[tex]y = x^{3} + 2[/tex]
[tex]y = g(x) + c[/tex]
Here, [tex]g(x) = x^{3}[/tex] and [tex]c = 2[/tex], the parent function is [tex]g(x)[/tex]. Because [tex]c > 0[/tex], the graph undergoes a vertical shift 2 units up along the y-axis.
1) The cubic function is [tex]x^3+1[/tex] and the parent function is [tex]x^3[/tex].
2) The transformation from parent function to function is vertical stretch.
A cubic function is a polynomial function of degree 3. So the graph of a cube function may have a maximum of 3 roots. i.e., it may intersect the x-axis at a maximum of 3 points.
The general form of the cubic function is [tex]ax^3+bx^2+cx+d=0[/tex], where a, b, c and d are real numbers.
Let the cubic function be [tex]x^3+1[/tex] and the parent function be [tex]x^3[/tex].
To find the transformation, compare the function and check to see if there is a horizontal or vertical shift, reflection about the x-axis or y-axis and if there is a vertical strech.
Horizontal shift: None
Vertical shift: Up 1 units
Reflection about the x-axis: None
Reflection about the y-axis: None
Vertical Compression or Stretch: None
Therefore,
1) The cubic function is [tex]x^3+1[/tex] and the parent function is [tex]x^3[/tex].
2) The transformation from parent function to function is vertical stretch.
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Evaluate 4x squared - 8x + 8 when x = -6
Answer:
44
Step-by-step explanation:
√4×-6+8×6+8=2×-6+48+8
-12+48+8
=48
Hey there!
4x^2 - 8x + 8
= 4(-6)^2 - 8(-6) + 8
= 4(6)(6) - 8(-6) + 8
= 4(36) - (-48) + 8
= 144 - (-48) + 8
= 144 + 48 + 8
= 192 + 8
= 200
Therefore, your answer is: 200
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
I have more questions then this
Answer:1-1/3
2-16 in.
3-10.49
4-1/10
Step-by-step explanation:
i hope this helps
Mr. Morgan's ice cream shop made $1,380 last weekend selling $2 scoops of ice cream. If he sells 100 more scoops this weekend, about how many scoops will he sell?
Answer:
1580$
Step-by-step explanation:
(3[tex]x^{2}[/tex]+[tex]y^{2}[/tex])Y+([tex]y^{2}[/tex]-[tex]x^{2}[/tex])x×[tex]\frac{dy}{dx}[/tex]=0
It looks like the given differential equation is
(3x² + y²) y + (y² - x²) x dy/dx = 0
Multiply both sides by 1/x³ to get
(3 + y²/x²) y/x + (y²/x² - 1) dy/dx = 0
(Note that in order to do this, we must have x ≠ 0, which means that if a solution exists, it would have to be on either (-∞, 0) or (0, ∞).)
Now substitute z = y/x, or y = xz, from which we get dy/dx = x dz/dx + z. Making this replacement and simplifying yields a separable equation:
(3 + z²) z + (z² - 1) (x dz/dx + z) = 0
(3 + z²) z + (z² - 1) x dz/dx + (z² - 1) z = 0
(z² - 1) x dz/dx = -(2z³ + 2z)
x dz/dx = (2z³ + 2z)/(1 - z²)
(1 - z²)/(2z (z² + 1)) dz = dx/x
Integrate both sides. On the left, split up the expression into partial fractions.
[tex]\dfrac{1-z^2}{z(z^2+1)} = \dfrac az + \dfrac{bz+c}{z^2+1}[/tex]
[tex]\dfrac{1-z^2}{z(z^2+1)} = \dfrac{a(z^2+1)+(bz+c)z}{z(z^2+1)}[/tex]
[tex]1-z^2 = (a+b)z^2 + cz + a[/tex]
for which we find a = 1, b = -2, and c = 0:
[tex]\dfrac{1-z^2}{2z(z^2+1)} = \dfrac12 \left( \dfrac1z - \dfrac{2z}{z^2+1} \right)[/tex]
Integrating and simplifying yields
1/2 ∫ (1/z - 2z/(z² + 1)) dz = ∫ dx/x
1/2 (ln|z| - ln(z² + 1)) = ln|x| + C
1/2 ln|z / (z² + 1)| = ln|x| + C
ln(√(z/(z² + 1))) = ln|x| + C
exp[ln(√(z/(z² + 1)))] = exp[ln|x| + C]
√(z/(z² + 1)) = exp[ln|x|] exp[C]
√(z/(z² + 1)) = Cx
z/(z² + 1) = Cx²
Replacing z = y/x then gives us an implicit solution of
(y/x) / (y²/x² + 1) = Cx²
xy / (y² + x²) = Cx²
y / (y² + x²) = Cx
y = Cx (y² + x²)
Cxy² - y + Cx³ = 0
though we can solve for y explicitly (assuming x > 0) using the quadratic formula to end up with
y = (1 + √(1 - Cx⁴))/(Cx)
(the other solution only differs by the sign on the square root)
5. Mohan and Sohan have the same storybook. Mohan has read 2/5 of the book and Sohan has read 2/7 of the book. Who has read more pages? 6. Sonali and Priya are classmates Sonali completed her homework in a of an hour and Priya in of an hour 3/4 . Who was faster?
