If x is increasing at a
rate of 2 units per second,
find the rate of change of theta
at the instant when x= 12 units.
Answers
Answer:
[tex]\frac{d\theta}{dt}=-\frac{2}{5}[/tex] at [tex]x=12[/tex]
Step-by-step explanation:
[tex]\frac{dx}{dt}=2[/tex]
[tex]\frac{d\theta}{dt}=?[/tex]
[tex]x=12[/tex]
[tex]cos(\theta)=\frac{adjacent}{hypotenuse}[/tex]
[tex]cos(\theta)=\frac{x}{13}[/tex]
[tex]\frac{d}{dt}cos(\theta)=\frac{d}{dt}\frac{x}{13}[/tex]
[tex]-sin(\theta)\frac{d\theta}{dt}=\frac{1}{13}\frac{dx}{dt}[/tex]
[tex]-sin(\theta)\frac{d\theta}{dt}=\frac{1}{13}(2)[/tex]
[tex]-sin(\theta)\frac{d\theta}{dt}=\frac{2}{13}[/tex]
[tex]\frac{d\theta}{dt}=\frac{2}{-13sin(\theta)}[/tex]
[tex]cos(\theta)=\frac{x}{13}[/tex]
[tex]cos(\theta)=\frac{12}{13}[/tex]
[tex]\theta=cos^{-1}(\frac{12}{13})[/tex]
[tex]\frac{d\theta}{dt}=\frac{2}{-13sin(\theta)}[/tex]
[tex]\frac{d\theta}{dt}=\frac{2}{-13sin(cos^{-1}(\frac{12}{13}))}[/tex]
[tex]\frac{d\theta}{dt}=\frac{2}{-13(\frac{5}{13})}[/tex]
[tex]\frac{d\theta}{dt}=\frac{2}{-5}[/tex]
[tex]\frac{d\theta}{dt}=-\frac{2}{5}[/tex]
The value of θ is given by the inverse sine function, from which the rate of
change of θ with respect to x can be derived.
The rate of change of θ at the instant when x = 12 units is -0.4 rad/sReasons:
[tex]\displaystyle \frac{dx}{dt} = \mathbf{2 \ units \ per \ second}[/tex]
[tex]\displaystyle cos(\theta) = \frac{x}{13}[/tex]
[tex]\displaystyle \theta = arccos \left(\frac{x}{13}\right)[/tex]
[tex]\displaystyle \frac{d}{dx} \theta = \frac{d\left(arccos \left(\frac{x}{13}\right)\right)}{dx} = \mathbf{\frac{\sqrt{169-x^2} }{x^2-169}}[/tex]
Using chain rule of differentiation, we have;
[tex]\displaystyle \frac{d\theta}{dt} = \mathbf{ \frac{d\theta}{dx} \times \frac{dx}{dt}}[/tex]
Therefore;
[tex]\displaystyle \frac{d\theta}{dt} =\frac{\sqrt{169-x^2} }{x^2-169}\times \frac{dx}{dt} = \mathbf{\frac{\sqrt{169-x^2} }{x^2-169}\times 2}[/tex]
When x = 12, we get;
[tex]\displaystyle \frac{d\theta}{dt} =\frac{\sqrt{169-12^2} }{12^2-169}\times 2 = -\frac{2}{5} = -0.4[/tex]
The rate of change of the angle, θ, with time at the instant when x = 12 is -0.4 rad/s
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Related Questions
Women comprise 83.3% of all elementary school teachers. In a random sample of 300 elementary school teachers, what is the probability that fewer than 260 are women?
Answers
Using the normal approximation to the binomial, it is found that there is a 0.9319 = 93.19% probability that fewer than 260 are women.
In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X. The binomial distribution is the probability of x successes on n trials, with p probability of a success on each trial. It can be approximated to the normal distribution with [tex]\mu = np, \sigma = \sqrt{np(1-p)}[/tex].In this problem:
Women comprise 83.3% of all elementary school teachers, hence [tex]p = 0.833[/tex]A sample of 300 teachers is taken, hence [tex]n = 300[/tex]The mean and the standard deviation for the approximation are given by:
[tex]\mu = np = 300(0.833) = 249.9[/tex]
[tex]\sigma = \sqrt{np(1 - p)} = \sqrt{300(0.833)(0.167)} = 6.46[/tex]
Using continuity correction, as the binomial distribution is discrete and the normal distribution is continuous, the probability that fewer than 260 are women is P(X < 260 - 0.5) = P(X < 259.5), which is the p-value of Z when X = 259.5, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{259.5 - 249.9}{6.46}[/tex]
[tex]Z = 1.49[/tex]
[tex]Z = 1.49[/tex] has a p-value of 0.9319.
