Answer:
Your answer is:
The Prime: 2 x 2 x 2 x 3 x 5
Exponential: 2^3 x 3^1 x 5^1
CSV: 2, 2, 2, 3, 5
Step-by-step explanation:
Hope this helped : )
Let p(x) be a polynomial of degree 4 having extremum at x = 1 ,2 and
[tex]\displaystyle\sf \lim_{x\to 0}\left( 1+\dfrac{p(x)}{x^2}\right) = 2 [/tex]
Then the value of p(2) is ?
PLEASE CHECK THE ATTACHED FILE
We are given that ;
[tex]{\quad \longrightarrow \displaystyle \sf \lim_{x\to 0}\bigg\{1+\dfrac{p(x)}{x^2}\bigg\}=2}[/tex]
Where p(x) is a polynomial of degree 4 , it will help us later, but let's do some manipulations first ;
Can be further written as ;
[tex]{:\implies \quad \displaystyle \sf 1+\lim_{x\to 0}\bigg\{\dfrac{p(x)}{x^2}\bigg\}=2}[/tex]
[tex]{:\implies \quad \displaystyle \sf \lim_{x\to 0}\bigg\{\dfrac{p(x)}{x^2}\bigg\}=1}[/tex]
So, here p(x) is polynomial of degree 4, so it will be a biquadratic polynomial, so we will write p(x) in the form of general biquadratic polynomial, so p(x) = ax⁴ + bx³ + cx² + dx + e
Now, first find p(x)/x² ;
[tex]{:\implies \quad \sf \dfrac{p(x)}{x^2}=\dfrac{ax^{4}+bx^{3}+cx^{2}+dx+e}{x^2}}[/tex]
[tex]{:\implies \quad \sf \dfrac{p(x)}{x^2}=ax^{2}+bx+c+\dfrac{d}{x}+\dfrac{e}{x^2}}[/tex]
So now, as [tex]{\bf{x\to 0}}[/tex] , for any values of a, b, c, d and e, the RHS will approach ∞ iff d ≠ e ≠ 0, as the denominator of d and e will be approaching 0 and so the whole limit will be ∞ , but we want the limit to be approaching 1, so when if d = e = 0, the denominator of d and e will be approaching 0 (not absolutely 0), and if d = e = 0, we will have the limit be approaching ax²+ bx + c for x approaching 0 being the limit 1 , and for any values of a, b and c . So now we have ;
[tex]{:\implies \quad \displaystyle \bf \lim_{x\to 0}\dfrac{p(x)}{x^{2}}=\begin{cases}\bf \infty \:, iff\: d\neq e\neq 0 \\ \\ \bf 1\:, iff\: d=e=0\end{cases}}[/tex]
So, now we had to consider the second case, for which the limit is approaching 1, for d = e = 0, so the limand here will just be ax² + bx + c
Now, we so have ;
[tex]{:\implies \quad \displaystyle \sf \lim_{x\to 0}ax^{2}+bx+c=1}[/tex]
Putting the limit we will have ;
[tex]{:\implies \quad \sf c=1}[/tex]
So, now as p(x) have extremum at 1 and 2, so p'(x) = 0, for x = 1, 2 , so now finding p'(x)
[tex]{:\implies \quad \sf p(x)=ax^{4}+bx^{3}+x^{2}\quad \qquad \{\because c=1\: and\: d=e=0\}}[/tex]
So, differentiating both sides wr.t.x ;
[tex]{:\implies \quad \sf p^{\prime}(x)=4ax^{3}+3bx^{2}+2x}[/tex]
Now, p'(1) and p'(2) must be 0
[tex]{:\implies \quad \sf p^{\prime}(1)=4a+3b+2=0}[/tex]
[tex]{:\implies \quad \sf p^{\prime}(2)=32a+12b+4=0}[/tex]
So, now we have ;
[tex]{\quad \longrightarrow \displaystyle \begin{cases}\bf 4a+3b=-2 \\ \\ \bf 32a+12b=-4\end{cases}}[/tex]
On multiplying first equation by 8 on both sides we can thus obtain ;
[tex]{\quad \longrightarrow \displaystyle \begin{cases}\bf 32a+24b=-16 \\ \\ \bf 32a+12b=-4\end{cases}}[/tex]
On solving both the equations we will be having ;
[tex]{\quad \longrightarrow \displaystyle \begin{cases}\bf a=\dfrac{1}{4} \\ \\ \bf b=-1\end{cases}}[/tex]
So , now as d = e = 0, c = 1, a = (1/4), b = -1, so putting all the values in p(x) we can obtain p(x) as ;
[tex]{:\implies \quad \sf p(x)=\dfrac{1}{4}(x)^{4}-(x)^{3}+x^{2}}[/tex]
Now, at x = 2 ;
[tex]{:\implies \quad \sf p(2)=\dfrac{1}{4}(2)^{4}-(2)^{3}+2^{2}}[/tex]
[tex]{:\implies \quad \sf p(2)=4-8+4=8-8}[/tex]
[tex]{:\implies \quad \bf \therefore \quad \underline{\underline{p(2)=0}}}[/tex]
This is the required answer
PLEASE HELP
Can kept track of the number of hours that he spent at the pool each week for several weeks. He spent 8, 2, 7, 4, and 4 hours. What is the median number of hours that Van spent at the pool each week?
