Step 2
−2y = 15 − 2z
should be
−2y = -30 + 4a
If f(x)=x-2 and g(x)=2x-6, then g(4)/f(3)
Answer:
2
Step-by-step explanation:
g(x) = 2x - 6
g(4) = 2*4 - 6
g(4) = 2
f(x) = x - 2
f(3) = 3 - 2
f(3) = 1
Thus g (4) / f (3) = 2 / 1 = 2
The value of the function g (4) / f (3) is 2.
What is a function?Function is a type of relation, or rule, that maps one input to specific single output.
We are given the function as;
f(x)=x-2 and g(x)=2x-6, then we need to find g(4)/f(3)
Therefore, g(x) = 2x - 6
g(4) = 2*4 - 6
g(4) = 2
Similalry,
f(x) = x - 2
f(3) = 3 - 2
f(3) = 1
Thus we have the value of function as
g (4) / f (3) = 2 / 1
g (4) / f (3) = 2
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There are10 members on a board of directors. If they must elect a chairperson, a secretary, and a treasurer, howmany different slates of candidates are possible
Answer:
The answer is "720"
Step-by-step explanation:
The amount of different slates candidates:
[tex]n=\frac{N!}{(N-k)!}\\\\[/tex]
[tex]=\frac{10!}{(10-3)!}\\\\=\frac{10!}{7!}\\\\=\frac{10\times 9 \times 8 \times 7! }{7!}\\\\=10\times 9 \times 8\\\\=90\times 8\\\\=720[/tex]
Find the range for the following data 14, 16, 16, 14, 22, 13, 15, 24, 12, 23, 14, 20, 17, 21, 22, 18, 18, 19, 20, 17, 16, 15, 11, 12, 21, 20, 17, 18, 19, 23
Answer:
12
Step-by-step explanation:
Range is the subtraction of the largest number and the smallest number.
The largest number is: 23
The smallest number is: 11
Now subtract:
23 - 11 = 12
Hope this helped.
Answer:
the lowest is 11 and the highest is 24 then subtract it you are going to have 13
Calculus II Question
Identify the function represented by the following power series.
[tex]\sum_{k = 0}^\infty (-1)^k \frac{x^{k + 2}}{4^k}[/tex]
With some rewriting, you get
[tex]\displaystyle \sum_{k=0}^\infty (-1)^k\frac{x^{k+2}}{4^k} = x^2 \sum_{k=0}^\infty \left(-\frac x4\right)^k[/tex]
Recall that for |x| < 1, you have
[tex]\displaystyle \frac1{1-x} = \sum_{k=0}^\infty x^k[/tex]
So as long as |-x/4| = |x/4| < 1, or |x| < 4, your series converges to
[tex]\displaystyle x^2 \sum_{k=0}^\infty \left(-\frac x4\right)^k = \frac{x^2}{1-\left(-\frac x4\right)} = \frac{x^2}{1+\frac x4} = \boxed{\frac{4x^2}{4+x}}[/tex]
Based on known expressions from Taylor series, the power series [tex]\sum \limits_{k = 0}^{\infty} (-1)^{k}\cdot \frac{x^{k+2}}{4^{k}}[/tex]Taylor series-derived formula of the rational function [tex]\frac{4\cdot x^{2}}{4+x}[/tex].
How to derive a function behind the approximated formula by Taylor seriesTaylor series are polynomic approximations used to estimate values both from trascendental and non-trascendental functions. It is commonly used in trigonometric, potential, logarithmic and even rational functions.
