°Step-by-step explanation:
To find the value of x we use sine
sin ∅ = opposite / hypotenuse
From the question
29 is the hypotenuse
9 is the opposite
sin x = 9/29
x = sin-¹ 9/29
x = 18.08°
Hope this helps you
Answer:
Angle=71.9°
using the trig inverse formula sec(angle)= hypotenuse/adjacent
The current l in an electrical conductor varies inversely as the resistance R of the conductor. The current is 1/6 ampere when the resistance is 32400 ohms. What is the current when the resistance is 22500 ohms
Answer:
I=0.24ampere
Step-by-step explanation:
Assuming that the voltage is the same:
I=V/R (V- voltage, I-current, R-resistance)
1/6ampere=V/3240ohms
V=1/6*3240
= 5400v
Voltage across =V=5400v
Since the voltage is the same when the resistance is 22500ohms
I=V/R
=5400/22500
=6/25
=0.24ampere