A. 6 hours
B. 25 hours
C. 4 hours
D. 5 hours
Answer: 4 Hours
Step-by-step explanation:
-x + 3 = 7
X=-4
X= 7
X= 4
X = -7
Answer:
x = -4
Step-by-step explanation:
Step 1: Write equation
-x + 3 = 7
Step 2: Solve for x
Subtract 3 on both sides: -x = 4Divide both sides by -1: x = -4Step 3: Check
Plug in x to verify it's a solution.
-(-4) + 3 = 7
4 + 3 = 7
7 = 7
Discuss the steps that you used to create your tangent line in #1. What was the most important step? Your discussion should be a minimum of three sentences
To create a tangent line, 1st we need to know the points at which the tangent is to be located, then calculate the slope and finally with the help of these points and slope we can construct the equation of tangent line.
We need to take the following steps in order to build a tangent line:
We start by locating the curve point to which we want to locate the tangent line. Say, these points are [tex]x_1[/tex] and [tex]y_1[/tex]The slope (m) of the curve at that point is then determined by taking the function's derivative. The slope displays the function's rate of change at that precise location. The equation of the tangent line is then created by entering the coordinates of the point and the slope using the line's point-slope form. This equation is as follows: [tex]y - y_1 = m (x - x_1)[/tex]Hence, the above three steps are crucial to create a tangent line.
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How many arrangements of the cabbages keep repeated words together.
It is 5,760.
Stay safe & humble <3
0.5(x4 − 9) + 17 PLS IN 3 MINS
Answer:
2x+12.5
Step-by-step explanation:
0.5(x4-9) +17
=0.5(4x-9)+12
=2x-4.5+17
=2x+12.5
Which sentence about the division of two fractions is true? A. If the dividend is greater than the divisor, the quotient will be greater than 1. B.If the dividend is less than the divisor, the quotient will be greater than 1 C. If the dividend is equal to the divisor, the quotient will be less than 1 D. If the dividend is greater than the divisor, the quotient will be less than 1.
Answer:
A. If the dividend is greater than the divisor, the quotient will be greater than 1.
Step-by-step explanation:
Checking all options
A. If the dividend is greater than the divisor, the quotient will be greater than 1.
That is,
4 ÷ 3 = 1.33
Where,
4 is the dividend
3 is the divisor
1.33 is the quotient
THIS IS TRUE
B.If the dividend is less than the divisor, the quotient will be greater than 1
That is,
3 ÷ 4 = 0.75
Where,
3 is the dividend
4 is the divisor
0.75 is the quotient
NOT TRUE
C. If the dividend is equal to the divisor, the quotient will be less than 1
That is,
3 ÷ 3 = 1
Where,
3 is the dividend
3 is the divisor
1 is the quotient
NOT TRUE
D. If the dividend is greater than the divisor, the quotient will be less than 1.
That is,
4 ÷ 3 = 1.33
Where,
4 is the dividend
3 is the divisor
1.33 is the quotient
NOT TRUE
Therefore, option A is TRUE
Help Help :(:(:(:(:(:(
Answer:
Kuroo Here!
Step-by-step explanation:
What do you need help with?
What is the slope of the line y
= -4?
Answer:
The slope is 0 or there is no slope.
Step-by-step explanation:
Only a y-intercept of -4.
Answer:
0
Step-by-step explanation:
The slope is defined as rise/run. Since y does not increase at all as x increases, the slope is 0.
Maria has already written 2/5 of her 1,000 word essay. If she continues writing at the same pace of 6One-half words per minute, which expression shows the amount of time it will take her to write the rest of the essay? please i just want to know how to get 3/5
Answer:
167 minutes
Step-by-step explanation:
i took the test this was right
hope this helps!
