a light is suspended at a height h above the floor. the illumination, i, at a point p is inversely proportional to the square of the distance, r, from the point p to the light and directly proportional to the cosine of the angle theta , I = k cos x / r² can be used to find the illumination at point p.
Light must be at the height of 7.07 for maximum illumination.
I = k cos x / r²
r² = h² + 10²
cos θ = h / [tex]\sqrt{h^{2} +10^{2} }[/tex]
then
I = [tex]k \frac{h}{(h^{2} + 100)^{2/3}}[/tex]
on differentiating, we get,
[tex]\frac{dI}{dh} = k\frac{h^{2} + 100^{3/2 - 3h^{2}(h^{2} + 100 )^{1/2} } }{(h^{2} +100)^{3} }[/tex]
[tex]= k\frac{100 - 2h^{2} }{(h^{2} + 100)^{5/2} } \\\frac{dI}{dh} = 0\\ It gives that \\h = \sqrt{50} = 7.07\\on differentiating again,\\\frac{d^{2} I}{dh^{2} } = k \frac{(6h^{3} - 900h )}{(h^{2} + 100)^{7/2} }[/tex]
for h = 7.07,
[tex]\frac{dI^{2} }{dh^{2} } = -10267.6[/tex]
So , we can conclude that the light must be at the height of 7.07 for maximum illumination.
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Find the volume of a rectangular prism if the length is x, the width is x2, and the height is 5x2 4x 1. use the formula v = l â‹… w â‹… h, where l is length, w is width, and h is height, to find the volume. 5x5 4x4 x3 5x4 4x3 x2 6x5 4x4 x3 6x4 4x3 x2
The volume of a rectangular prism if the length is 10ft is 250ft2.
What is a prism?A transparent optical prism is a device intended to refract light and has flat, polished surfaces. Prisms do not have two parallel surfaces; at least one of their surfaces must be slanted. Since a triangular prism with a triangular base and rectangular sides is the traditional geometrical shape of an optical prism, this type is typically meant when the word "prism" is used in everyday speech. Certain optical prism varieties don't actually have geometric prism shapes. Any material that transmits the wavelengths for which it is intended can be used to create prisms. Glass, acrylic, and fluorite are common building blocks.
From description, l = 2h = 2w
Since it has a square base,w=h
V = lwh = 2w•w•w = 2w3
Surface area, A = 2(wl+hl+hw) = 2(2w2+2w2+w2) = 250
5w2=250/2 = 125
w2= 25
V= 2(5)3 = 2(125)= 250 ft2
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Which expression is equivalent to
X^-5/3
Answer:
[tex]\frac{1}{x^{\frac{5}{3}}}[/tex]
Step-by-step explanation:
[tex]\frac{-5}{3}=-\frac{5}{3}\\x^{-\frac{5}{3}}\\x^{-\frac{5}{3}}=\frac{1}{x^{\frac{5}{3}}}\\\frac{1}{x^{\frac{5}{3}}}[/tex]
➲ Hope this helps.
help pls quickly!!!!
Answer:
answer is 4!
Step-by-step explanation:
Which two integers is –135 between?
Answer: -136 and -134
Step-by-step explanation:
Answer: 11 and 12
Step-by-step explanation:
you have to find the square root of 135. The square root of 135 is 11.6189
so the answer is between 11 and 12
PLEASE HELP ITS DUE TODAY
Answer: 1/36 ==> c
Step-by-step explanation:
[tex]6 ^{-2}[/tex]=
[tex]6 ^{-1*2}[/tex]=
[tex](6^{-1}) ^{2}[/tex]=
[tex](\frac{1}{6} ) ^{2}[/tex]=
[tex]\frac{1^{2}}{6^2}[/tex]=1/36 ==> c
A line passes through the points (1, 4) and (3, â€"4). which is the equation of the line? y = negative 4 x 8 y = â€"2x 6 y = negative one-fourth x 2 y = 2x 2
Answer:
declares that human rights are universal – to be enjoyed by all people, no matter who they are or where they live
Step-by-step explanation:
Write an equivalent expression by distributing the "-−" sign outside the parentheses:
-(-9d+4.9)
Step-by-step explanation:
- 1(- 9d + 4.9)
9d -4.9 would be your answer because the negative sign outside the parenthesis equals -1. Hope that helps!!
