Given:
The equation is
[tex]y=5x^3-6x^2-4x+8[/tex]
To find:
The coordinates of the turning point.
Solution:
We have,
[tex]y=5x^3-6x^2-4x+8[/tex]
Differentiate with respect to x.
[tex]\dfrac{dy}{dx}=5(3x^2)-6(2x)-4(1)+(0)[/tex]
[tex]\dfrac{dy}{dx}=15x^2-12x-4[/tex]
For the turning points [tex]\dfrac{dy}{dx}=0[/tex].
[tex]15x^2-12x-4=0[/tex]
Using quadratic formula:
[tex]x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
[tex]x=\dfrac{-(-12)\pm \sqrt{(-12)^2-4(15)(-4)}}{2(15)}[/tex]
[tex]x=\dfrac{12\pm \sqrt{144+240}}{30}[/tex]
[tex]x=\dfrac{12\pm \sqrt{384}}{30}[/tex]
Now,
[tex]x=\dfrac{12+\sqrt{384}}{30}\text{ and }x=\dfrac{12-\sqrt{384}}{30}[/tex]
[tex]x\approx 1.053\text{ and }x\approx-0.253[/tex]
Putting x=1.053 in the given equation, we get
[tex]y=5(1.053)^3-6(1.053)^2-4(1.053)+8[/tex]
[tex]y\approx 2.973[/tex]
Putting x=−0.253 in the given equation, we get
[tex]y=5(-0.253)^3-6(-0.253)^2-4(-0.253)+8[/tex]
[tex]y\approx 8.547[/tex]
Therefore, the turning points are (1.053,2.973) and (-0.253, 8.547).
Hai thinks there must be about 600 sprinkles on his donut. Hai starts by eating 25% of the donut. About how many sprinkles does he eat?
Answer:
45
Step-by-step explanation:
Write the equation of the line that passes through (4, -6) and (8, 10)
Answer:
Line equation: y=4x−22
Slope: 4
Intercept: -22
Step-by-step explanation:
A party cap is in the form of a frustum. The radii of its ends are 10cm and 30 cm. The volume of the cap is 9100. What is the height of the cap?
Answer:
4.46cm
Step-by-step explanation:
Volume of a frustum is expressed as;
V = (1/3) * π * h * (r₁² + r₂² + (r₁* r₂))
h is the height of the frustum
r₁ and r₂ are the radii of its ends
V is the volume
Given
V = 9100cm₃
r₁ = 10cm
r₂ = 30cm
Substitute
9100 = (1/3) * (3.14) * h * (10² + 30² + (10* 30))
9100 = 1/2(3.14)*h*(100+900+300)
9100 = 1.57*h*(1300)
9100 = 2,041h
h = 9100/2,041
h = 4.46cm
Hence the height of the cap is 4.46cm
The ratio of the measure of the sides of a triangle is 9:7:3. If the perimeter of the triangle is 266 inches, find the length of the shortest side. Help me please!!
Answer:
shortest side = 42 inches
Step-by-step explanation:
9x + 7x + 3x = 266
x = 14
3x = 42
what is the value of x in 75x -89 ÷ 7791 +7829 ×8391 =314682
please help it almost due to 15 points
Answer:
a=30
b=15
c=3
d=30
e=10
Step-by-step explanation:
Solve for A first and continue solving for one variable at a time
I NEED HELP PLEASE ASAP, It's due soon.
A turkey was cut into 10 equal pieces. If Katie ate 210 of the turkey, and Lorenzo ate 510 of the turkey, how many whole pieces of the turkey are left?
Answer:
3 Whole pieces
Step-by-step explanation:
A turkey was cut into 10 equal pieces.
For Katie
If Katie ate 2/10 of the turkey
Number of Whole pieces of turkey Katie ate =
2/10 × 10 whole pieces = 2 whole pieces
For Lorenzo
Lorenzo ate 5/10 of the turkey
Number of Whole pieces of turkey Lorenzo ate =
5/10 × 10 whole pieces = 5 whole pieces
how many whole pieces of the turkey are left?
This is calculated as:
10 pieces - (2 piece + 5 pieces)
10 pieces - 7 pieces
= 3 pieces
Therefore, we have 3 whole pieces of turkey left.
Answer:
3 Whole pieces
Step-by-step explanation:
A turkey was cut into 10 equal pieces.
For Katie
If Katie ate 2/10 of the turkey
Number of Whole pieces of turkey Katie ate =
2/10 × 10 whole pieces = 2 whole pieces
For Lorenzo
Lorenzo ate 5/10 of the turkey
Number of Whole pieces of turkey Lorenzo ate =
5/10 × 10 whole pieces = 5 whole pieces
how many whole pieces of the turkey are left?
This is calculated as:
10 pieces - (2 piece + 5 pieces)
10 pieces - 7 pieces
= 3 pieces
Therefore, we have 3 whole pieces of turkey left.
The area of a rectangular room is 240 square feet. The width is 12 feet. What is the length?
Answer:
20 ft
A=wl
l=A/W=240/12=20ft
question 6 smart ppl i need you !!!!!!!!!!!!!!
Answer: The answer is 5/16
Brainlist plz
Step-by-step explanation:
Consider the function f(x) =2x+3 Find the average rate of change from the following points x=2 and x= 6
Step-by-step explanation:
step 1. m = 2.
step 2. for a linear equation the average rate of change between any points is the slope m.
help me please, lolllllllllllllllllll
Answer:
1728ft³
Step-by-step explanation:
Split the shape into the two rectangular prism that make it up
Volume of a rectangular prism=length*width*height
Small prism=10*12*3=360ft³
Big prism=19*12*6=1368ft³
Total=360ft³+1368ft³=1728ft³
Slope of 4,-9 and 8,-3
Answer:
3+5=8 its question answer ok
Answer:
slope=. y2-y1/x2-x1
= -3+9/8-4
= 6/4
=3/2
30 is 60% of what number
Answer:
the answer is 50
Step-by-step explanation:
x=30×100/60
x=50
7.5 is what percent of 50?