#5
Mohan read =2/5Sohan read=2/7Compare
[tex]\\ \sf\longmapsto \dfrac{2}{5}>\dfrac{2}{7}[/tex]
Mohan read more pages.#6
Sonali completed in=1/2Priya completed in=3/4[tex]\\ \sf\longmapsto \dfrac{1}{2}=\dfrac{2}{4}[/tex]
Compare
[tex]\\ \sf\longmapsto \dfrac{2}{4}<\dfrac{3}{4}[/tex]
Sonali was faster
what is the slope will mark brainlist
The equation of slope is y2 - y1/x2 - x1
0 - 4/0 - 5
-4/5
Another method in image added.
select all the ways you can describe the given polygon
Answer:
Isoceles and obtuse
Step-by-step explanation:
Please take a look at the picture
Answer:
A) -3/-11
Step-by-step explanation:
-3/-11-3/11
-3/-11
Reduce the fraction with -1.
3/11
Hope this help :)
Quick Computing installed its previous generation of computer chip manufacturing equipment 3 years ago. Some of that older equipment will become unnecessary when the company goes into production of its new product. The obsolete equipment, which originally cost $40 million, has been depreciated straight-line over an assumed tax life of 5 years, but it can be sold now for $18 million. The firm’s tax rate is 35%. What is the after-tax cash flow from the sale of the equipment?
The company's after-tax cash flow is a measure of the company's cash
generation ability.
The after-tax cash flow from the sale of the equipment is $16.1 millionReasons:
The given parameter are;
Original cost of the equipment = $40 million
The type of depreciation = Straight line depreciation
Number of years of depreciation = 5 years
Current price at which it can be sold = $18 million
The tax rate of the firm = 35%
Required:
The after-tax cash flow from the sale of the equipment.
Solution:
The Cash Flow After Tax, CFAT, is given as follows;
CFAT = Net income + Amortization + Depreciation + Other non-Cash Cash Charges
The annual depreciation is given as follows;
[tex]Annual \ depreciation = \dfrac{\$40 \ million - \$18 \ million}{5 \ years} = \$4.4 \ million \ per \ year[/tex]
Selling the equipment gives;
The Earnings Before Tax (EBT) = $18 million
The Net Income = Income - Tax = $18 million - (35% × $18 million)
The Net Income = $11.7 million
Cash Flow After Tax CFAT = Net income + Depreciation
∴ CFAT = $11.7 million + $4.4 million = $16.1 million
The after-tax cash flow = $16.1 millionLearn more here:
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PLEASE HELP I will mark you BRAINLIST
Answer:
Angle B: 180-135=45° - supplementary angle rule
Angle C: 180-45-70=65° - sum of interior angles of triangle is 180
Angle D= Angle B : 45° - Alternate interior angles
Angel E=Angle A: 70° - Alternate interior angle.
Angle F: 180-Angle E(70) = 110° - supplementary angle rule
Step-by-step explanation:
The result of a division problem is the a ) divisor . b ) quotient . c ) factor . d ) remainder .
Answer:
b) quotient
Step-by-step explanation:
divisor is the number/value you are dividing with.
A remainder is a number that remains after you divide.
A factor is a number that can divide into a number or numbers without leaving a remainder
Elli left home8:30 and returned at 1:25how long was she away from home?
Answer:
3 hours and 45 minutes assuming its from am to pm
Step-by-step explanation:
Hope This Helps
2. What is the largest composite number less than 40?
Answer:
39
Step-by-step explanation:
39
Step-by-step explanation:
13 × 3 = 39
The largest composite number less than 40 is 39
solve the equation 3/4x - 5 = x give your answers correct to 2 decimal places
Answer:
3/4x - 5 = x
= -3/10 -> -0.15
2 Decimal places = 0.150
Find the derivative of the function y = ln(3t+4)
Answer:
3 / (3t+4) is the answer
i really need help on my question!
Answer:
your answer is C
Step-by-step explanation:
Answer:
20
Step-by-step explanation:
It is asking how many people have MORE than two fish. Not two fish.
15 + 3 + 2 = 20
a pyramid whose altitude is 5ft weighs 800lbs. at what distance from its vertex must it be cut by a plane parallel to its base so that the two solids of equal weight will be formed?
A structure which has a square base and four triangular sides meeting at a point is called pyramid.