In this question we must use series properties and common Taylor series-derived formulas to infer the expression behind the given series. Now we proceed to find the expression:
[tex]\sum \limits_{k = 0}^{\infty} (-1)^{k}\cdot \frac{x^{k+2}}{4^{k}}[/tex]
[tex]x^{2}\cdot \sum\limits_{k = 0}^{\infty} \left(-\frac{x}{4} \right)^{k}[/tex]
[tex]x^{2}\cdot \left(\frac{1}{1+\frac{x}{4} } \right)[/tex]
[tex]\frac{4\cdot x^{2}}{4+x}[/tex]
Based on power and series properties and most common Taylor series- derived formulas, the power series [tex]\sum \limits_{k = 0}^{\infty} (-1)^{k}\cdot \frac{x^{k+2}}{4^{k}}[/tex] represents a Taylor series-derived formula of the rational function [tex]\frac{4\cdot x^{2}}{4+x}[/tex]. [tex]\blacksquare[/tex]
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The number of defective circuit boards coming off a soldering machine follows a Poisson distribution. During a specific ten-hour period, one defective circuit board was found. (a) Find the probability that it was produced during the first hour of operation during that period. (Round your answer to four decimal places.) (b) Find the probability that it was produced during the last hour of operation during that period. (Round your answer to four decimal places.) (c) Given that no defective circuit boards were produced during the first five hours of operation, find the probability that the defective board was manufactured during the sixth hour. (Round your answer to four decimal places.)
Answer:
a) the probability that the defective board was produced during the first hour of operation is [tex]\frac{1}{10}[/tex] or 0.1000
b) the probability that the defective board was produced during the last hour of operation is [tex]\frac{1}{10}[/tex] or 0.1000
c) the required probability is 0.2000
Step-by-step explanation:
Given the data in the question;
During a specific ten-hour period, one defective circuit board was found.
Lets X represent the number of defective circuit boards coming out of the machine , following Poisson distribution on a particular 10-hours workday which one defective board was found.
Also let Y represent the event of producing one defective circuit board, Y is uniformly distributed over ( 0, 10 ) intervals.
f(y) = [tex]\left \{ {{\frac{1}{b-a} }\\\ }} \right _0[/tex]; ( a ≤ y ≤ b )[tex]_{elsewhere[/tex]
= [tex]\left \{ {{\frac{1}{10-0} }\\\ }} \right _0[/tex]; ( 0 ≤ y ≤ 10 )[tex]_{elsewhere[/tex]
f(y) = [tex]\left \{ {{\frac{1}{10} }\\\ }} \right _0[/tex]; ( 0 ≤ y ≤ 10 )[tex]_{elsewhere[/tex]
Now,
a) the probability that it was produced during the first hour of operation during that period;
P( Y < 1 ) = [tex]\int\limits^1_0 {f(y)} \, dy[/tex]
we substitute
= [tex]\int\limits^1_0 {\frac{1}{10} } \, dy[/tex]
= [tex]\frac{1}{10} [y]^1_0[/tex]
= [tex]\frac{1}{10} [ 1 - 0 ][/tex]
= [tex]\frac{1}{10}[/tex] or 0.1000
Therefore, the probability that the defective board was produced during the first hour of operation is [tex]\frac{1}{10}[/tex] or 0.1000
b) The probability that it was produced during the last hour of operation during that period.
P( Y > 9 ) = [tex]\int\limits^{10}_9 {f(y)} \, dy[/tex]
we substitute
= [tex]\int\limits^{10}_9 {\frac{1}{10} } \, dy[/tex]
= [tex]\frac{1}{10} [y]^{10}_9[/tex]
= [tex]\frac{1}{10} [ 10 - 9 ][/tex]
= [tex]\frac{1}{10}[/tex] or 0.1000
Therefore, the probability that the defective board was produced during the last hour of operation is [tex]\frac{1}{10}[/tex] or 0.1000
c)
no defective circuit boards were produced during the first five hours of operation.