Answer:
I think the answer would be 1000 x 2 Over 5 divided by 13 Over 2
Step-by-step explanation:
Sorry if I'm wrong I'm in the test
The science club is planning a field trip to a museum. Each student will pay $10 for admission and an equal share of the $200 transportation cost. The total cost per student is given by the expression LaTeX: C=\frac{200}{S}+10C = 200 S + 10, where LaTeX: SS is the number of students that went on the field trip. What does the term LaTeX: \frac{200}{S}200 S in the expression represent?
Answer: [tex]\dfrac{200}{S}[/tex] represents the transport cost per student in the expression.
Step-by-step explanation:
Given: For trip,
Admission fee per student = $10
Transport cost (for all students0 = $200
Here, S represents the number of students went on the field trip.
Transport cost per student = (Total cost) ÷ Total student
So, [tex]\dfrac{200}{S}[/tex] represents the transport cost per student.
Hence, [tex]\dfrac{200}{S}[/tex] represents the transport cost per student in the expression.
Please help!!!!!!!!!
HELP ASAP LOOK AT PICTURE
Answer:
A XD (um i dont know what else to put sof frpijfpoemd-eod)
A truck costs $80,000. It depreciates in value $6,000 per year. Write a linear model in the form v(t)=mt + b where v(t) represents the current value of the truck after t years of ownership.
The required expression is v(t) = 80,000 - $6000t
Cost of the truck = $80,000
Depreciation rate = $6000/year
What is cost price?
Cost price is that price for buyer which he pays to seller for an object or product.
Required expression-
m = $6000
t = time in years
b = original price
v(t) = mt + b
v(t) = -$6000t + $80000
negative sign for depreciation
Thus, the required expression is v(t) = 80,000 - $6000t
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A mother shared a sum of money amongst his three sons Jorge, Luis and Robert in the ratio of 3:5:4 respectively. If Robert received $320. How much was the total money shared?
she cut the sum in (3+5+4) in 12 parts
J had 3/12 of the sum S
L had 5/12 of the sum S
and R had 4/12 of the sum S
4/12 x S = 320
S = 320 x 12/4
S = 960
$960 shared
if x=13 what is 5x - 2 =
Answer:
63
Step-by-step explanation:
5(13)-2 is 65-2 or 63.
I need help figuring this out and how to do it
Answer:
5) y=2x^2+16x+32
Step-by-step explanation:
So the following equations on your paper are in vertex form. We want to turn these into standard form.
Remember, standard form is ax^2+bx+c and vertex form is y=a(x-h)^2+k
Lets expand our first problem, y=2(x+4)^2
y=2(x+4)(x+4)
y=2(x^2+8x+16)
y=2x^2+16x+32
Our answer for question 5 is y=2x^2+16x+32
If you need help with the other questions just add a comment.
Answer:
#5
y = 2(x + 4)^2 y = 2((x + 4)(x + 4))y = 2(x(x + 4) + 4(x + 4))y = 2(x^2 + 4x + 4x + 16) y = 2(x^2 + 8x + 16) y = 2x^2 + 16x + 32#6
y = -2(x + 2)^2 y = -2((x + 2)(x + 2)) y = -2(x(x + 2) + 2(x + 2)) y = -2(x^2 + 2x + 2x + 4) y = -2(x^2 + 4x + 4) y = -2x^2 - 8x - 8#7
y = -(x + 7)^2 y = -((x + 7)(x + 7)) y = -(x(x + 7) + 7(x + 7))y = -(x^2 + 7x + 7x + 49) y = -(x^2 + 14x + 49) y = -x^2 - 14x - 49#8
y = (x - 5)^2 + 9 y = (x - 5)(x - 5) + 9 y = x(x - 5) + (-5)(x - 5) + 9 y = x^2 - 5x - 5x + 25 + 9 y = x^2 - 10x + 25 + 9 y = x^2 - 10x + 36is the mean of 2 3 4 6 x and 8 is 5 find the value of x
Step-by-step explanation:
The mean is the total sum of the numbers all over the amount of numbers in the question.