Answer:
15%
Step-by-step explanation:
Write as a fraction greater than one. (an improper fraction)
HURRY PLZZZZZZZZZZZZZZZ. ill mark brailyist thingy
Answer:
13/3
Step-by-step explanation:
The formula to calculate that is 4*3+1=12+1=13/3 so the answer is 13/3.
Answer:
13/3
Step-by-step explanation:
(4x3+1)/3
=(12+1)/3
=13/3
A TRIANGLE has a base of 20 inches and height of 9 inches. What is its area? (a = 1/2bh)
Answer:
90
Step-by-step explanation:
1/2x20x9=90
What is the average rate of change of g over the interval [-2,4]
Answer:
3Average = sum of all the observations
Total number of observations
Average = 2+4
2
Average = - 6
2
3
Three friends are comparing their weekly paychecks. Donald discovers that he earned one-third of Michael's paycheque, and $80 less than Jacob's paycheque. Together, the three friends earned $2920 in one week. How much did each friend earn?
Answer: Michael's paycheque = $ 1704
Donald's paycheque = $ 568
Jacob's paycheque = $ 648
Step-by-step explanation:
Let x = Michael's paycheque
Donald's paycheque = [tex]\dfrac13x[/tex]
Jacob's paycheque = [tex]\dfrac 13 x+80[/tex]
Together, the three friends earned $2920 in one week.
[tex]\Rightarrow\ x+\dfrac13x+\dfrac13 x+80=2920\Rightarrow\ (\dfrac{3+1+1}{3})x=2920-80\\\\\Rightarrow\ \dfrac{5}{3}x=2840\\\\\Rightarrow\ x=2840\times\dfrac{3}{5}\\\\\Rightarrow\ x=1704[/tex]
Michael's paycheque = $ 1704
Donald's paycheque = [tex]\dfrac{1704}{3}=\$ 568[/tex]
Jacob's paycheque = $ 568+80 = $ 648
need help to find X
thank you
Answer:
121
Step-by-step explanation:
Answer:
63.33 or 190/3
Step-by-step explanation:
1. vertical opposite angles are equal
2. corresponding angles some up to 180°
=> 3x - 20 + 10 = 180
=> 3x = 180+10
=> 3x = 190
=> x = 190/3
=> x = 63.333333333333333
Fill in the blanks to write the fraction 3/4 as in different ways
Answer:
1.3/4 × 2/2 = 6/8
2.3/4 × 3/3 = 9/12
3.3/4 × 4/4 = 12 /16
4. 3/4 × 5/5 = 15/20
please help this is algebra II
Answer:
m=5
Step-by-step explanation:
2 1/7+1 2/5 Give your answer as a mixed number where appropriate.
Answer:
3 19/35
Step-by-step explanation:
Find the least common denominator of the two.
The LCD is 35.
Now convert the fractions to a denominator of 35.
This will be it>>>
2 5/35 + 1 14/35.
Now the answer to that will be: 3 19/35
An octagonal prism has...........lateral faces.
8
2
7
5
Answer:
an octagonal prism has 8 lateral faces
Answer:
8
Step-by-step explanation:
An octagonal prism has 8 lateral faces.
An octagonal prism has 10 faces – 8 lateral faces and 2 bases, 16 vertices, and 24 edges
Suppose we know that the birth weight of babies is Normally distributed with a mean 3500g and a standard deviation of 500g. What is the probability that a baby is born that weighs less than 3100g?
Answer:
0.21186
Step-by-step explanation:
We solve the above question using the z score formula.
z = (x-μ)/σ, where
x is the raw score = 3100g
μ is the population mean = 3500g
σ is the population standard deviation = 500g
z = 3100 - 3500/500
z = -0.8
Probability value from Z-Table:
P(x<3100) = 0.21186
The probability that a baby is born that weighs less than 3100g is 0.21186
I have to solve this
4x-5=2-x
Answer:x=7/5
Step-by-step explanation:
Answer:
x= [tex]\frac{7}{\\5}[/tex]
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
4x−5=2−x
4x+−5=2+−x
4x−5=−x+2
Step 2: Add x to both sides.
4x−5+x=−x+2+x
5x−5=2
Step 3: Add 5 to both sides.
5x−5+5=2+5
5x=7
Step 4: Divide both sides by 5.
[tex]\frac{5x}{5}[/tex] = [tex]\frac{7}{5}[/tex]
Having trouble solving this:
Answer:
option b.
61/1000.
................
Answer:
B: 61/1000
Step-by-step explanation:
B: 61/1000 = 0.061
as a percent is 6.1%
Therefore B or 61/1000 is correct hope this helped!
simplify the expression
16+(-5)-2/5j-4/5j+6
Answer:
17 - 6j / 5
Step-by-step explanation:
Think of a favorite dance move, such as the Running Man. Determine whether there is periodicity associated with this dance move.
Answer:
I don't remember if Alan Walker can dance :/
Step-by-step explanation:
Dream did it better than me, you should see his answer.
Answer:
I don't know
Step-by-step explanation:
pls help with this math question !
thx !
To find your answer I believe you need to add or multiply your exponents and since their is already three p then your answer is 3p^ and then you put your answer. Hopefully this helps.
