[tex]\dfrac{\dfrac{1}{p-2}}{\dfrac{4p^2}{p^2+p-6}}=\\\\\\\dfrac{1}{p-2}\cdot\dfrac{p^2+p-6}{4p^2}=\\\\\dfrac{1}{p-2}\cdot\dfrac{p^2+3p-2p-6}{4p^2}=\\\\\dfrac{1}{p-2}\cdot\dfrac{p(p+3)-2(p+3)}{4p^2}=\\\\\dfrac{1}{p-2}\cdot\dfrac{(p-2)(p+3)}{4p^2}=\\\\\dfrac{p+3}{4p^2}[/tex]
--------------------------------------------------------------------
[tex]\dfrac{6n}{3n+2}-\dfrac{2}{2n-2}=\\\\\dfrac{6n(2n-2)}{(3n+2)(2n-2)}-\dfrac{2(3n+2)}{(3n+2)(2n-2)}=\\\\\dfrac{12n^2-12n-(6n+4)}{6n^2-6n+4n-4}=\\\\\dfrac{12n^2-12n-6n-4}{6n^2-2n-4}=\\\\\dfrac{12n^2-18n-4}{6n^2-2n-4}=\\\\\dfrac{2(6n^2-9n-2)}{2(3n^2-n-2)}=\\\\\dfrac{6n^2-9n-2}{3n^2-n-2}[/tex]
----------------------------------------------------------------------
[tex]\dfrac{2x}{3x^2+18x}+\dfrac{3}{2}=\\\\\dfrac{2}{3x+18}+\dfrac{3}{2}=\\\\\dfrac{2\cdot2}{2(3x+18)}+\dfrac{3(3x+18)}{2(3x+18)}=\\\\\dfrac{4+9x+54}{6x+36}=\\\\\dfrac{9x+58}{6x+36}[/tex]
Answer:
p^3−10p^2+1
—————— We find roots of zeros F(p) = p^3 - 10p^2 + 1 and see there
p^2 are no rational roots
Step-by-step explanation:
p^2
Simplify ——
p^2
1.1 Canceling out p^2 as it appears on both sides of the fraction line
Equation at the end of step 1
:1
((————-(4•1))+p)-6
(p^2)
STEP 2: working left to right
1
Simplify ——
p^2
Equation at the end of step 2:
1 /p^2 ((—— - 4) + p) - 6
STEP 3:
Rewriting the whole as an Equivalent Fraction
3.1 Subtracting a whole from a fraction
Rewrite the whole as a fraction using p^2 as the denominator :
4 4 • p^2
4 = — = ——————
1 p^2
Equivalent fraction
: The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
Adding fractions that have a common denominator :
3.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
1 - (4 • p^2) 1 - 4p^2
———————————— = ———————
p^2 p^2
Equation at the end of step 3:
(1 - 4p^2)
(————————— + p) - 6
p^2
STEP 4:
Rewriting the whole as an Equivalent Fraction
4.1 Adding a whole to a fraction
Rewrite the whole as a fraction using p2 as the denominator :
p p • p^2
p = — = ——————
1 p^2
Trying to factor as a Difference of Squares:
4.2 Factoring: 1 - 4p^2
Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)
Proof : (A+B) • (A-B) =
A2 - AB + BA - B2 =
A2 - AB + AB - B2 =
A2 - B2
Note : AB = BA is the commutative property of multiplication.
Note : - AB + AB equals zero and is therefore eliminated from the expression.
Check : 1 is the square of 1
Check : 4 is the square of 2
Check : p^2 is the square of p^1
Factorization is : (1 + 2p) • (1 - 2p)
Adding fractions that have a common denominator :
4.3 Adding up the two equivalent fractions
(2p+1) • (1-2p) + p • p^2 p^3 - 4p^2 + 1
———————————————————————— = ————————————
p^2 p^2
Equation at the end of step
4:
(p^3 - 4p^2 + 1)
—————————————— - 6
p^2
STEP 5:
Rewriting the whole as an Equivalent Fraction
5.1 Subtracting a whole from a fraction
Rewrite the whole as a fraction using p^2 as the denominator :
6 6 • p^2
6 = — = ——————
1 p^2
Polynomial Roots Calculator :
5.2 Find roots (zeroes) of : F(p) = p^3 - 4p^2 + 1
Polynomial Roots Calculator is a set of methods aimed at finding values of p for which F(p)=0
Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers p which can be expressed as the quotient of two integers
The Rational Root Theorem states that if a polynomial zeroes for a rational number P/Q then P is a factor of the Trailing Constant and Q is a factor of the Leading Coefficient
In this case, the Leading Coefficient is 1 and the Trailing Constant is 1.
