d
Step-by-step explanation:
6-2=n will be used because when 2 goes to other side then positive sign turns to negative sign
find the slope of the tangent line of the curve r = cos (3theta) at theta = pi / 3
The slope of the tangent line to the curve at a point (x, y) is dy/dx. By the chain rule, this is equivalent to
dy/dθ × dθ/dx = (dy/dθ) / (dx/dθ)
where y = r(θ) sin(θ) and x = r(θ) cos(θ). Then
dy/dθ = dr/dθ sin(θ) + r(θ) cos(θ)
dx/dθ = dr/dθ cos(θ) - r(θ) sin(θ)
Given r(θ) = cos(3θ), we have
dr/dθ = -3 sin(3θ)
and so
dy/dx = (-3 sin(3θ) sin(θ) + cos(3θ) cos(θ)) / (-3 sin(3θ) cos(θ) - cos(3θ) sin(θ))
When θ = π/3, we end up with a slope of
dy/dx = (-3 sin(π) sin(π/3) + cos(π) cos(π/3)) / (-3 sin(π) cos(π/3) - cos(π) sin(π/3))
dy/dx = -cos(π/3) / sin(π/3)
dy/dx = -cot(π/3) = -1/√3
Equivalent expression -(-5.6m-n+9.9
Answer:
5.6m + n - 9.9
Step-by-step explanation:
-(-5.6m-n+9.9)
5.6m + n - 9.9
Which of the following best describes the slope of the line below?
A. Zero
B. Negative
C. Positive
< PREVIOUS
Answer:
A. Zero.
Step-by-step explanation:
Technically, the correct answer is "undefined", as there will be infinite change in the slope amount. However, of all the given choices, Zero should be the best answer. However, if it is wrong, do ask your teacher, and state that undefined should be the answer choice, and that credit should be rewarded for such.
what's the median of -13.78, -3.01, -2.41, -0.28, 0.66, 0.67, 1.05, 1.39, 2.03, 2.2, 2.64, 4.02
maths class 9
Multiply: 4√12 2√12
Answer:
[tex]4 \sqrt{122} \sqrt{12} \\ (4 \times 2) \times ( \sqrt{12} \times \sqrt{12} ) \\ (4 \times 2) \times 12 \\ 8 \times 12 \\ 96[/tex]
Someone help please
Answer: Choice A
[tex]\tan(\alpha)*\cot^2(\alpha)\\\\[/tex]
============================================================
Explanation:
Recall that [tex]\tan(x) = \frac{\sin(x)}{\cos(x)}[/tex] and [tex]\cot(x) = \frac{\cos(x)}{\sin(x)}[/tex]. The connection between tangent and cotangent is simply involving the reciprocal
From this, we can say,
[tex]\tan(\alpha)*\cot^2(\alpha)\\\\\\\frac{\sin(\alpha)}{\cos(\alpha)}*\left(\frac{\cos(\alpha)}{\sin(\alpha)}\right)^2\\\\\\\frac{\sin(\alpha)}{\cos(\alpha)}*\frac{\cos^2(\alpha)}{\sin^2(\alpha)}\\\\\\\frac{\sin(\alpha)*\cos^2(\alpha)}{\cos(\alpha)*\sin^2(\alpha)}\\\\\\\frac{\cos^2(\alpha)}{\cos(\alpha)*\sin(\alpha)}\\\\\\\frac{\cos(\alpha)}{\sin(\alpha)}\\\\[/tex]
In the second to last step, a pair of sine terms cancel. In the last step, a pair of cosine terms cancel.
All of this shows why [tex]\tan(\alpha)*\cot^2(\alpha)\\\\[/tex] is identical to [tex]\frac{\cos(\alpha)}{\sin(\alpha)}\\\\[/tex]
Therefore, [tex]\tan(\alpha)*\cot^2(\alpha)=\frac{\cos(\alpha)}{\sin(\alpha)}\\\\[/tex] is an identity. In mathematics, an identity is when both sides are the same thing for any allowed input in the domain.
You can visually confirm that [tex]\tan(\alpha)*\cot^2(\alpha)\\\\[/tex] is the same as [tex]\frac{\cos(\alpha)}{\sin(\alpha)}\\\\[/tex] by graphing each function (use x instead of alpha). You should note that both curves use the exact same set of points to form them. In other words, one curve is perfectly on top of the other. I recommend making the curves different colors so you can distinguish them a bit better.
√3 is a polynomial of degree ________.
Step-by-step explanation:
Therefore, the degree of polynomial √3 is zero.
