Answers
Answer:
[tex]\frac{dy}{dx}[/tex] = 2x + 3
Step-by-step explanation:
The gradient function is the derivative [tex]\frac{dy}{dx}[/tex]
Differentiate using the power rule
[tex]\frac{d}{dx}[/tex] (a[tex]x^{n}[/tex] ) = na[tex]x^{n-1}[/tex] and [tex]\frac{d}{dx}[/tex] ( constant ) = 0
Given
y = x² + 3x + 1, then
[tex]\frac{dy}{dx}[/tex] = 2[tex]x^{2-1}[/tex] + 3[tex]x^{1-1}[/tex] + 0 = 2x + 3[tex]x^{0}[/tex] = 2x + 3 ← gradient function
Related Questions
Two cylindrical soup cans have a volume of 40 cubic inches. Can their surface areas be unequal?
Answers
solve the system of equations
−4x−3y=-21
x=y
Answers
Answer: x and y = 3
Step-by-step explanation:
What is the equation of the line that passes through the point (-5,5)and has a slope of -1
Answers
Answer:
y = - xStep-by-step explanation:
The point-slope form of the equation is y - y₀ = m(x - x₀), where (x₀, y₀) is any point the line passes through and m is the slope:
m = -1
(-5, 5) ⇒ x₀ = -5, y₀ = 5
The point-slope form of the equation:
y - 5 = -1(x + 5)
So:
y - 5 = -x - 5 {add 5 to both sides}
y = -x ← the slope-intercept form of the equation
The function (n) = nr can be used to find the volume of air inside a basketball given its radius. What does V(r)
represent?
O the radius of the basketball when the volume is V
O the volume of the basketball when the radius is r
O the volume of the basketball when the radius is V
the radius of the basketball when the volume is r
Answers
Answer:
I believe it represents the volume of the basketball when the radius is r?
A parabola can be drawn given a focus of (8, 6) and a directrix of x=4. Write the equation of the parabola
Answers
Answer:
The equation of the Parabola
(y - 6 )² = 8 (x -6)
Step-by-step explanation:
Step(i):-
Given directrix x = 4
we know that x = h - a = 4
h -a = 4 ...(i)
Given Focus = ( 8,6)
we know that the Focus of the Parabola
( h + a , k ) = ( 8,6)
comparing h + a = 8 ...(ii)
k = 6
solving (i) and (ii) and adding
h - a + h+ a = 8 +4
2 h = 12
h =6
Put h = 6 in equation (i)
⇒ h - a =4
⇒ 6 - 4 = a
⇒ a = 2
Step(ii):-
The equation of the Parabola ( h,k) = (6 , 6)
( y - k )² = 4 a ( x - h )
(y - 6 )² = 4 (2) (x -6)
(y - 6 )² = 8 (x -6)
Issa jogged two-thirds of the way home from school. Then he was tired, so he walked the remaining 3,200 m.
How many kilometers did Issa travel from school to his house?
Answers
Answer:
9.6km
Step-by-step explanation:
3200/(1/3)=
3200*3/1=9600 m=9.6km
Graph the line.
Y+4=1/5(x-1)
Answers
Answer:
graph the point (0, -5) and from that point go up 1 unit and to the right 5 units (5, -4) and plot that point; connect the two points
Step-by-step explanation:
helpppppppppppp???????????????????????????????????????????????\\
Answers
B. B, C, F
C. A
D. if you can type two letters in AC, If only one try A
lua is creating a rectangular prism the base of her prism is shown below she plans to have a height of 7 cubes
what will the volume of the completed figure be?
_______ cubic units
Answers
Answer:
63
Step-by-step explanation:
hhehehehhehehehehh hope this helps
HURRY I NEED THIS IN 20 mins please help me
Write an equation for the function g whose graph is the graph off
f(x) = -100(1.05)
translated to the right 5 units and up 50 units.
Answers
Answer:
f(x) = -100(1.05)^(x+5) + 50
Step-by-step explanation:
Here, we want to write an equation that represents the transformation
5 units right means 5 units on the positive x-axis
50 units up means we add this to the total y value
So the resulting equation will be;
f(x) = -100(1.05)^(x+5) + 50
The sales tax rate is 5%. If Rebecca buys a lawn mower priced at $61, how much tax will she pay?
Answers
Answer:
3.05
Step-by-step explanation:
Step-by-step explanation:
(9a4 + 2a2 + 5) – (16a4 – 7a2 + 1)
A. 25a4 – 5a2 – 4
B. –7a4 – 5a2 + 6
C. 25a8 + 9a4 + 6
D. –7a4 + 9a2 + 4
5.Multiply 9x2(2x2 + 8x).