The factor(s) are:
of the Leading Coefficient : 1
of the Trailing Constant : 1
Let us test ....
P Q P/Q F(P/Q) Divisor
-1 1 -1.00 -4.00
1 1 1.00 -2.00
Polynomial Roots Calculator found no rational roots
Adding fractions that have a common denominator :
5.3 Adding up the two equivalent fractions
(p3-4p2+1) - (6 • p2) p3 - 10p2 + 1
————————————————————— = —————————————
p2 p2
Polynomial Roots Calculator :
5.4 Find roots (zeroes) of : F(p) = p3 - 10p2 + 1
See theory in step 5.2
In this case, the Leading Coefficient is 1 and the Trailing Constant is 1.
The factor(s) are:
of the Leading Coefficient : 1
of the Trailing Constant : 1
Let us test ....
P Q P/Q F(P/Q) Divisor
-1 1 -1.00 -10.00
1 1 1.00 -8.00
Polynomial Roots Calculator found no rational roots
Final result :
p3 - 10p2 + 1
—————————————
p2
PLEASE HELP! I need this answered ASAP ;-; (Question is shown below in the attachment)
Answer:
3.14 units²
Step-by-step explanation:
The key realization here is that this shape is one quarter of a circle.
Therefore, it's area will be [tex]\frac{1}{4}[/tex] of the whole circle's area.
So, let's first find the area as if this were a whole circle.
The formula is [tex]\pi r^2[/tex], and we know that the radius, r, is 2. So:
[tex]\pi\cdot2^2\\\\\pi\cdot4\\\\3.14\cdot4\\\\12.56[/tex]
Now we need to find one fourth of this, we can do this by dividing by 4.
[tex]12.56\div4=3.14[/tex]
Hope this helped!
Answer:
pi units squared
Step-by-step explanation:
(cant find pi sign)
(pi times r^2)/4
4pi/4
pi
you move right 3 units and left 4 units. you end at (-3,-1). where did you start?
Answer:
(-2,-1) is where u start
Step-by-step explanation:
Answer:
(-2,-1)
Step-by-step explanation:
The point we ended at is (-3,-1)
We have moved 4 units left so we will add 4 to -3
● -3+4 = 1
We have moved 3 unirs right so we will substract 3 from 1
● 1-3 = -2
So the initial point was (-2,-1)
Find f-1.
f(x)=4 log2 (x – 7)
Answer:
f(1) = 10.33985 + 18.1294406 i
Step-by-step explanation:
f(1) = 4log2(1-7)
f(1) = 10.33985 + 18.1294406 i
1. Association Suppose you were to collect data for each pair of
variables. You want to make a scatterplot. Which variable would
you use as the explanatory variable and which as the response
variable? Why? What would you expect to see in the scatter-
plot? Discuss the likely direction, form, and strength.
a) Apples: weight in grams, weight in ounces
b) For each week: ice cream cone sales, air-conditioner sales
c) College freshmen: shoe size, grade point average
d) Gasoline: number of miles you drove since filling up, gallons
remaining in your tank
An executive drove from his home at an average speed of 35 mph to an airport where a helicopter was waiting. The executive then boarded the helicopter and flew to the corporate offices at an average speed of 78 mph. The entire distance from his home to the office was 169.5 if the executive spent the same amount of time in the car as he did the helicopter how long did it take the executive to get to work
Answer:
3 hours
Step-by-step explanation:
Speed is the ratio of distance traveled to time taken, it is given as:
Speed = distance / time
An executive drove from his home at an average speed of 35 mph to an airport where a helicopter was waiting. He then took the helicopter and flew to the corporate offices at an average speed of 78 mph. Given that the executive spent the same amount of time in the car as he did the helicopter how long did it take the executive to get to work.
Let the amount of time the executive spent in the car be t hours, therefore the amount of time spent in the helicopter = t hours.