[tex]\sf\huge\underline\color{pink}{༄Answer:}[/tex]
[tex]\tt{\sqrt{3}}[/tex] is a polynomial of degree 0
[tex]\sf\huge\underline\color{pinl}{༄Note:}[/tex]
The expression is constant, which means it can be rewritten with a factor of x^0. The degree is the largest exponent on the variable.[tex]\color{pink}{==========================}[/tex]
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-༄⁂✰Park Hana Moon
make a factor tree for 42
Answer:
The number 43 is a composite number because 42 can be divided by 1, by itself and at least by 2, 3, and 7. So it is possible to draw its prime tree. The prime factorization of 42=2*3*7
Step-by-step explanation:
hope this helps :)
Chris drives 240 miles from his home in Atlanta, Georgia, at 60 miles per hour. How many minutes longer would the return trip take if he travels at 50 miles per hour
Answer:
48 minutes
240 at 60mph = 4 hrs.
240 at 50 mph = 4.8 hrs.
it would take an extra 60*.8 or 48 minutes
Step-by-step explanation:
The trip will be of 48 minutes longer when the speed is decreased by 10 miles per hour.
What is the formula for time?
The time is given by distance/speed. The unit of time is minutes or seconds.
What will be the time difference?When distance of 240 miles is cover by the speed of 60 miles per hour then the time take to travel this distance will be 240/60=4 hours
When distance of 240 miles is cover by the speed of 50 miles per hour then the time take to travel this distance will be 240/50=4.8 hours
The difference between 4.8 hours and 4 hours is of 0.8 hours or 0.8*60=48 minutes.
Therefore, the trip will be of 48 minutes longer.
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Tell whether the number pair (2,1) is a solution to the equation y = 3x - 5.
Answer:
Yes
Step-by-step explanation:
Plugging in the values in the equation, we have
1=3*(2)-5, 1=1 which is TRUE
PLEASE HELP, solve for X
Answer:
27
Step-by-step explanation:
(whole secant) x (external part) = (tangent)^2
(48+x) * 48 = 60^2
(48+x)48=3600
Divide each side by 48
48+x =75
Subtract 48
48+x-48 = 75-48
x =27
Alex wants to test the reliability of “lie detector tests,” or polygraph tests. He performs a polygraph test on a random sample of 12 individuals. If there is more than a 50% chance that the tests result in no false positives (that is, the test does not result in a true statement being recorded as a lie), Alex will conclude that the tests are reliable. If the probability of a lie detector test resulting in a false positive is 5.5%, what will Alex conclude? Use Excel to find the probability, rounding to three decimal places.
The correct statement is test is reliable and authentic as the probability of no false positives is more than 0.5
Given that
[tex]H_o:P= 0.50\\\\H_1:P>0.50[/tex]
Now following calculations to be done to reach the conclusion:
There is no false positive as
= 100 - 5.5
= 94.5%
[tex]\hat P =0.945, n = 12[/tex]
Now
[tex]z = \frac{\hat P - P}{\sqrt\frac{P(1-P)}{n} }\\\\=\frac{0.945-0.5}{\sqrt\frac{0.5\times0.5}{12} } \\\\= 3.08[/tex]
So
P value = P(z >3.08) = 0.0010
Therefore we can conclude that test is reliable and authentic as the probability of no false positives is more than 0.5
Learn more about the polygraph test here:
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What is 55 increased by 10%?
Answer:
10% of 55
=> 10/100 × 55
=> 1/10×55
=> 5.5
55 increased by 10% => 55 + 5.5
=> 60.5
hope that helps ✌
Answer:
Step-by-step explanation:
10% of 55
10/100*55
1/10*55
5.5 <--- That is 10% of 55
55+5.5 = 60.5
The equation y=1/4x represents a proportional relationship. What is the constant of proportionality?
A. 1/4
B. x
C. 0
D. 4
Answer:
k = 1/4
Step-by-step explanation:
A proportional relationship is
y = kx where k is the constant of proportionality
y = 1/4x
k = 1/4
Answer:
a. 1/4
Step-by-step explanation:
1/4 shows the relation of y and x. (that y is one fourth of x)
Which equation is equivalent to x^2 +24-8=0?
A.(x+12)^2 =152
B.(x-12)^2=136
C.(x+8)^2=144
D.(x+12)^2 =144
Answer:
D) is your correct answer
If each side of a cube is doubled, its volume?
If you double each side the volume is 8 times
Must click thanks and mark brainliest
Select the equation written in slope intercept form that corresponds to the given slope y intercept
Answer:
[tex]y = -6x + 1[/tex]
[tex]y = 6x - 2[/tex]
[tex]y = -2x + 4[/tex]
[tex]y = x + 6[/tex]
Step-by-step explanation:
Given
See comment for missing part of the question
Required
The equation in slope intercept form
A linear equation is of the form:
[tex]y = mx + b[/tex]
(a) m = -6, b =1
Using the above format, we have:
[tex]y = -6x + 1[/tex]
(b) m =6, b = -2
[tex]y = 6x - 2[/tex]
(c) m = -2, b = 4
[tex]y = -2x + 4[/tex]
(d) m = 1, b = 6
[tex]y = x + 6[/tex]
Calculus!