probability that the defective board was manufactured during the sixth hour will be;
P( 5 < Y < 6 | Y > 5 ) = P[ ( 5 < Y < 6 ) ∩ ( Y > 5 ) ] / P( Y > 5 )
= P( 5 < Y < 6 ) / P( Y > 5 )
we substitute
[tex]= (\int\limits^{6}_5 {\frac{1}{10} } \, dy) / (\int\limits^{10}_5 {\frac{1}{10} } \, dy)[/tex]
[tex]= (\frac{1}{10} [y]^{6}_5) / (\frac{1}{10} [y]^{10}_5)[/tex]
= ( 6-5 ) / ( 10 - 5 )
= 0.2000
Therefore, the required probability is 0.2000
Plz someone help me
Step-by-step explanation:
yo
so sorry I can't
really answer it
If JKL = TUV which of the following can you not conclude as being true
Answer:
Step-by-step explanation:
D
Answer:
∠J ≅ ∠V
Step-by-step explanation: I took the same test (:
The two countries with the highest cocoa production are the
Ivory Coast and Ghana. The Ivory Coast produces three times the amount of cocoa
produced in Ghana. (Source: International Cocoa Organization) Express the
amount of cocoa produced in the Ivory Coast in terms of the amount of cocoa produced in Ghana.
Answer:
38 percent of the Cocoa is produced in the ivory coast, with thousands being produced in Ghana, so Ghana is the main production rate of the cocoa, with the ivory coast producing less than half.
Step-by-step explanation:
A square prism and a cylinder have the same height. The area of the cross-section of the square prism is 628 square units, and the area of the cross-section of the cylinder is 200π square units. Based on this information, which argument can be made?
The volume of the square prism is one third the volume of the cylinder.
The volume of the square prism is half the volume of the cylinder.
The volume of the square prism is equal to the volume of the cylinder.
The volume of the square prism is twice the volume of the cylinder.
Answer:
C. The volume of the square prism is equal to the volume of the cylinder.
Step-by-step explanation:
I took the test and it was right
Which of the following behaviors would best describe someone who is listening and paying attention? a) Leaning toward the speaker O b) Interrupting the speaker to share their opinion c) Avoiding eye contact d) Asking questions to make sure they understand what's being said
Answer:
D
Step-by-step explanation:
I explained why 5 minutes ago on a different question
PLEASE HELPP ASAP!!
5.(06.02 MC)
Line BC contains points B (4, -5) and C (3, 2). Line DE contains points D (2,0) and E (9, 1). Lines BC and DE are (1 point)
parallel
perpendicular
neither
Answer:
Answer: Option A.
Step-by-step explanation:
Hey there!
Given; The Line BC contains points B (4, -5) and C (3, 2).
And the Line DE contains points D (2,0) and E (9, 1)
Note: Use double point formula for finding the equation and then find slopes of both then put the condition for perpendicular lines and parallel lines.
From line BC;
The points are B (4, -5) and C (3, 2).
Using double point formula;
[tex](y - y1) = \frac{y2 - y1}{x2 - x1}(x - x1) [/tex]
Keep all the value;
[tex](y + 5) = \frac{2 + 5}{3 - 4} (x - 4)[/tex]
Simplify it;
[tex]y + 5 = - 7x + 28[/tex]
Therefore, the equation is y = -7x+23........(I)And slope(m1) is -7 {comparing the equation (I) with y=Mx+c}
Again;
The points D (2,0) and E (9, 1)
Using double point formula;
[tex](y - y1) = \frac{y2 - y1}{x2 - x1} (x - x1)[/tex]
Keep all values;
[tex](y - 0) = \frac{9 - 2}{1 - 2} (x - 2)[/tex]
[tex]y = - 7x + 14[/tex]
Therefore, the equation is y = -7x+14......(ii)And the slope (m2) is -7. {comparing the equation (ii) with y= mx+c}
Check:
For parallel lines:
m1= m2
-7 = -7 (true)
Therefore, the lines are parallel.
Hope it helps!
Which of the following statements best describes the effect of replacing the graph of y = f(x) with the graph of y = f(x) − 11? The graph of y = f(x) will shift up 11 units. The graph of y = f(x) will shift right 11 units. The graph of y = f(x) will shift left 11 units. The graph of y = f(x) will shift down 11 units.