For car:
Speed = distance / time
35 = distance ([tex]d_1[/tex]) / t
[tex]d_1=35t[/tex]
For helicopter:
Speed = distance / time
78 = distance ([tex]d_2[/tex]) / t
[tex]d_2=78t[/tex]
The total distance traveled = 169.5 miles
[tex]d_1+d_2=169.5\\35t+78t=169.5\\113t=169.5\\t=169.5/113\\t=1.5\ hours[/tex]
The time taken for the executive to get to work = time spent on car + time spent on helicopter = 1.5 + 1.5 = 3 hours
HELPP! QUICKKKK! Lol
Problem:
Last year I attended the Jurassic World Dinosaur Exhibit with my family and my friend and her family. My
family includes 2 adults (including myself) and my child we paid a total of $94. Her family includes 2
adults and 2 children she paid a total of $110. What was the admission price for an adult ticket and how
much was it for the admission price for a child ticket?
Let a represent adult ticket price
Let c represent child ticket price
Answer:
Child ticket = $16.
Step-by-step explanation:
Let adult tickets = a;
child ticket = c.
2a + c = 94 — eq no. 1,
2a + 2c = 110 — eq no. 2,
then,from eq 1,
c = 94 - 2a. —eq no. 3.
Substitute eq 3 into eq 2,
2a + 2(94 - 2a) = 110
2a - 4a = 110 - 188
-2a /-2 = -78 / -2
a = 39.
Substitute value of a into eq 3,
c = 94 - 2(39)
= 94 - 78
c = 16.
Thus, child ticket = $16.
kristen and melissa spent 35% of their $32 on movie tickets. how much money did they spend
Answer:
11.2$
Step-by-step explanation:
Kristina and Melissa had 32$ at total
● 32$ => 100%
They have spent 35%
Let x be that amount
● x => 35%
●32 => 100
● x => 35
● x = (35×32)/100 = 11.2$
They have spent 11.2$
Answer:
They spent $20.80
Step-by-step explanation:
Since they had $32 and spent 35% of it you would do 32 * 35%
then you would get 11.2
now that is not the answer because that is just what 35% of 32 is
to get the answer you would then subtract 11.2 from 32 to get 20.8
and since this is a matter of money you would write 20.8 as $20.80.
Please Answer ASAP!!!
-343x , x = -2
g(x) { (x-1)(x+2) , x = -1
x^3 - x^2 + 1 , x is not equal to -2, -1
What is g(1) ???
Answer: g(1) is 1.
Step-by-step explanation:
If we are solving for g of 1 then the first equation can't be used to solve for g of 1 because it only works in x is equal to -2.
The same way the second function will not work because x has to equal to -1.
But in the last function which is written as a polynomial it will work for this situation because x is not equal to -2 or -1 so apart from those numbers every number will work the same way 1 will work.
So plot 1 into the function and solve for it .
g(1) = 1^3 - 1^2 + 1
g(1)= 1 - 1 + 1
g(1)= 1
15 POINTS IF SOMEONE ANSWERS QUICK
Answer:
The 16 cases will fit the box as shown.
Step-by-step explanation:
One disk case has the dimensions 14.2 cm by 19.3 cm, with thickness 1.6 cm.
Temporarily ignoring the 14.2 cm and 19.3 cm measurements, we multiply this 1.6 cm thickness by 16, obtaining a total thickness for the stack of cases of 25.6 cm.
1) The 16 cases, arranged as shown, and measuring 25.6 cm from left to right in this diagram, will fit within the 26 cm horizontal distance shown.
2) The horizontal length of each case is 14.2 cm. Stacked as shown, the 16 cases will fit within the 15 cm depth of the box.
3) The vertical measurement of each case is 19.3 cm. The 20 cm vertical measurement of the box can accommodate this 19.3 height within 20 cm.
All indications are that the 16 cases will fit comfortably inside the box.
Answer:
16 discs capacity of the cuboid.
Step-by-step explanation:.
for simplicity...
i would just divide 26cm to 1.6cm = 16 .25
therefore, 16 discs capacity of the cuboid.
f(x) = [tex]\sqrt{x+7} -\sqrt{x^2+2x-15}[/tex] find the domain
Answer:
x >= -7 ................(1a)
x >= 3 ...............(2a1)
Step-by-step explanation:
f(x) = [tex]\sqrt{x+7}-\sqrt{x^2+2x-15}[/tex] .............(0)
find the domain.