0.9319 = 93.19% probability that fewer than 260 are women.
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If angle CAB= x+40, angle ACB=3x+10, angle CBD= 6x, what is angle CAB
Answers
I’m pretty sure it’s B
Explanation:
Add 3x+10 + x+40 and set it equal to 6x. then when you solve for x you get 25
Hope this helps!
please help!! easy but i don't understand <3
Answers
in essence it's just asking on getting the equation of that line in more or less slope-intercept form, hmmm well, it's a line, so all we need is two points to get it, hmmm let's see let's use the starting point and terminal point, so we know it goes through the origin, (0,0) and also goes through (1, 0.7), let's change 0.7 to a fraction, so its 7/10, ok, let's use those two points from it.
[tex](\stackrel{x_1}{0}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{\frac{7}{10}}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{\frac{7}{10}}-\stackrel{y1}{0}}}{\underset{run} {\underset{x_2}{1}-\underset{x_1}{0}}}\implies \cfrac{~~ \frac{7}{10}~~}{1}\implies \cfrac{7}{10}[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{0}=\stackrel{m}{\cfrac{7}{10}}(x-\stackrel{x_1}{0})\implies y = \cfrac{7}{10}x[/tex]
Use the formula Sn =a (1 - rn ) ÷ (1 – r) to find the sum Sn for each of the infinite and finite geometric series.
9. The first 9 terms of 12, – 6 ,+ 3, - …
10. The first 15 terms of -1, + 1, -…
11. The first 6 terms of 1, + 3, + …
12. The first 10 terms of 2, – 4, + …
Answers
Answer: 11
Step-by-step explanation:
9. The Sum of 9 terms is 513/64.
10. The sum of 15 terms is -1.
11. The sum of 6 terms is 364
12. The sum of 10 terms is -682.
We have,
Sn =a (1 - [tex]r^n[/tex] ) ÷ (1 – r)
9. 12, -6, 3, .....
Here, r= -6/ 12= -1/2
So, S(9)
= 12 (1- [tex](-1/2)^9[/tex])/ (1 - (-1/2))
= 513/ 64
10.-1, +1, -.....
Here, r= 1/ (-1)= -1
So, S(15) = 1 (1- [tex](-1)^{15[/tex])/ (1 - (-1))
= -1
11. 1, 3, .....
Here, r = 3/1 = 3
So, S(6) = 1 (1- [tex](3)^{6[/tex])/ (1 - 3)
= 364
12. 2, -4, ...
Here, r= (-4)/ 2= -2
So, S(10) = -682
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Find the equation of the line passing through the point (−5,−9) and parallel to the line y=3x+2 .
Answers
Answer:
Root:(-⅗,0)
vertical intercept:(0,5)
Step-by-step explanation:
Omar deposited $4000 into an account with 4.4% interest, compounded quarterly. Assuming that no withdrawals are made, how much will he have in the account after 10 years?
Do not round any intermediate computations, and round your answer to the nearest cent.
Answers
future value
principal
int
compound
years
PLEASE HELP I WILL MARK YOU BRAINLEST!!!
please read the question on the photo and these are the choices bellow!!
A-translation, reflection
B- rotation, reflection
C-reflection, rotation
D-rotation, translation
Answers
Line j has an equation of y = 1/5x + 7. Perpendicular to line j is line k, which passes through
the point (-1, -3). What is the equation of line k?
Write the equation in slope-intercept form. Write the numbers in the equation as simplified
proper fractions, improper fractions, or integers.