Answer:
The graph of y = f(x) will shift down 11 units
Step-by-step explanation:
a figure skating school offers introductory lessons at $25 per session. There is also a registration fee of $30
Answer:
Part A: y = 25x + 30
Part B: $180
Step-by-step explanation:
for part A, 25 is the constant so that goes with the x, and you just add 30 because it is the extra fee. slope intercept form is y = mx + b
for part B you just plug 6 into the slope intercept equation
y = 25(6) + 30
y = 150 + 30
y = 180
$180
A study is conducted to compare the lengths of time required by men and women to assemble a certain product. Past experience indicates that the distribution of times for both men and women is approximately normal but the variance of the times for women is less than that for men. A random sample of times for 11 men and 14 women produced the following data:
Men:
n1= 11
s1= 6.1
Women:
n2= 14
s2= 5.3
Test the hypothesis that the variance for men is greater than for women. Use both p-value method and critical value approach.
Answer:
1.33 < 2.67 ; Fail to reject H0 at 0.05
Step-by-step explanation:
Given the data :
Men:
n1= 11
s1= 6.1
Women:
n2= 14
s2= 5.3
The hypothesis :
H0 : σ1² = σ2²
H1 : σ1² > σ2²
To calculate the test statistic ; we use th Ftest statistics ;
F statistic = Larger sample variance / Smaller sample variance
Fstatistic = s1² / s2² = 6.1² / 5.3² = 37.21/28.09 = 1.325
The F critical value at :
df numerator = n - 1 = 11 - 1 = 10
df denominator = n - 1 = 14 - 1 = 13
Using the F distribution table :
F critical = 2.671
Since
F statistic < F critical ; Fail to reject H0 at 0.05
We fail to reject the null hypothesis at significance level of H0 : s1² = s2²
For the men, we have:
n1= 11 s1= 6.1
For the women, we have:
n2= 14 s2= 5.3The null and the alternate hypotheses are:
Null hypothesis H0 : s1² = s2²Alternate hypothesis H1 : s1² > s2²
The numerator and the denominator degrees of freedom are calculated as:
[tex]\mathbf{df = n -1}[/tex]
So, we have:
[tex]\mathbf{df_1 = 11 -1}[/tex]
[tex]\mathbf{df_1 = 10}[/tex] ----- numerator
[tex]\mathbf{df_2 = 14 -1}[/tex]
[tex]\mathbf{df_2 = 13}[/tex] ----- denominator
The test statistic of the f test is:
[tex]\mathbf{t = \frac{s_1^2}{s_2^2}}[/tex]
So, we have:
[tex]\mathbf{t = \frac{6.1^2}{5.3^2}}[/tex]
[tex]\mathbf{t = \frac{37.21}{28.09}}[/tex]
[tex]\mathbf{t = 1.325}[/tex]
The critical values at [tex]\mathbf{t = 1.325}[/tex] and the degrees of freedom is:
[tex]\mathbf{F= 2.671}[/tex]
By comparison, 1.325 is less than 2.671.
Hence, we fail to reject the null hypothesis at H0 : s1² = s2²
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Angelica’s bouquet of dozen roses contains 5 white roses. The rest of the roses. What fraction of the bouquet is pink? There are 12 roses in a dozen
Answer:
7/12
Step-by-step explanation:
total: 12 roses
white roses: 5
pink roses: 7
fraction of pink roses = 7/12
i need help on this pls
Answer:
Shawn earns $11 per hour.
Step-by-step explanation:
When looking at the x axis (hours), and find where 1 hour intersects with the y axis It intersects with the point labeled at $11. This means after working for 1 hour, Shawn earned $11.
Use the slope-intercept form of the linear equation to write an equation of the line with given slope and y-intercept.