A. 18x4 + 72x3
B. 18x2 + 72x3
C. 11x4 – 17x3
D. 90x4
Simplify (right answer only ) : 2(x – 9)
Answers
Answer:
2x-18
Step-by-step explanation:
2(x-9)
distribute the 2 in the ( )
2x-18
Hope this Helps!!!
What makes a linear pair with 84°?
Answers
Answer:
as per linear pair axiom it will be X + 84= 180
this answer is 106 degrees
Which equation is true?
O 1150) = - 150
01 - 150 = 150
- 150 = 150
O-1 - 150= 150
Answers
THe 3rd equation is true
Kayla and totsakan each improved their yards by planting hostas and shrubs. They bought their supplies from the same store. Kayla spent $80 on 8 hostas and 5 shrubs. Totsakan spent $85 on 9 hostas and 5 shrubs, find the cost of one hosta and the cost of obe shrub.
Answers
Answer: one hosta = $5
One shrub = $8.
Step-by-step explanation:
Let the cost of one hosta be h
Let the cost of one shrub be s
Kayla spent $80 on 8 hostas and 5 shrubs. This can be written as:
8h + 5s = 80 ..... i
Totsakan spent $85 on 9 hostas and 5 shrubs. This can be written as:
9h + 5s = 85 ..... ii
8h + 5s = 80 ..... i
9h + 5s = 85 ..... ii
Subtract i from ii.
h = 5
The cost of one hosta is $5
Since 8h + 5s = 80
8(5) + 5s = 80
40 + 5s = 80
5s = 80 - 40
5s = 40
s = 40/5 = 8
One shrub cost $8.
help , read the question. please help me
BRAINLIEST !
Answers
Answer:
9.76 years turns 900 dollars into 1200 dollars.
Step-by-step explanation:
A(t) = 900*(1.03)^t
1200 = 900 * (1.03)^t Divide by 900
1200/900 = (1.03)^t
1.333 = 1.03^t Take the log of both sides.
log(1.3333) = t * log(1.03)log 1.3333 = .1249log 1.03 = .01281.249 = 0.0128*t
1.249/0.0128 t = 9.76 years.
What is the sum of (8a+2b-4)
Answers
Answer:
2(4a+b-2)
Step-by-step explanation:
All you need to do is factor out 2 from the expression. (sorry if this is wrong)
Alicia drew a map of Texas. In the scale Alicia used for the map, 1/2 inch represents 20 miles. What is the distance between two cities on the map if the actual distance between the two cities is 360 miles?
Answers
Answer:
9 inches
Step-by-step explanation:
Given that,
For the graph, 1/2 inch represents 20 miles.
We need to find the distance between the cities on the map if the actual distance between the two cities is 360 miles.
1/2 inch = 20 miles
1 mile = [tex]\dfrac{\dfrac{1}{2}}{20}=0.025\ \text{inches}[/tex]
For 360 miles, = 0.025 × 360
= 9 inches
Hence, the required answer is 9 inches.
You must be at least 42 inches tall to ride the bumper cars at an amusement park. Write an inequality that represents this situation. Let x represent the heights of people who are allowed to ride the bumper cars.
Answers
Answer:
x ≥ 42
Step-by-step explanation:
If you must be at least 42 inches tall to ride the bumper cars at an amusement park, this means that the minimum average height you can have is 42in i.e you can be more than 42inches tall.
The right inequality sign to represent this situations is a "greater than or equal to sign"(≥)
If x represent the heights of people who are allowed to ride the bumper cars, the required inequality expression will be x ≥ 42
Set up the equation you would use to solve the problem.Do not actually solve the equation.
A plane flies 390 miles with the wind and 325 miles against the wind in the same length of time. If the speed of the wind is 10 miles per hour, fine the speed of the plane in still air. (Let x = speed of the plane.)
A. 390/x+20 = 395/x
B. 390/x+10 = 325/x-10
C. 390/x = 325/x-20
D. 390/x-10 = 325/x+10
Answers
Explanation
I believe it’s B because it says when the plane fly with the wind it’s 390miles so if we want to know the speed of the plane In still air it should be 390/x + 10 because we need to consider that the speed of the plane + the speed of wind. While the plane fly at 325 against the wind so it should be 325/x - 10 cuz this time it goes against the wind.
Which equation is equivalent to 8x + 2y = 10?