Mean=(2+3+4+6+x+8)÷6
NB: 6 is the number of figures available in the question
If Mean =5
5=(23+x)÷6
Multiply both side by 6
5 x 6 = 23 + x
30 = 23 + x
30 - 23 = x
7 = x
Answer:
7
Step-by-step explanation:
We can start by counting the number of values we have, which would be 6 if we count the x. Now multiply 5 by 6 and we get 30. Now we know that 2+3+4+6+x+8 is 30 and so we can subtract all the values, giving us x=7. If we substitute it back in, we get 2+8 which is 10, 4+6 which is also 10, and 7+3 which is 10 again. 10+10+10=30 and now divide 30 by 6 and we get 5; the mean. Hope this helps!
Graph the inequality: 2x+y>4
Step-by-step explanation:
Took the test! Good luck
sure thing but first start off by creating the function that we want to plot but isolating y.
y>-2x+4
Technically we are graphing the line of equation y=-2x+4 and finding the values where y>-2x+4
Now using the original equation;
2x+y>4
let's take the origin (0,0) as our reference.
substitute the values in the equation
2(0)+0>4
0>4
False, then this part of the graph is rejected and we want to take the other side :P
st
2. Find the surface area of the sphere below.
.
3.1 m
-
Answer:
120.7016
Step-by-step explanation:
surface area of sphere=4πr²
solution
=4*3.14*3.1*3.1
=120.7016
Approximately 9% of men have a type of color blindness that prevents them from distinguishing between red and green. suppose that 8 men are selected at random. what is the probability that at least one of them will have this type of red-green color blindness
Use a net to find the surface area of the right triangular prism
35 sq. ft.
80 sq. ft.
84 sq. ft.
244 sq. ft
256 sq. ft.
258 sq. ft.
270 sq. ft.
286 sq. ft.
5,040 sq. ft.
Answer:
244 sq. ft.
Step-by-step explanation:
The net for a triangular prism consists of a central rectangle and two triangles. The length of the central rectangle is equal to the perimeter of the triangular faces.
__
The area of the central rectangle of the net is ...
A = LW = (12 +7 +10 ft)(6 ft) = 174 ft²
The two triangles are right triangles, so the area of each is half the product of the leg lengths.
A = 1/2(bh) = 1/2(10 ft)(7 ft) = 35 ft²
Then the sum of the rectangle and two triangles is ...
surface area = 174 ft² +2 × 35 ft² = 244 ft²
HELPPP FOR FOR BRIANLEST!!!!
Using the pythagorean theorem, we have :
[tex]4^{2} + x^{2} = 8.5^{2}[/tex]
[tex]x^{2} = 72.25 - 16 = 56.25 \\x = \sqrt{56.25} = 7.5[/tex]
(a+7)2
please expand it
r + 11 + 8r= 29
Show answer
Answer:
r=2
Step-by-step explanation:
r + 8 r + 11 = 29
( 1 + 8 ) r + 11 = 29 9 r + 11 = 29
Now we can isolate and solve for r while always keeping the equation balanced: First, subtract 11 from each side of the equation:
9 r + 11 − 11 = 29 − 11
9 r + 0 = 18
9 r = 18
Now we can divide each side of the equation by 9 to get
r : 9 over 9 = 18 under 9
1 r = 2
r = 2
Answer: r = 2
Steps:
r + 8r + 11 = 29
9r + 11 = 29
9r + 11 - 11 = 29 - 11
9r = 18
r = 2
plz mark brainliest
Which matrix can be multiplied to the left of a vector matrix to get a new vector matrix? A. B. C. D.
Answer:
i think the answer will gonna be C.
Answer:
C plato
Step-by-step explanation:
What cup should Jacob pick
volume of cylinder = 3.14×1.5×1.5×4
1.34×2.25×4=
1.34×9=
12.06 in³
volume of cone =1/3×3.14×2×2×6
1/3×3.14×4×6
1/3×3.14×24
3.14×8
=25.12 in³
therefore he need to buy the cone shaped cup
A teacher has a bag of 100 unit cubes. She gives an equal number of cubes to each of the 7 groups in her class. She gives each group as many unit cubes as she can. How many unit cubes are left over?
Answer: There’s 2 cubes left
Step-by-step explanation:
100 divided by 7 is 14 . 7 • 14 = 98100-2 , She is left w a remaining of 2 unit cubes . Meanwhile each table receives 14 marbles each .
If WX≅WZ and m∠WYX=48°, what is m∠WYZ?
Answer:
48 degrees
Step-by-step explanation:
Since triangles WZY and WXY are congruent by HL, angles WYZ and WYX are congruent by CPCTC.
Find the common difference of the arithmetic sequence.
4, 10, 16, 22, . . .
Answer:
The answer is 6
Step-by-step explanation:
This is due to the nth term sequence going up by 6