To find the (real) domain, we need to ensure that each term remains a real number.
which means the following conditions must be met
x+7 >= 0 .....................(1)
AND
x^2+2x-15 >= 0 ..........(2)
To satisfy (1), x >= -7 .....................(1a) by transposition of (1)
To satisfy (2), we need first to find the roots of (2)
factor (2)
(x+5)(x-3) >= 0
This implis
(x+5) >= 0 AND (x-3) >= 0.....................(2a)
OR
(x+5) <= 0 AND (x-3) <= 0 ...................(2b)
(2a) is satisfied with x >= 3 ...............(2a1)
(2b) is satisfied with x <= -5 ................(2b1)
Combine the conditions (1a), (2a1), and (2b1),
x >= -7 ................(1a)
AND
(
x >= 3 ...............(2a1)
OR
x <= -5 ................(2b1)
)
which expands to
(1a) and (2a1) OR (1a) and (2b1)
( x >= -7 and x >= 3 ) OR ( x >= -7 and x <= -5 )
Simplifying, we have
x >= 3 OR ( -7 <= x <= -5 )
Referring to attached figure, the domain is indicated in dark (purple), the red-brown and white regions satisfiy only one of the two conditions.
3 to the power of 5 equals 243. Explain how to use that fact to quicky evaluate 3 to the power of 6.
Answer:
3^6 = 729
Step-by-step explanation:
3 to the power of 5 equals 243. Explain how to use that fact to quickly evaluate 3 to the power of 6
Symbolically, we have:
3^5 = 243 (given)
Multiplying both sides by 3, we get:
3^6 = 3(243)
If you want to take this further, multiply 3(243): 3^6 = 729
The value of [tex]3^6[/tex] is 729.
Important information:
[tex]3^5=243[/tex]Exponents:We need to find the value of [tex]3^6[/tex].
Using the rules of exponents, we get
[tex]3^6=3^{5+1}[/tex]
[tex]3^6=3^{5}*3^{1}[/tex] [tex][\because a^{m+n}=a^ma^n][/tex]
[tex]3^6=243*3[/tex]
[tex]3^6=729[/tex]
Therefore, the value of [tex]3^6[/tex] is 729.
Find out more about 'Exponents' here:
https://brainly.com/question/14404700
can somewon help me plz can somewon help me
Hey there! I'm happy to help!
Let's look at our diameters.
[tex]1*10^2^1\\5*10^2^2[/tex]
We want to see how many times greater the diameter of the IC 1101 is than the Milky Way. So, we will divide it's diameter by the diameter of the Milky Way.
[tex]\frac{5*10^2^2}{1*10^2^1} \\[/tex]
We divide the numbers without exponents, giving us 5. Then, we divide the 10s with exponents. When dividing exponents, you subtract the numbers in the exponent to get your result. For example, x³÷x²=x
[tex]\frac{5*10^2^2}{1*10^2^1} = 5*10=50[/tex]
Therefore, your answer is 50.
Have a wonderful day! :D
20x-4y=40
Find the slope of the linear equation
Answer:
the slope is 5
Step-by-step explanation:
Solve for y
20x -4y = 40
Subtract 20x from each side
20x-20x -4y = -20x +40
-4y = -20x+40
Divide each side by -4
-4y/-4 = -20x/-4 +40/-4
y = 5x -10
This is in slope intercept form y = mx+b where m is the slope and b is the y intercept
The slope is 5
Solve for y:
20x - 4y = 40
Subtract 20x to both sides
-4y = 40 - 20x
Divide -4 to everything
y = -10 + 5x
Therefore, the slope is 5
Best of Luck!
The function f is defined by f(x) = (x + 3)(x + 1).
The graph of f in the xy-plane is a parabola. Which
of the following intervals contains the x-coordinate
of the vertex of the graph of f?
Answer:
Below in bold.
Step-by-step explanation:
The zeroes ( = x-intercepts) are x = -3 and x = -1.
So the x -coordinate of the vertex is between x = -3 and x = -1.
The actual x-coordinate is halfway between these value: at x = -2.
Answer:
x = -3 or x = -1
Step-by-step explanation:
f(x) = (x + 3)(x + 1)
⇒ x = -3 or x = -1
The Greenbaum family agreed to pay for 3 months of an online TV service in exchange for a $5 credit on the bill each month. If the Greenbaums spend a total of $11.85 on the service over the 3 months, what is the normal price of one month of online TV service?