Answers
keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above
[tex]\begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}\qquad \impliedby y=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{1}{5}}x+7 \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}} {\stackrel{slope}{\cfrac{1}{5}}\qquad \qquad \qquad \stackrel{reciprocal}{\cfrac{5}{1}}\qquad \stackrel{negative~reciprocal}{-\cfrac{5}{1}\implies -5}}[/tex]
so then line K has a slope of -5 and pass through (-1, -3)
[tex](\stackrel{x_1}{-1}~,~\stackrel{y_1}{-3})\qquad \qquad slope=m=-5 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-3)}=\stackrel{m}{-5}[x-\stackrel{x_1}{(-1)}] \\\\\\ y+3=-5(x+1)\implies y+3=-5x-5\implies y=-5x-8[/tex]
if z1= 3+3i and z2=7(cos(5pi/9) + i sin (5pi/9)), then z1/z2= blank
Answers
[tex]z1=\stackrel{a}{3}+\stackrel{b}{3}i~~ \begin{cases} r = \sqrt{a^2+b^2}\\ r = \sqrt{18}\\[-0.5em] \hrulefill\\ \theta =\tan^{-1}\left( \frac{b}{a} \right)\\ \theta =\frac{\pi }{4} \end{cases}~\hfill z1=\sqrt{18}\left[\cos\left( \frac{\pi }{4} \right) i\sin\left( \frac{\pi }{4} \right) \right] \\\\[-0.35em] ~\dotfill[/tex]
[tex]\cfrac{z1}{z2}\implies \cfrac{\sqrt{18}\left[\cos\left( \frac{\pi }{4} \right) i\sin\left( \frac{\pi }{4} \right) \right]} {7\left[\cos\left( \frac{5\pi }{9} \right) i\sin\left( \frac{5\pi }{9} \right) \right]} \\\\[-0.35em] ~\dotfill\\\\ \qquad \textit{division of two complex numbers} \\\\ \cfrac{r_1[\cos(\alpha)+i\sin(\alpha)]}{r_2[\cos(\beta)+i\sin(\beta)]}\implies \cfrac{r_1}{r_2}[\cos(\alpha - \beta)+i\sin(\alpha - \beta)] \\\\[-0.35em] ~\dotfill[/tex]
[tex]\cfrac{z1}{z2}\implies \cfrac{\sqrt{18}}{7}\left[\cos\left( \frac{\pi }{4}-\frac{5\pi }{9} \right)+i\sin\left( \frac{\pi }{4}-\frac{5\pi }{9} \right) \right] \\\\\\ \cfrac{\sqrt{18}}{7}\left[\cos\left( \frac{-11\pi }{36} \right) +i\sin\left( \frac{-11\pi }{36} \right) \right]\implies \cfrac{\sqrt{18}}{7}\left[\cos\left( \frac{83\pi }{36} \right) +i\sin\left( \frac{83\pi }{36} \right) \right] \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \cfrac{z1}{z2}\approx 0.348~~ + ~~0.496i~\hfill[/tex]
The value of z1/z2 is √18/ 7 (cos ( 11π/36 ) - isin ( 11π/36 )).
What is complex number?"A complex number is the sum of a real number and an imaginary number and it is of the form x + iy and is usually represented by z".
For the given situation,
z1= 3+3i and
z2= 7(cos(5π/9) + i sin (5π/9))
To divide the complex numbers, both should be in same form.
Convert z1 in polar form.
z is of the form x+iy, so, r=[tex]\sqrt{x^{2}+y^{2} }[/tex]
⇒[tex]r=\sqrt{3^{2}+3^{2} }[/tex]
⇒[tex]r=\sqrt{18}[/tex]
θ = [tex]tan^{-1}(\frac{b}{a} )[/tex]
⇒[tex]tan^{-1}(\frac{3}{3} )[/tex]
⇒[tex]tan^{-1}(1)[/tex]
⇒[tex]45[/tex]°
The polar form is of the form, z= r (cosθ + i sinθ),
⇒ z1 = [tex]\sqrt{18}[/tex] (cosπ/4 + isinπ/4)
The formula for dividing complex number is
z1/z2 = r1(cos θ1 + isin θ1) / r2(cos θ2 + isin θ2)
⇒ z1/z2 = r(cosθ + isinθ)
where, r = r1/r2 and θ = (θ1 - θ2)
z1/z2 = [tex]\sqrt{18}[/tex] (cos π/4 + isin π/4) / 7 (cos 5π/9 + isin 5π/9)
⇒ r = [tex]\sqrt{18}[/tex] / 7 and
θ = (π/4 - 5π/9 )
⇒ θ = (-11π/36)
cos(-θ) = cos θ
⇒cos( -11π/36 ) = cos ( 11π/36 )
sin(-θ) = -sin θ
⇒ sin ( -11π/36 ) = -sin ( 11π/36 )
Thus, z1/z2 = [tex]\sqrt{18}[/tex] / 7 (cos ( 11π/36 ) - isin ( 11π/36 ))
Hence we can conclude that the value of z1/z2 is
√18/ 7 (cos ( 11π/36 ) - isin ( 11π/36 )).