At distance of 3.97 feet from its vertex , pyramid is cut by plane so that the two solids of equal weight will be formed.
It is assumed that weight of pyramid is proportional to its volume.
So, [tex]w = k V[/tex] , where V is volume of original pyramid and v is volume of small pyramid and k is constant.
Let us consider that at h distance, pyramid is cut from its vertex. So a small pyramid is also formed.
Assume that base area of original pyramid is A and base of small pyramid is a.
Volume of original pyramid is, [tex]V= \frac{1}{3} *A* 5[/tex]
So, weight of original pyramid, [tex]W = k *(\frac{1}{3} *A* 5) = 800[/tex]
Volume of small pyramid is, [tex]v = \frac{1}{3}* a* h[/tex]
So, weight of small pyramid, [tex]w = k*(\frac{1}{3}* a* h)=400[/tex]
Since, base and height of small pyramid and original pyramid are in proportion.
So, [tex]\frac{a}{A} = (\frac{h}{5}) ^{2}[/tex]
[tex]a = (\frac{h}{5} )^{2}A[/tex]
Substituting value of a in equation [tex]k*(\frac{1}{3}* a* h)=400[/tex]
So, [tex]k*(\frac{1}{3}* \frac{h^{2} }{25}A * h)=400[/tex]
[tex](k*\frac{1}{3}* A*5)*\frac{1}{5} *\frac{h^{2} }{25} * h)=400[/tex]
Since, [tex](k *\frac{1}{3} *A* 5) = 800[/tex], substitute in above equation.
So, [tex]800*\frac{h^{3} }{125}=400\\\\h^{3}=\frac{125}{2}\\\\h=\sqrt[\frac{1}{3} ]{62.5}\\\\h=3.97 feet[/tex]
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what does (-x)+(-x)+(-x)=
Answer: -3x
Step-by-step explanation:
(-x)+(-x)=-2x
-2x+(-x)=-3x
How long is a distance of 8 km if measured on a map with a scale of 1:50,000?
Answer: 400,00 km
Step-by-step explanation: 1:50,000 = 8:x
8 * 50,000 = 400,000
So, 8km on the map is 400,000 km in real life.
Would appreciate brainly <3
What are the odds of not rolling a three on a standard six-sided die?
Answer:
5/6
Step-by-step explanation:
Hope this is helpful
Answer:
5/6
Step-by-step explanation:
solve pls brainliest
Answer:
Mixed number: 5(1/10)
Improper fraction: (51/10)
Step-by-step explanation:
Hope this helps!
Answer:
Mixed number: 5 1/10 and improper fraction: 52/10
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
If a submarine dives 378 feet in 14 seconds, the average change in elevation is feet per second.
Answer:
27 feet per second.
Step-by-step explanation:
You already have your time unit in second and length measurement in feet so just divide the two 378/14=27 feet per second.
Answer:
-27 feet per second
Step-by-step explanation:
378 ÷ 14 = 27
because the submarine is going down, the sign has to be negative
Someone pleases answer!
Answer:
Both are 65 degrees
Step-by-step explanation:
because you have parrallel lines, 2 would be the same as 65
Because 1 is on the opposite of 2, it would be the same
The area under the graph line
made with the x-axis represents
the change in position of the
object on a velocity versus time
graph. (5 points)
The statement is true: the area under the graph line made with the x-axis
represents the change in position of the object on a velocity versus time
graph.
Reasons:
[tex]\displaystyle Velocity = \frac{Dislacement}{Time}[/tex]
The area under the velocity time graph is given by the integration of the function for the velocity over the time interval.
A constant velocity is an horizontal line and the integration of a constant with time, gives the product of time and the constant, which is area under the rectangular graph.
Therefore, the area under the graph line made with the x-axis represents the change in position of the object on a velocity versus time graph.
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Answer: True
Step-by-step explanation:
y=7x+7 convert in standard form
Answer:
y/7=x+1
hope this helps you!!
What is the measurement of the angle shown below?
Answer:
The correct answer is (c) 30°
Hope it helps
what ordered pair is a solution of 3x - y = 13
Answer:
x=6,. y=5. is the answer
how would is solve this?
Find the area of the shaded region. Round your answer to the nearest hundredth.
it will be 36
Step-by-step explanation:
fgdsb b zgffhxgv
Can someone help me on this? Thanks!
Answer:
it's the graph c
Step-by-step explanation:
(0, -2)
(1, 0)
(2, 2)
what is the slope and the y intercept of y= -9x + 15
Answer:
Step-by-step explanation:
the slope for y = -9x + 15
Slope: -9
y-intercept: y= -9(0) + 15 = 0 + 15 = 15
(0, 15)
Answer:
-9
(0, 15)
Step-by-step explanation:
y = mx + c
y = -9x + 15
so m = -9
y intercept is when x = 0
c = 15
(0, 15)