Slope: -6/5 y intercept (0,8)
Answer:
5y + 6x = 40
Step-by-step explanation:
hope it is well understood?
somebody help me please
Answer:
115
Step-by-step explanation:
Since the lines are parallel, PWX+WXR=180, WXR=65. So PWX=(180-65)=115
Kayla made two paper chains. The paper links on one represented the number of days until her birthday, and the other showed the days until summer vacation. Altogether, she made 135 links for her chains. The birthday chain had twice as many links as the vacation chain. How many links are on Kayla's birthday chain?
Answer:
90 days
Step-by-step explanation:
b= number of days til her birthday
s = number of days til summer
b+s =135
b = 2s
2s+s = 135
3s = 135
Divide by 3
3s/3 =135/3
s =45
b = 2s = 2(45) = 90
Find the value of x on this triangle
Answer:
x = 35
Step-by-step explanation:
We can use the Pythagorean theorem since this is a right triangle
a^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse
x^2 + 12^2 = (x+2)^2
FOIL
x^2+144=x^2+4x+4
Subtract x^2 from each side
144= 4x+4
Subtract 4 from each side
140 = 4x
Divide by 4
35 =x
find the LCM of 210, 280, 360 by prime factorisation
Answer:
Step-by-step explanation:
210=2x3x5x7
280=2x2x2x5x7
360=2x2x2x3x3x5
Answer:
210= 2×3×5×7
280=2×2×2×5×7
360=2×2×2×3×3×5
common factors=2×2×2×3×5×7=840
uncommon factors=3
L.C.M=Common factors× uncommon factors
L.C.M=840×3
L.C.M=2520
Step-by-step explanation:
i hope it will be helpful
plzz mark as brainliest
need help asap :) ty
Answer:
3:7
Step-by-step explanation:
i hope this helps
I really need the help please and thank you
Answer:
B. [tex]f^{-1}(x)=\frac{x-4}{5}[/tex]
Step-by-step explanation:
To find the inverse of a function/equation:
Replace f(x) with y: y=5x+4 Switch x and y: x=5y+4 Solve for y: x-4=5y -> [tex]y=\frac{x-4}{5}[/tex]Write in standard inverse notation: [tex]f^{-1}(x)=\frac{x-4}{5}[/tex]I hope this helps!!
gl!
Many individuals over the age of 40 develop intolerance for milk and milk-based products. A dairy has developed a line of lactose-free products that are more tolerable to such individuals. To assess the potential market for these products, the dairy commissioned a market research study of individuals over 40 years old in its sales area. A random sample of 250 individuals showed that 86 of them suffer from milk intolerance. Based on the sample results, calculate a 90% confidence interval for the population proportion that suffers milk intolerance. Interpret this confidence interval. a) First, show that it is okay to use the 1-proportion z-interval. b) Calculate by hand a 90% confidence interval. c) Provide an interpretation of your confidence interval. d) If the level of confidence was 95% instead of 90%, would the resulting interval be narrower or wider
Answer:
a) To show that we can use the 1 proportion z-interval, we know that 250 ( size sample) is big enough to approximate the binomial distribution ( tolerance-intolerance) to a normal distribution.
b) See step by step explanation
CI 90 % = ( 0,296 ; 0,392)
c) We can support that with 90 % of confidence we will find the random variable between this interval ( 0,296 ; 0,392)
d) the CI 95 % will be wider
Step-by-step explanation:
Sample Information:
Sample size n = 250
number of people with milk intolerance x = 86
p₁ = 86 / 250 p₁ = 0.344 and q₁ = 1 - p₁ q₁ = 0,656
To calculate 90 % of Confidence Interval α = 10% α/2 = 5 %
α/2 = 0,05 z(c) from z-table is: z(c) = 1.6
Then:
CI 90 % = ( p₁ ± z(c) * SE )
SE = √ (p₁*q₁)/n = √ 0,225664/250
SE = 0,03
CI 90 % = ( 0,344 ± 1,6* 0,03 )
CI 90 % = ( 0,344 - 0,048 ; 0,344 + 0,048)
b) CI 90 % = ( 0,296 ; 0,392)
a) To show that we can use the 1 proportion z-interval, we know that 250 ( size sample) is big enough to approximate the binomial distribution ( tolerance-intolerance) to a normal distribution.