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a. How much higher is 500 than 400 m?
b. How much higher is 500 than -400 m?
C. What is the change in elevation from 8,500 m to 3,400 m?
d. What is the change in elevation between 8,500 m and -300 m?
Answers
B 900m
C -5,100m
D- 8,800
Sara has $65 and wants to buy the following items from a store. Board game: $14.95 Building blocks: $25.49 Art kit: $35.79 At the store, all items are one-fourth off of the original price and there is a 5% sales tax. Sara wants to know if she can buy all of these items. Which statement is TRUE?
Answers
The correct statement is Sara can afford to purchase the items because the final price of the items is $60.
The first step is to determine the total cost of the items Sara wants to buy. The total cost can be determined by adding the cost of the items together.
Total cost = $14.95 + $25.49 + $35.79 = $76.23
The second step is to determine the cost of the items after the discount.
Price of the items = total cost x (1 - discount)
= total cost x (1 - 1/4)
total cost x 3/4
$76.23 x 3/4 = $57.17
The third step is to determine the cost of the items after tax.
Cost = (1.05) x $57.17 =$60.03
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round 3,817,453 to the nearest 100
Answers
Answer:
The nearest hundredth would be 3,817,500
Step-by-step explanation:
The hundreds place is the four and the five behind it rounds the number to a up to a 5
the line passes through the point (4,7) and has a slope that is reciprocal of the slope of the line y=1/3x+2
point slope form and slope intercept form pls
Answers
first you have to change 1/3 to -3
y=-3x+2
then you have to replace 2 with 'b' because you don't know the y intercept yet
y=-3x+b
then you substitute the point (4,7) into the equation
7= -3(4) + b
7= -12 + b
19 = b
y = -3x + 19 is the equation in slope intercept form
for point slope form:
-3x is still the slope and you replace x and y with the point 4,7
y- 7= -3 (x-4)
GUYS PLEASE HELP ME ON THIS ONE!, i will give brainliest to the right answers
Aisha has $40 to spend for her ornithology club. She spends some of it buying birdseed and saves the rest. Her savings is given by f(x)=40−1.25x, where x is the number of pounds of birdseed she buys at $1.25 per pound.
Answers
Answer:
Step-by-step explanation:
Given f(x)=40-1.25x, where x=pounds of birdseed and 40=her saved amount, and birdseed costs 1.25/lb.
f(3)=40-1.25(3)
f(3)40-3.75
f(3)=36.25
If she buys (3 pounds) of birdseed, she saves ($36.25).
f(18)=40-1.25(18)
f(18)=40-22.5
f(18)=17.5
If she buys (18 pounds) of birdseed, she saves ($17.5)
f(36)=40-1.25(36)
f(36)=40-45
f(36)=-5
If she buys (36 pounds) of birdseed, she will need an extra $5 to pay off her debt.
If she buys (36 pounds) of birdseed, she will need an extra $5 to pay off her debt.
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
Given function f(x)=40-1.25x,
where x=pounds of birdseed and 40 is her saved amount, and birdseed costs is 1.25/lb.
f(3)=40-1.25(3)
f(3)40-3.75
f(3)=36.25
If she buys (3 pounds) of birdseed, she saves ($36.25) then;
f(18)=40-1.25(18)
f(18)=40-22.5
f(18)=17.5
If she buys (18 pounds) of birdseed, she saves ($17.5) then;
f(36)=40-1.25(36)
f(36)=40-45
f(36)=-5
If she buys (36 pounds) of birdseed, she will need an extra $5 to pay off her debt.