Answer:
9d - 4.9
Step-by-step explanation:
- ( - 9d + 4.9) ← multiply each term in the parenthesis by - 1
= 9d - 4.9
第 5 个问题 a multiple choice exam has 10 questions. each question has 3 possible answers, of which one is correct. a student knows the correct answers to 4 questions and guesses the answers to the other 6 questions. it turns out that the student answered the first question correctly. what are the chances that the student was merely guessing?
The chances that the student was merely guessing is 1/3.
Bayes Theorem determines the conditional probability of an event A given that event B has already occurred.
denoted by
[tex]P(A/B)=\frac{P(A)*P(B/A)}{P(B)}[/tex]
let A be the event that the student knows the answer .
B be the event that the student does not knows the answer .
and
E be the event he gets answer correct .
According to the given question
[tex]P(A)=\frac{4}{10} \\\\ P(B)=1-\frac{4}{10} =\frac{6}{10}[/tex]
Probability that the answer is correct ,given that he knows the answer is
[tex]P(E/A)=1[/tex]
Probability that the answer is correct ,given that he guesses it is
[tex]P(E/B)=\frac{1}{3}[/tex] [as the MCQ has 3 options and only one is correct]
We need to find the probability that he guesses the answer given that it is correct.
Required probability [tex]P(B/E)=\frac{P(B)*P(E/B)}{P(A)*P(E/A)+P(B)*P(E/B)}[/tex]
Substituting the values we get
[tex]P(B/E)=\frac{\frac{6}{10} *\frac{1}{3} }{\frac{4}{10} *1+\frac{6}{10} *\frac{1}{3} }[/tex]
[tex]=\frac{6}{30}*\frac{30}{18} \\ \\ =\frac{6}{18} \\ \\ =\frac{1}{3}[/tex]
Therefore , the chances that the student was merely guessing is 1/3.
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400
,
000
=
4
×
10
6
True or false
Answer: False
Step-by-step explanation:
4 x 106 = 424
Answer: false
Step-by-step explanation: I'm not even going to explain it just multiply 4 x 106
Find the distance between the two points rounding to the nearest tenth (if necessary)(9,5)and(4,-7)
Answer:
Step-by-step explanation:
Help me!
In below Diagram.
Answer:
23.3cm
Step by step:
Tri;APQ~Tri;ABC(A.A.A)
AP/AB=AQ/AC=PQ/BC
AP/AP+BP=AQ/AQ+QC
3/3+AQ=AQ/AQ+49/3
3AQ+49=3AQ+AQ^2
AQ^2=49
AQ=7
#AC=AQ+QC
=7+(49/3)
=23.333
(Thu Zar You should give me brainlist)
Find the first term, the common difference, and the sum of the first thirty-three terms of an arithmetic sequence in which t5=8, t10 = 15.5
The first term, the common difference, and the sum of the first thirty-three terms of the arithmetic sequence is 2, 1.5 and 68.5 respectively.
Arithmetic sequencet5 = 8t10 = 15.5First term = aCommon difference = da + 4d = 8
a + 9d = 15.5
Subtract to eliminate a9d - 4d = 15.5 - 8
5d = 7.5
d = 7.5/5
d = 1.5
substitute into
a + 4d = 8
a + 4(1.5) = 8
a + 6 = 8
a = 8 - 6
a = 2
Sum of the first 33 termsS33 = n/2 + {2a (n - 1)d}
= 33/2 + {2×2 + (33 - 1)1.5}
= 16.5 + {4 + (32)1.5}
= 16.5 + (4 + 48)
= 16.5 + 52
= 68.5
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A number is divided by 5.
Answer:
50 divided by 5 is 10
Step-by-step explanation:
Answer:
x/5
Step-by-step explanation:
Calculate the unknown angle of k
Answer:
60°
Step-by-step explanation:
since it is an equilateral triangle all sides are equal. let's make the other 2 angles k.
k+k+k=180°{sum of angles in a triangle}
3k=180°
k=60°(each of them is 60°)
-9x(-9)x(-9) what does it =
Answer:
-729
Step-by-step explanation:
-9 × (-9) × (-9) =
= 81 × (-9)
= -729
The area of a desert in africa is 5 times the area of a desert in asia . If the area of a desert in asia is x square miles , express the area of a desert in africa as an algebraic expression x.