Answers
Answer:
y=-4x+5
Step-by-step explanation:
8x+2y=10
2y=10-8x
divide by 2
y=5-4x
y=-4x+5
Last one... hehe- sorry
Answers
Answer:
113
Step-by-step explanation:
I have no idea Imao
The new pastry chef at Jackson's Bakery specializes in sheet cakes for parties. She sold 17 small, 11 medium, and 20 large sheet cakes in one week. How much money did Jackson's Bakery make in one week from sheet cakes?
Answers
Answer:
Therefore the total amount that Jackson's Bakery made in one week from sheet cakes is: = $2,238
Step-by-step explanation:
Step One:
To arrive at the total amount made from the sheet cakes, we have to assign the prices of each type of cake. They are:
Small Sheet Cake - $36Medium Sheet Cake - $46Large Sheet Cake - $56Step Two:
If the new pastry sold 17 small, 11 medium and 20 large sheet cakes respectively, the total money made comes to the following:
= (36 x 17) + (11 x 46) + (56 x 20)
= 612 + 506 + 1120
Therefore the total amount that Jackson's Bakery made in one week from sheet cakes is:
= $2,238
Cheers!
helpppp plzzzzzzzzzzzzzzz
Answers
Answer:
y= 0.2(0.05)^x
Nayeli brought Jamba Juice smoothies for herself and Evelyn after school one day the smoothies cost 4.95 each plus 8.5% tax how much charge did she receive from a $20 bill
Answers
Answer: $9.26
Step-by-step explanation:
The total cost for each of their smoothies was:
= 4.95 * 2
= $9.90
Including taxes it will rise to:
= 9.90 * (1 + tax)
= 9.90 * (1 + 8.5%)
= $10.74
Change she will receive is:
= 20 - 10.74
= $9.26
7x (6 x t) and (7 x 6) x t
Answers
If your question is which propperty is used in that opperation
Answer: The commutative property of multiplication
Step-by-step explanation: The comutative property of multiplication says that the order in which elements are multiplied the result is the same.
The figures below are made out of circles, semicircles, quarter circles, and a square. Find the area and the perimeter of each figure and give your answers as a completely simplified exact value in terms of π (no approximations).
Answers
Answer:
Area of the shaded region = 16(π - 2) in²
Perimeter of the shaded region = 4(π + [tex]2\sqrt{2}[/tex]) in
Step-by-step explanation:
Since, BDC is a quarter of the circle with radius = 8 in.
Area of the quarter of the circle = [tex]\frac{1}{4}(\pi)(r)^2[/tex]
= [tex]\frac{1}{4}(64)\pi[/tex]
= 16π in²
Area of ΔBCD = [tex]\frac{1}{2}(\text{Base})(\text{Height})[/tex]
= [tex]\frac{1}{2}(8)(8)[/tex]
= 32 in²
Since, area of the shaded part = Area of quarter of the circle - Area of triangle BCD
= (16π - 32)
= 16(π - 2) in²
Therefore, area of the shade region = 16(π - 2) in²
Similarly, length of arc BD = [tex]\frac{1}{4}(2\pi r)[/tex]
= [tex]\frac{8\pi }{2}[/tex]
= 4π in.
Length of the diagonal of a square = (Side)√2
= 8√2 in
Perimeter of the shaded region = Length of arc BD + Length of diagonal BD
= 4π + 8√2
= 4(π + 2√2) in.
Select the table that represents a proportional relationship between X and Y
Answers
The answer is A
Step-by-step explanation:
A family went out to eat. The bill is $65.82. The family wants to leave a 20% tip. How much tip will be added on to the cost of dinner?
Answers
Answer:
$13.16
Step-by-step explanation:
These three points are collinear. (3, 6), (-2, -9), (0, -4)
True False
Answers
Answer:
False
Step-by-step explanation:
to determine if the points are collinear, determine the rate of change(slope) between (-2, -9) and (0, -4) and then the rate of change between (0, -4) and (3,6) and rate of change between (-2, -9) and (3, 6). if the rates are equivalent then the points are all collinear
between (-2, -9) and (0, -4):
m=(y2-y1)/(x2-x1)
=(-4-(-9))/(0-(-2))
=5/2
between (0, -4) and (3,6):
m=(y2-y1)/(x2-x1)
=(6-(-4))/(3-0)
=10/3
because 5/2 does not equal 10/3 the rates of change are not equal and the points are not collinear, do not need to consider slope between (-2, -9) and (3, 6)