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HELP ME. NO LINKS!! PLEASE
Answers
Answer: 99% sure its b
Step-by-step explanation:
PLEASE ANSWER FOR 30 POINTS
Answers
Answer:
One Solution
Step-by-step explanation:
x + 3y = 3
x - y = -3
4y = 6 Subtract to solve by elimination.
y = [tex]\frac{3}{2}[/tex] Divide by 4.
x - [tex]\frac{3}{2}[/tex] = -3 Substitute [tex]\frac{3}{2}[/tex] for y in the original equation.
x = -[tex]\frac{3}{2}[/tex] Add [tex]\frac{3}{2}[/tex].
log x √x + log √c c² = ?
[tex] log_{x}\sqrt{x} + log_{ \sqrt{c} } {c}^{2} = \\ [/tex]
please help me!!!!?;
Answers
Given that
log √x (x) + log c² (c)
⇛ log x^1/2 (x) + log c² (c)
We know that
log a^m (b^n) = m/n log a (b)
⇛ 1/2 log x (x) + 2 log c (c)
We know that
log a ( a) = 1
⇛ (1/2)(1) + 2(1)
⇛ (1/2)+2
⇛ (1+4)/2
⇛ 5/2
Answer:- log √x (x) + log c² (c) = 5/2
[(x) ,(c) , (a) represents the bases ]
Additional comment:
(a+b)(a-b) = a²-b²log a^m (b^n) = m/n log a (b)log a ( a) = 1also read similar questions: if log^2(x)=log^2(a)+log^2(b)-log^2(c) then x is....
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simplify the following expression. log(x2) - log(x) A. log(x^2+x) B. log(x^3) C. log(x^2-x) D. log(x)....
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Please look at picture for question
Answers
Answer:
a=0.62
b=7/9
c=10/9
On the 1st January 2014 Carol invested some money in a bank account.
The account pays 2.5% compound interest per year.
On 1st January 2015 Carol withdrew £1000 from the account.
On 1st January 2016 she had £23517.60 in the account.
Work out how much Carol originally invested in the account.
Answers
Answer:
didn't know how to workout iam only 3rd standard
Answer:
Step-by-step explanation:
bubble gum
A wall map of the United States has a distance of 8.5 in. between Memphis and Denver, two cities that are actually 1040 mi apart. The actual distance between St. Louis and Des Moines is 333 mi. How far apart are St. Louis and Des Moines on the map?
Answers
Answer:
2.72 inches
Step-by-step explanation:
1040/8.5=122.35
1 inch on the map = 122.35 miles actual distance
333/122.35=2.72
Determine the area of the yellow sector
Answers
Answer:
146 is the answer im positive
HELP!! I'm not sure what goes in the blank.
Answers
Answer:
10[tex]sin^{2} ([/tex]β[tex])[/tex]
Step-by-step explanation:
We can find this two ways, first by seeing in the step after it, cosines are canceled out. Since you already have 10[tex]sin^{2} ([/tex]β[tex])[/tex] on the next step, you can assume that (since only the cosines changed and the cosine next ot the blank was removed), the value is 10[tex]sin^{2} ([/tex]β[tex])[/tex].
You can also use double angle formulas from the previous step:
(sin(2β) = 2 sin(β) cos(β))and find that:
5 sin (2β) sin(β) = 5 * (2 sin(β) cos(β)) sin(β)) = (10 sin(β) sin(β)) cos(β) =
10[tex]sin^{2} ([/tex]β[tex])[/tex] cos(β)
But since cos(β) is already present, we can see that the answer is 10[tex]sin^{2} ([/tex]β[tex])[/tex]
Line f is parallel to line g.which statements about line f and g is true
Answers
Answer:
Step-by-step explanation:
They have different y intercepts.
They have the same slope.
Here are 2 examples
y = 3x + 5
y = 3x + 19
The slopes are both three. The y intercepts are 5 for the top equation and 19 for the bottom equation.
They are both lines. That means their domain is -infinity <x < + infinity
Their range is - infinity <y < + infinity.
We are excluding examples like x = 3 and x = 5 and y = 1 and y = 3.
It is true that they both are parallel in both cases, but the discussion for each pair is a little different.