The volume of a substance, A, measured in cubic centimeters increases according to the exponential growth model dA/dt = 0.3A, where t is measured in hours. The volume of another substance, B, also measured in cubic centimeters increases at a constant rate of 1 cm^3 per hour according to the linear model dB/dt = 1. At t = 0, substance A has a volume A(0) = 3 and substance B has size B(0) = 5. At what time will both substances have the same volume?
Would it be correct to write the growth model of substance B as x + 5? And how could I write the growth model of substance A? Thank you in advance, and sorry for the poor formatting.
Answer:
The two substances will have the same volume after approximately 3.453 hours.
Step-by-step explanation:
The volume of substance A (measured in cubic centimeters) increases at a rate represented by the equation:
[tex]\displaystyle \frac{dA}{dt} = 0.3 A[/tex]
Where t is measured in hours.
And substance B is represented by the equation:
[tex]\displaystyle \frac{dB}{dt} = 1[/tex]
We are also given that at t = 0, A(0) = 3 and B(0) = 5.
And we want to find the time(s) t for which both A and B will have the same volume.
You are correct in that B(t) is indeed t + 5. The trick here is to multiply both sides by dt. This yields:
[tex]\displaystyle dB = 1 dt[/tex]
Now, we can take the integral of both sides:
[tex]\displaystyle \int 1 \, dB = \int 1 \, dt[/tex]
Integrate. Remember the constant of integration!
[tex]\displaystyle B(t) = t + C[/tex]
Since B(0) = 5:
[tex]\displaystyle B(0) = 5 = (0) + C \Rightarrow C = 5[/tex]
Hence:
[tex]B(t) = t + 5[/tex]
We can apply the same method to substance A. This yields:
[tex]\displaystyle dA = 0.3A \, dt[/tex]
We will have to divide both sides by A:
[tex]\displaystyle \frac{1}{A}\, dA = 0.3\, dt[/tex]
Now, we can take the integral of both sides:
[tex]\displaystyle \int \frac{1}{A} \, dA = \int 0.3\, dt[/tex]
Integrate:
[tex]\displaystyle \ln|A| = 0.3 t + C[/tex]
Raise both sides to e:
[tex]\displaystyle e^{\ln |A|} = e^{0.3t + C}[/tex]
Simplify:
[tex]\displaystyle |A| = e^{0.3t} \cdot e^C = Ce^{0.3t}[/tex]
Note that since C is an arbitrary constant, e raised to C will also be an arbitrary constant.
By definition:
[tex]\displaystyle A(t) = \pm C e^{0.3t} = Ce^{0.3t}[/tex]
Since A(0) = 3:
[tex]\displaystyle A(0) = 3 = Ce^{0.3(0)} \Rightarrow C = 3[/tex]
Therefore, the growth model of substance A is:
[tex]A(t) = 3e^{0.3t}[/tex]
To find the time(s) for which both substances will have the same volume, we can set the two functions equal to each other:
[tex]\displaystyle A(t) = B(t)[/tex]
Substitute:
[tex]\displaystyle 3e^{0.3t} = t + 5[/tex]
Using a graphing calculator, we can see that the intersect twice: at t ≈ -4.131 and again at t ≈ 3.453.
Since time cannot be negative, we can ignore the first solution.
In conclusion, the two substances will have the same volume after approximately 3.453 hours.
Factorize :solve no g and h
Answer:
Hello,
do you mean factorise but not solve ?
Just one formula:
[tex]\boxed{a^2-b^2=(a-b)(a+b)}[/tex]
Step-by-step explanation:
[tex]g)\\\\16x^3y-81xy^5\\\\=xy(16x^2-81y^4)\\\\=xy(4x^2+9y^2)(4x^2-9y^2)\\\\=xy(2x-3y)(2x+3)(4x^2+9y^2)\\\\\\\\h)\\\\x^8-y^8\\\\=(x^4+y^4)(x^4-y^4)\\\\=(x^4+y^4)(x^2+y^2)(x^2-y^2)\\\\=(x-y)(x+y)(x^2+y^2)(x^4+y^4)\\[/tex]
Answer:
here only one formula to use in both question
a^2+b^2= (a+b)(a-b)
i need help with this question pls! :)
Hi there!
[tex]\large\boxed{\text{9 quarters}}[/tex]
We can let x = dimes and y = quarters.