The algebraic expression for the area of desert in Africa is 5 x
What are algebraic expressions?Algebraic expressions are expressions that are comprised of variables, terms, factors, coefficients, and constants.
They are also made up of mathematical operations such as addition, subtraction, multiplication, division, etc.
From the information given, we have;
Area of desert in Africa is 5 timesArea of desert in Asia is x square unitsThis can be expressed as;
Area of desert in Africa = 5 x
Thus, the algebraic expression for the area of desert in Africa is 5 x
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need help with homework
Answer:
b
Step-by-step explanation:
The base of Jada's toy box is a rectangle with length 4 feet and width 3 feet. The height of the toy box is 2 feet. What is the volume of the toy box?
The volume of the toy box is 24 cubic feet.
What is the volume of the toy box?
Remember that for a rectangular prism of length L, width W, and height H the volume is given by the formula:
V = L*W*H
In this case, we know that:
L = 4ft
W = 3ft
H = 2ft
Replacing that in the volume formula we get.
V = 4ft*3ft*2ft = 24ft^3
The volume of the toy box is 24 cubic feet.
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Pick the correct inequality sign to make the statement true.
|-53|∣−53∣_____|53|∣53∣
Pick the correct inequality sign to make the statement true.
|-53|∣−53∣_____|53|∣53∣
<<
>>
==
Considering the absolute value function, the correct statement is given by:
|-53| = |53|.
What is the absolute value function?The absolute function is defined by:
|x| = x, x ≥ 0.|x| = -x, x < 0.It measures the distance of a point x to the origin. For this problem, we have that:
-53 < 0, hence |-53| = -(-53) = 53.53 > 0, hence |53| = 53.Thus, the correct statement is given by:
|-53| = |53|.
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Use the given endpoint R and the midpoint M of segment RS to find the
coordinates of the other endpoint S. (Hint: Use the midpoint formula to
find the other endpoint.)
R(7,-17) and M (-2, 3)
Answer:
RS (-11,23)
Step-by-step explanation:
Don't know if this will help but if your looking for an endpoint, I did -2 = x+7/2 To find X. I got -2 from the X coordinate with midpoint. To get rid of the fraction I multiplied by 2 which leads to -4=x+7 since it cancels out the denominator/bottom fraction. X should be -11. Same thing with Y coordinate. 3= y- 17/2. Should give you 6=y- 17 which then becomes Y=23.
Sorry I'm not good at explaining
A smart-phone plan charges a fixed fee plus the cost of the data. If a plan with 2GB of data costs $75 and one with 5 GB costs $120, what is the rate charged for the data?
Answer:
61.2
Step-by-step explanation:
1) 75:2=37.2
2) 120:5=24
3) 37.2+24=61.2
A cyclist rides around a flat, circular track at constant speed. is the cyclist's acceleration vector zero?
The cyclist's acceleration vector is not zero.
For given question,
A cyclist goes around a level, circular track at constant speed.
We know that , acceleration is the rate at which velocity changes with time, in terms of both speed and direction.
When cyclist move around a circular track with constant speed cyclist's direction of motion changes with time.
This means, cyclist's velocity will change means cyclist's will have acceleration.
And cyclist's acceleration will not be zero.
Therefore, the cyclist's acceleration vector is not zero.
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Use the GCF and the Distributive Property to
rewrite the following expression:
48 + 60 I really need help
Hey there!
48 + 60 = 108
The DISTRIBUTIVE formula:
12(4 + 5)
= 12(4) + 12(5)
= 48 + 60
= 108
OR EVEN
12(4 + 5)
= 12(9)
= 108
Therefore, your answer should be:
12(4 + 5)
Goof luck on your assignment & enjoy your day!
~Amphitrite1040:)
Solve the equation below for x.
x – 15.2 = 76
A. x = 5
B. x = 60.8
C. x = 91.2
D. x = 1,155.2
The answer is C (x = 91.2)
Step-by-step explanation:
x - 15.2 = 76
x = 76 + 15.2
x = 91.2
questionamy is eight years older than twice her cousin alicia’s age. the sum of their ages is less than 32.let x represent alicia's age.which inequality represents alicia’s possible age?
An inequality that represents Alicia’s possible age is x < 8.
For given question,
let x represent Alicia's age.