c) We can support that with 90 % of confidence we will find the random variable between this interval ( 0,296 ; 0,392) .
d) CI 95 % then significance level α = 5 % α/2 = 2.5 %
α/2 = 0,025 z(c) = 1.96 from z-table
SE = 0,03
And as 1.96 > 1.6 the CI 95 % will be wider
CI 95% = ( 0,344 ± 1.96*0,03 )
CI 95% = ( 0,344 ± 0,0588 )
CI 95% = ( 0,2852 ; 0,4028 )
What dimensions would you need to calculate the volume of a basketball?
radius and height
length, width and slant height
radius
length, width, and height
Answer:
Radius on it's own is enough
Step-by-step explanation:
you could get the radius from the other informations, but after all you will calculate the volume with it and not the otheds, so just take radius. a sphere is, in terms of information, the simplest 3D-body to describe, like with a circle in 2D
The dimensions would you need to calculate the volume of a basketball is Radius on its own is enough
We have given that,
radius and height
length, width, and slant height
radius
length, width, and height
We have to determine the dimensions would you need to calculate the volume of a basketball.
What is the dimension?
Dimensions in mathematics are the measure of the size or distance of an object or region or space in one direction.
you could get the radius from the other information, but after all, you will calculate the volume with it and not the others, so just take the radius.
A sphere is, in terms of information, the simplest 3D body to describe, like a circle in 2D.
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trong một thùng có chứa 3 bi đỏ 4 bi đen
Answer:
The FitnessGram™ Pacer Test is a multistage aerobic capacity test that progressively gets more difficult as it continues. The 20 meter pacer test will begin in 30 seconds. Line up at the start. The running speed starts slowly, but gets faster each minute after you hear this signal. [beep] A single lap should be completed each time you hear this sound. [ding] Remember to run in a straight line, and run as long as possible. The second time you fail to complete a lap before the sound, your test is over.ep explanation:
There is a path of width 2.5 m inside around a square garden of length 45m.
(a) Find the area of the path.
(b) How many tiles will be required to pave in the path by the square tiles of length 0.5m? Find it.
Help ! 도와주세요, 제발 :(
Answer:
2.5+2.5+45+45
=95.0m
therefore area of the square= 95.0m
45m×0.5=45.5÷95=
Step-by-step explanation:
2.5m
2.5 m tiles are required
[tex]area = 2.5 \times 45 = 192.5 \: squared \: cenimetre \\ \\ no \: of \: tiles = 0.5 \times 0.5 = 0.25 \\ 192.5 \div 0.25 = 770tiles[/tex]
tìm tích phân tổng quát
xy'lny/x=x+ylny/x
Answer:
rhe
ehd
end
Step-by-step explanation:
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Two sides of a triangle have lengths 13 m and 19 m. The angle between them is increasing at a rate of 2°/min. How fast is the length of the third side increasing when the angle between the sides of fixed length is 60°? (Round your answer to three decimal places.)
Answer:
The third side is increasing at an approximate rate of about 0.444 meters per minute.
Step-by-step explanation:
We are given a triangle with two sides having constant lengths of 13 m and 19 m. The angle between them is increasing at a rate of 2° per minute and we want to find the rate at which the third side of the triangle is increasing when the angle is 60°.
Let the angle between the two given sides be θ and let the third side be c.
Essentially, given dθ/dt = 2°/min and θ = 60°, we want to find dc/dt.
First, convert the degrees into radians:
[tex]\displaystyle 2^\circ \cdot \frac{\pi \text{ rad}}{180^\circ} = \frac{\pi}{90}\text{ rad}[/tex]
Hence, dθ/dt = π/90.