$5.00
$6.85
$8.95
$30.55
Triangle ABC is dilated to form new triangle DEF. If angle A is congruent to angle D, what other information will prove that the two triangles are similar by the AA similarity postulate?
Angle B is congruent to angle E.
Side AB is congruent to side DE.
Angle C is congruent to angle D.
Side BC is congruent to side EF.
Answer:
Step-by-step explanation:
option A , angle B is congruent to angle E { SINCE IT IS AA POSTULATE
Answer:
B=E (b)
Step-by-step explanation:
Write a equation representing the area Bruce covered, y, in terms of the number of tiles he used,x.
A equation representing the area Bruce covered, y, in terms of the number of tiles he used x is y = 4x
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. For example, 3x – 5 = 16 is an equation
According to the question
The area Bruce covered shows by y axis
The number of tiles he used is x axis .
The tiles Bruce used is 1/4 of a square foot in area .
Therefore,
Area of tiles in square foot = 4 number of titles
= 4x
now,
Equation will be :
y = 4x
Hence, A equation representing the area Bruce covered, y, in terms of the number of tiles he used x is y = 4x
To know more about equation here:
https://brainly.com/question/10413253
#SPJ3
Please help I don't understand this problem!
Answer:
-17
Step-by-step explanation:
First thing to do in this equation is to multiply both sides by 22.
This becomes, -5+x=-22
Add 5 to both sides.
x=-17
Answer:
x = -17
Step-by-step explanation:
-5+x
-------- = -1
22
Multiply each side by 22
-5+x
-------- * 22= -1 *22
22
-5 +x = -22
Add 5 to each side
-5+x +5 = -22 +5
x = -17
The height of a kicked football can be represented by the polynomial –16t2 + 47t + 3 = 0, where t is the time in seconds. Find the time in seconds of when the football hits the ground.
Step-by-step explanation:
-16t2 + 47t + 3 = 0
-16t2 + 48t - t + 3 = 0
-16t( t - 3) - 1 ( t - 3) = 0
-16t - 1 = 0. t - 3 = 0
-16t = 1 t = 3
t = 1/ - 16.
PLEASE HELP ASAP WILL GIVE BRAINLY!!!!!!
What is the value of the discriminant of the quadratic equation -2x2=-8x+8, and what does its value mean about the number of real number solutions the equation has?
The discriminant is equal to 0, which means the equation has no real number solutions.
The discriminant is equal to 0, which means the equation has one real number solution.
The discriminant is equal to 128, which means the equation has no real number solutions.
The discriminant is equal to 128, which means the equation has two real number solutions.
Answer:
B: The discriminant is equal to zero which means it has one real number solution
Step-by-step explanation:
Hello Again!!
Your right answer will be is B. The discriminant is equal to 0, which means the equation has one real number solution.
For this case we have the following quadratic equation:
2x^2 - 8x + = 0
Where:
a = 2
B = -8
c = 8
The discriminant is given by:
d = b^2 - 4(a)(c)
Substituting the values we have:
d = (-8)^2 - 4(2)(8)
d = 64 - 64
d = 0
So, Your best answer choice is B.
Good Luck!!
•Comments•
Ask if you need help! Because I'm glad to help you.
By ☆Itsbrazts☆
if all the possible values of x are indicated by the shaded part of the number line above, which number line best shows all possible values of 1/x? (the shaded part in the number line is 0.5 to 1.5, the whole number line segment is from 0 to 3)
Answer:
can i see a picture of the number line?
Step-by-step explanation:
What type of number is −7? There may be more than one correct answer. Select all that apply. If only one answer is correct, select "only" and the answer that applies. integer only whole rational natural
Answer:
-7 is a Negative Number, which is also an integer.
Step-by-step explanation:
Negative numbers are any number less than 0. The greater a negative number is, is the smaller its value.
How would I solve this question? y = -1 1/8 - 7/8x -4x + 9y = -22 x = ?, y = ?
Find the measure of b+d.