We know that one dime = $0.10 and a quarter = $0.25, so:
$3.05 = $0.10x + $0.25y
And:
17 = x + y
Solve the system of equations. We can rearrange the bottom equation to create an expression equal to y:
17 - x = y
Substitute this into the top equation for y:
3.05 = 0.10x + 0.25(17 - x)
Distribute and simplify:
3.05 = 0.10x + 4.25 - 0.25x
3.05 = 4.25 - 0.15x
Solve for x:
-1.2 = -0.15x
x = 8
Find y using the above expression:
17 - 8 = y
y = 9
help me out .... I will mark u as brilliant students
oe which question are you figure it out
Write the ratio: 3 1/6 to 17/6
as a fraction in lowest terms.
Answer: [tex]\frac{19}{6} : \frac{17}{6}[/tex]
Step-by-step explanation:
Let us first represent the ratio.
3[tex]\frac{1}{6} : \frac{17}{6}[/tex]
Now we need to convert 3[tex]\frac{1}{6}[/tex] into a improper fraction.
[tex]\frac{19}{6} : \frac{17}{6}[/tex]
Now it is in its simplest form.
The final answer is [tex]\frac{19}{6} : \frac{17}{6}[/tex]
16. What is the measure of ZAOB?
What is the value of x?
Answer:
x = 54.6 m
Step-by-step explanation:
Δ MAB and Δ MNP are similar, then corresponding sides are in proportion, that is
[tex]\frac{MA}{MN}[/tex] = [tex]\frac{MB}{MP}[/tex] , substitute values
[tex]\frac{80.5-35}{80.5}[/tex] = [tex]\frac{x}{96.6}[/tex]
[tex]\frac{45.5}{80.5}[/tex] = [tex]\frac{x}{96.6}[/tex] ( cross- multiply )
80.5x = 4395.3 ( divide both sides by 80.5 )
x = 54.6
Answer:
Answer:
Answer:x = 25°
Answer:x = 25°Step-by-step explanation:
Answer:x = 25°Step-by-step explanation:The secant- secant angle FGE is one half the difference of the intercepted arcs, that is (135 - x) = 55 ( multiply both sides by 2 to clear the fraction )
Answer:x = 25°Step-by-step explanation:The secant- secant angle FGE is one half the difference of the intercepted arcs, that is (135 - x) = 55 ( multiply both sides by 2 to clear the fraction )135 - x = 110 ( subtract 135 from both sides )
Answer:x = 25°Step-by-step explanation:The secant- secant angle FGE is one half the difference of the intercepted arcs, that is (135 - x) = 55 ( multiply both sides by 2 to clear the fraction )135 - x = 110 ( subtract 135 from both sides )- x = - 25 ( multiply both sides by - 1 )
Answer:x = 25°Step-by-step explanation:The secant- secant angle FGE is one half the difference of the intercepted arcs, that is (135 - x) = 55 ( multiply both sides by 2 to clear the fraction )135 - x = 110 ( subtract 135 from both sides )- x = - 25 ( multiply both sides by - 1 )x = 25°
Hence the answer is 25.
Given the a center (-1, -2) and a radius r = 2. Identify the circle.
Answer:
1st option
1st graph has the centre on (-1,-2) and the distance of the circumference from the centre is 2
Answered by GAUTHMATH
Deion is saving up to buy a new phone. He already has $95 and can save an additional $7 per week using money from his after school job. How much total money would Deion have after 6 weeks of saving? Also, write an expression that represents the amount of money Deion would have saved in w weeks.
The expression that represents the amount of money Deion would have saved in w weeks is 95 + 7w and the total savings after 6 weeks will be $137.
What is an expression?A statement expressing the equality of two mathematical expressions is known as an equation.
A mixture of variables, numbers, addition, subtraction, multiplication, and division are called expressions.
An expression is a mathematical proof of the equality of two mathematical expressions.
As per the given,
Initial fixed money = $95
Per week saving $7/week
Total money = fixed money + money in w weeks.
⇒ 95 + 7w
For 6 weeks, w = 6
⇒ 95 + 7× 6 = $137.
Hence "The expression that represents the amount of money Deion would have saved in w weeks is 95 + 7w and the total savings after 6 weeks will be $137".
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An 8μC charge is moving through a 10T magnetic field at a speed of 2.5⋅107 m/s perpendicular to the direction of the field. What is the force on the charge
THIS IS YOUR ANSWER
HOPE IT HELPS YOU
answer please lol so uh yeah
Answer:
5x=20
5x/5=20/5
x=4
Step-by-step explanation:
substitute the 5x
divide both sides by 5 it will be 20 divide by 5
answer is x =4
Pls help ———————————-
-1/4 (x+2)+5=-x I really need help
Answer:
x = -6
Step-by-step explanation:
Answer:
-6
Step-by-step explanation:
-1/4 (x+2)+5=-x
-1/4x-1/2+5=-x
-1/4x+4.5=-x
+1/4x +1/4x
(4/3) 4.5=-3/4x (4/3)
6=x
x=6