From the Law of Cosines:
[tex]\displaystyle c^2 = a^2 + b^2 - 2ab\cos \theta[/tex]
Since a = 13 and b = 19:
[tex]\displaystyle c^2 = (13)^2 + (19)^2 - 2(13)(19)\cos \theta[/tex]
Simplify:
[tex]\displaystyle c^2 = 530 - 494\cos \theta[/tex]
Take the derivative of both sides with respect to t:
[tex]\displaystyle \frac{d}{dt}\left[c^2\right] = \frac{d}{dt}\left[ 530 - 494\cos \theta\right][/tex]
Implicitly differentiate:
[tex]\displaystyle 2c\frac{dc}{dt} = 494\sin\theta \frac{d\theta}{dt}[/tex]
We want to find dc/dt given that dθ/dt = π/90 and when θ = 60° or π/3. First, find c:
[tex]\displaystyle \begin{aligned} c &= \sqrt{530 - 494\cos \theta}\\ \\ &=\sqrt{530 -494\cos \frac{\pi}{3} \\ \\ &= \sqrt{530 - 494\left(\frac{1}{2}\right)} \\ \\&= \sqrt{283\end{aligned}[/tex]
Substitute:
[tex]\displaystyle 2\left(\sqrt{283}\right) \frac{dc}{dt} = 494\sin\left(\frac{\pi}{3}\right)\left(\frac{\pi}{90}\right)[/tex]
Solve for dc/dt:
[tex]\displaystyle \frac{dc}{dt} = \frac{494\sin \dfrac{\pi}{3} \cdot \dfrac{\pi}{90}}{2\sqrt{283}}[/tex]
Evaluate. Hence:
[tex]\displaystyle \begin{aligned} \frac{dc}{dt} &= \frac{494\left(\dfrac{\sqrt{3}}{2} \right)\cdot \dfrac{\pi}{90}}{2\sqrt{283}}\\ \\ &= \frac{\dfrac{247\sqrt{3}\pi}{90}}{2\sqrt{283}}\\ \\ &= \frac{247\sqrt{3}\pi}{180\sqrt{283}} \\ \\ &\approx 0.444\text{ m/min}\end{aligned}[/tex]
The third side is increasing at an approximate rate of about 0.444 meters per minute.
9514 1404 393
Answer:
0.444 m/min
Step-by-step explanation:
I find this kind of question to be answered easily by a graphing calculator.
The length of the third side can be found using the law of cosines. If the angle of interest is C, the two given sides 'a' and 'b', then the third side is ...
c = √(a² +b² -2ab·cos(C))
Since C is a function of time, its value in degrees can be written ...
C = 60° +2t° . . . . . where t is in minutes, and t=0 is the time of interest
Using a=13, and b=19, the length of the third side is ...
c(t) = √(13² +19² -2·13·19·cos(60° +2t°))
Most graphing calculators are able to compute a numerical value of the derivative of a function. Here, we use the Desmos calculator for that. (Angles are set to degrees.) It tells us the rate of change of side 'c' is ...
0.443855627418 m/min ≈ 0.444 m/min
_____
Additional comment
At that time, the length of the third side is about 16.823 m.
__
c(t) reduces to √(530 -494cos(π/90·t +π/3))
Then the derivative is ...
[tex]c'(t)=\dfrac{494\sin{\left(\dfrac{\pi}{90}t+\dfrac{\pi}{3}\right)}\cdot\dfrac{\pi}{90}}{2\sqrt{530-494\cos{\left(\dfrac{\pi}{90}t+\dfrac{\pi}{3}}}\right)}}}\\\\c'(0)=\dfrac{247\pi\sqrt{3}}{180\sqrt{283}}\approx0.443855...\ \text{m/min}[/tex]
e movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer. How could you correctly rewrite the equation 4(10+5) = 6(12 - 2) using the distributive property
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Answer:
4·10 +4·5 = 6·12 -6·2
Step-by-step explanation:
Each outside factor multiplies each inside term.
4(10 +5) = 6(12 -2)
4·10 +4·5 = 6·12 -6·2