Answer:
=90
Step-by-step explanation:
because d=32° and b=58°
this is because corresponding angles are equal
Answer:
Step-by-step explanation:
b+d =90 degree
hope it helps
Fill in the blank with a constant, so that the resulting quadratic expression is the square of a binomial. $\[x^2 + 22x + \underline{~~~~}.\]$
Answer:
[tex]$\[x^2 + 22x + 121\]$[/tex]
Step-by-step explanation:
Given
[tex]$\[x^2 + 22x + \underline{~~~~}.\]$[/tex]
Required
Fill in the gap
Represent the blank with k
[tex]$\[x^2 + 22x + k\]$[/tex]
Solving for k...
To do this, we start by getting the coefficient of x
Coefficient of x = 22
Divide the coefficient by 2
[tex]Result = 22/2[/tex]
[tex]Result = 11[/tex]
Take the square of this result, to give k
[tex]k= 11^2[/tex]
[tex]k= 121[/tex]
Substitute 121 for k
[tex]$\[x^2 + 22x + 121\]$[/tex]
The expression can be factorized as follows;
[tex]x^2 + 11x + 11x + 121[/tex]
[tex]x(x + 11)+11(x+11)[/tex]
[tex](x+11)(x+11)[/tex]
[tex](x+11)^2[/tex]
Hence, the quadratic expression is [tex]$\[x^2 + 22x + 121\]$[/tex]
Two-ninths of the total number of batteries in Richard's desk drawer is made
up of 16 batteries. How many batteries are there in the drawer?
You are told 2/9 = 16
Let total number of batteries = x
So you now have 2/9x = 16
To find x divide both sides by 2/9
X = 72 total batteries
Awnser
72
i dunno how to explain i did it in my head
A dance studio charges $12 per dance class. The studio is offering a 15% discount if you pay a set of 5 classes now. How much does it cost to buy 5 classes with this offer?
Answer:
The cost might be or would be$53.00
Simplify (−3c3w5)3. −9c6w8 −9c9w15 −27c6w8 −27c9w15
Answer:
-6723cw
Step by Step:
(-3c * 3w * 5) * 3 - 9c * 6w* 8 - 9c * 9w * 15 - 27c * 6w * 8 - 27c * 9w * 15
If [tex]\frac{x}{y}[/tex] = [tex]\frac{3}{4}[/tex], [tex]\frac{y}{z}[/tex] = [tex]\frac{2}{3}[/tex], [tex]\frac{z}{w}[/tex] = [tex]\frac{5}{8}[/tex], what is the value of [tex]\frac{x+y+w}{w}[/tex]?
Please Help me!! An 8 foot high camel is loping away from a streetlight. The camel is loping at 12 feet/second. The streetlight is 20 feet high. How fast is the camel’s shadow growing?
Answer:
Camel's shadow is growing at a rate of 8 ft/sec.
Step-by-step explanation:
Given:
Height of camel = 8 ft
Height of streetlight = 20 ft
Speed of camel = 12 ft / sec
To find:
How fast is the camel's shadow growing = ?
Solution:
First of all, have a look at the image attached for the situation as given in the question statement.
PQ be the streetlight.
AB be the camel.
Camel is loping away from the streetlight.
BT will be the shadow of the camel.
We are given that speed of camel = 12 ft / sec
And we know that Speed is the Rate of change of distance w.r. to time.
i.e. as per the image, we are given:
[tex]\dfrac{dx}{dt} = 12 ft /sec[/tex]
And we have to find the value of:
[tex]\dfrac{ds}{dt} = ?[/tex]
(Because s is the shadow length and we have to find the rate of change of shadow's length w.r.to time.)
Here, let us consider the two similar triangles [tex]\triangle TAB\ and\ \triangle TPQ[/tex]as per the image attached:
Ratio of corresponding sides will be same.
[tex]\dfrac{AB}{PQ}=\dfrac{TB}{TQ}\\\Rightarrow \dfrac{8}{20}=\dfrac{s}{s+x}\\\Rightarrow 8s+8x=20s\\\Rightarrow 12s = 8x\\\Rightarrow s = \dfrac{2}{3}x[/tex]
Now, differentiating w.r.to t:
[tex]\dfrac{ds}{dt}=\dfrac{2}{3}\dfrac{dx}{dt}\\\Rightarrow \dfrac{ds}{dt}=\dfrac{2}{3}\times 12\\\Rightarrow \dfrac{ds}{dt}=\bold{8\ ft/sec}[/tex]
Camel's shadow is growing at a rate of 8 ft/sec.