Amy is eight years older than twice her cousin Alicia’s age.
So, Amy's age would be 2x + 8
The sum of their ages is less than 32.
We write above statement in mathematical expression.
sum of their ages = (2x + 8) + x
= 3x + 8
The sum of their ages is less than 32.
We use the symbol < for 'less than'
So, the mathematical expression form of given statement would be,
(3x + 8) < 32
So, we get an inequality 3x + 8 < 32
⇒ 3x < 32 - 8
⇒ 3x < 24
⇒ x < 24/3
⇒ x < 8
Therefore, an inequality that represents Alicia’s possible age is x < 8.
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Solve the given equation. If necessary, round to four decimal places.
log3^0.1+ 2log3^x = log3^2 + log3^ 5
Answer: log3^0.1+\:2log3^x\:=\:log3^2\:+\:log3^{\:}5
Step-by-step explanation: go to symbolab.com to get the step by step explanation or to answer problems like this hope this helps.
State which metric unit you would probably use to measure each item.
mass of a book
The gram and kilogram are two units used to measure mass in the metric system .
We need to find the metric unit to find mass of a book.
What is Mass?The resistance that a body of matter offers to a change in its speed or position upon the application of a force.
1 kilogram of a substance is equal to 1000 grams and 1 gram is equal to 0.001kg. Therefore, to convert the mass of a book weighing 12,321g into kg, we will multiply it by 0.001kg. The book's mass in kg is 12.321 kg.
Therefore mass is measured by kilogram or grams.
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If a right-angled triangle has two acute angles (each of which measures less than 90), then why is there a value for sin, cos, tan of obtuse angles (which are greater than 90)?
Step-by-step explanation:
Because in this situation you have 2 ways to solve it
Use angel without any change to get sinBut in this case you can't so we have another solution
Subtract angel from 360 it will give you result with negative or different results
If you have angel 100
The sin maybe equal sin100 or sin 360-100
Factorize it please
Answer: -m*(x-3y)*(3x-y)
(*=multiply btw)
Step-by-step explanation:
STEP 1:
Equation at the end of step 1
(m • ((x + y)2)) - 4m • (x - y)2
STEP2:
Equation at the end of step 2
m • (x + y)2 - 4m • (x - y)2
STEP3:
3.1 Evaluate : (x+y)2 = x2+2xy+y2
3.2 Evaluate : (x-y)2 = x2-2xy+y2
STEP4:
Pulling out like terms
4.1 Pull out like factors :
-3mx2 + 10mxy - 3my2 = -m • (3x2 - 10xy + 3y2)
Trying to factor a multi variable polynomial :
4.2 Factoring 3x2 - 10xy + 3y2
Try to factor this multi-variable trinomial using trial and error
Found a factorization : (x - 3y)•(3x - y)
A soup recipe requires 6 ounces of bouillon plus 2 ounces for each quart of water used.
This relationship is represented by the equation b = 2q +6, where b represents the
number of ounces of bouillon and q represents the number of quarts of water
Answer:
Slope=1.000/2.000=0.500
b-i
q-i
b-(2*q+6)=0
Step-by-step explanation:
1.1 Solve b-2q-6 = 0
Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).
"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.
In this formula :
y tells us how far up the line goes
x tells us how far along
m is the Slope or Gradient i.e. how steep the line is
b is the Y-intercept i.e. where the line crosses the Y axis
The X and Y intercepts and the Slope are called the line properties. We shall now graph the line b-2q-6 = 0 and calculate its properties
Notice that when b = 0 the value of q is 3/-1 so this line "cuts" the q axis at q=-3.00000
q-intercept = 6/-2 = 3/-1 = -3.00000
When q = 0 the value of b is 6/1 Our line therefore "cuts" the b axis at b= 6.00000
b-intercept = 6/1 = 6.00000
Slope is defined as the change in q divided by the change in b. We note that for b=0, the value of q is -3.000 and for b=2.000, the value of q is -2.000. So, for a change of 2.000 in b (The change in b is sometimes referred to as "RUN") we get a change of -2.000 - (-3.000) = 1.000 in q. (The change in q is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)
Slope = 1.000/2.000 = 0.500
Slope = 1.000/2.000 = 0.500
b-intercept = 6/1 = 6.00000
q-intercept = 6/-2 = 3/-1 = -3.00000