A movie theater charges $8.00 for adults and $5.00 for children. If there were 40 people altogether and the theater collected $272.00 at the end of the day, how many
of them were adults?
A. 29 adults
B. 16 adults
C. 24 adults
D.10 adults
Answers
Answer:
C.24
Step-by-step explanation:
First multiply 8 by 24 this is so you know how much 24 adults would be. You will get 192 so next you need to subtract 192 from the total money 272 to get 80 and 80 should be how much all of the kids cost now to check and make sure there are 40 people divide 80 by 5 to get 16 which is the total number of kids no just add 16 and 24 together to get 40
Apply distributive 15+22
Answers
Answer:37
Step-by-step explanation:
pls help. Have tried this problem a couple times but my answers didnt work
Answers
Answer:
infinite solutions...
Step-by-step explanation:
Is there more information to this problem? It can be pretty much anything.
N=3M
Nina can be 30 and Maryna 10, Nina can be 3 and Maryna 1, Nina can be 15 and Maryna 5...
Answer:
N - 4 = 3(M - 4). Simplified further, N - 4 = 3(M - 4)
Given,
Nina is N years old now and;
Maryna is M years old now
If four years ago, Nina was three times as old as Maryna was, then
Four years ago, Nina's age was N - 4
Four years ago, Maryna's age was M - 4
Given that Nina was three times as old as Maryna was four years ago, it means that
N - 4 = 3(M - 4)
To solve further
N = 3m - 12 + 4
N = 3M - 8
Step-by-step explanation:
help me pleas, I need the energy.
Answers
Answer:
negative
Step-by-step explanation:
Answer:
negative
Step-by-step explanation:
as it goes further right, it goes further down, so it is a negative slope
Mai makes her favorite shade of green paint by using 5 cups of blue paint for every 3 cups of yellow paint. Priya makes her favorite shade of green paint by using 7 cups of blue paint for every 5 cups of yellow paint. Whose favorite shade of green paint has more of a blue tint? Explain how you know.
Answers
Answer:
Priya
Step-by-step explanation:
Mai= 5:3 Priya=7:5
Mai= 15:15 Priya=21:15
The ratios above are blue:yellow so Priya's shade has more of a blue tint because it is 21:15 and Mai's is 15:15 so it is evenly spread.
I need to know the area of this triangle and I would like to have an explanation because I dont know how to do it I know the formula just not how to get the height
Answers
Answer:
18 square units
Step-by-step explanation:
When one side is vertical or horizontal, it is convenient to find the height from the opposite vertex to that side. It is generally an integer number of grid squares.
Here, the height is 4 -(-2) = 6. The base length is 1 -(-5) = 6. That means the area is ...
A = 1/2bh
A = 1/2(6)(6) = 18 . . . . square units
_____
Alternate solution
If you want to go at this the hard way, you can find the length of LK and the distance of J to that line.
The length of LK is ...
d = √((x2 -x1)^2 +(y2 -y1)^2) = √((4 -(-2))^2 +(3 -(-5))^2) = √(36 +64) = 10
The distance to line LK can be found by writing the equation of the line LK in general form:
4x -3y -7 = 0
Then the distance formula for point (x, y) is ...
d = |4x -3y -7|/√(4^2 +3^2)
d = |4(-2) -3(1) -7|/5 = |-8 -3 -7|/5 = 3.6
Using the area formula with these dimensions gives ...
A = 1/2bh = 1/2(10)(3.6) = 18 . . . . square units
Answer:
18 square units
Step-by-step explanation:
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From a sample of 45 students exam scores, it was found that there was a mean score was 75 and a standard deviation of 5. Assume the distribution of exam scores is normal.
construct and interpret a 95% confidence interval for the true mean score.
Answers
Answer:
The 95% confidence interval for the true mean score is [tex][73.539,76.461][/tex]
Step-by-step explanation:
Note that [tex]CI=\bar x\pm z\frac{s}{\sqrt{n}}[/tex] where [tex]\bar x[/tex] is the sample mean, [tex]z[/tex] is the upper critical value for the desired confidence level, [tex]s[/tex] is the sample standard deviation, and [tex]n[/tex] is the sample size.
Therefore, [tex]CI=75\pm 1.96\frac{5}{\sqrt{45}}\approx[73.539,76.461][/tex]