Answer:
y = 2w / x^2.
Step-by-step explanation:
w = 1/2x^2 y
We divide both sides by 1/2 x^2
y = w / (1/2 x^2)
y = 2w / x^2.
1. Find the equation of the tangent line to the parabola y = x^3 at the point P(2,8).
Use x = 2.1, 2.01, 2.001, 2.0001, 2.00001; 1.9,1.99, 1.999,1.9999, 1.99999 to find slope.
Answer:
a) Equation of the tangent of the parabola
12 x - y -16=0
b)
slope of the tangent at x=2.1
[tex](\frac{dy}{dx}) = 3(2.1)^{2} = 13.23[/tex]
slope of the tangent at x=2.01
[tex](\frac{dy}{dx}) = 3(2.01)^{2} = 12.1203[/tex]
Step-by-step explanation:
Step(i):-
Given parabola y = x³ ....(i)
Differentiating equation (i) with respective to 'x'
[tex]\frac{dy}{dx} = 3x^{2}[/tex]
slope of the tangent
[tex](\frac{dy}{dx})_{(2,8)} = 3x^{2} = 3(2)^{2} =12[/tex]
Step(ii):-
Equation of the tangent of the parabola
[tex]y-y_{1} = m (x-x_{1} )[/tex]
y-8 = 12 (x -2)
12 x - 24 -y +8 =0
12 x - y -16=0
b)
slope of the tangent at x=2.1
[tex](\frac{dy}{dx}) = 3(2.1)^{2} = 13.23[/tex]
slope of the tangent at x=2.01
[tex](\frac{dy}{dx}) = 3(2.01)^{2} = 12.1203[/tex]
(-2)(3-4-(-1)+6 pls help
Answer:
6
Step-by-step explanation:
(-2)(3-4-(-1)+6
(-2)(-1-(-1)+6
(Since a negative and a negative make a positive that becomes -1+1.)
(-2)(0)+6
0+6
6
Answer:
Hello! :) I hope I am correct!
Step-by-step explanation:
The answer would be -12
(Look below for steps!!)
-2(-1-(-1)+6)
⇒-2(0+6)
⇒(-2)(6)
(Do the calculations above to find the answer)
=-12
Hope this helps!
By; BrainlyAnime
(Also I attached a picture of other ways to solve this problem!)
x + 1 > -5( 7-2x) I need help please.
Answer:
x<4
Step-by-step explanation:
[tex]x + 1 > -5( 7-2x) \\\\\mathrm{Expand\:}-5\left(7-2x\right):\quad -35+10x\\x+1>-35+10x\\\\\mathrm{Subtract\:}1\mathrm{\:from\:both\:sides}\\x+1-1>-35+10x-1\\\\Simplify\\x>10x-36\\\\\mathrm{Subtract\:}10x\mathrm{\:from\:both\:sides}\\x-10x>10x-36-10x\\Simplify\\-9x>-36\\\\\mathrm{Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right)}\\\left(-9x\right)\left(-1\right)<\left(-36\right)\left(-1\right)\\\\Simplify\\9x<36[/tex]
[tex]\mathrm{Divide\:both\:sides\:by\:}9\\\frac{9x}{9}<\frac{36}{9}\\\\x<4[/tex]
For the following system, if you isolated x in the first equation to use the substitution method, what expression would you substitute into the second equation? −x + 2y = −6 3x + y = 8
Answer:
[tex]x=2y+6[/tex]
Step-by-step explanation:
So we have the system:
[tex]-x+2y=-6\\3x+y=8[/tex]
If we isolate the x-variable in the first equation:
[tex]-x+2y=-6[/tex]
Subtract 2y from both sides:
[tex]-x=-6-2y[/tex]
Divide both sides by -1:
[tex]x=2y+6[/tex]
Therefore, we would substitute the above into the second equation:
[tex]3x+y=8\\3(2y+6)+y=8[/tex]
The answer is 2y+6
Further notes:
To solve for the system, distribute:
[tex]6y+18+y=8[/tex]
Simplify:
[tex]7y+18=8[/tex]
Subtract:
[tex]7y=-10[/tex]
Divide:
[tex]y=-10/7\approx-1.4286[/tex]
Now, substitute this value back into the isolated equation:
[tex]x=2(-10/7)+6\\x=-20/7+42/7\\x=22/7\approx3.1429[/tex]
Step-by-step explanation:
Start by solving the equation for x (☓)
[tex] - x + 2y = 6 \\ \: \: \: \: \: 3 + y = 8[/tex]
[tex]x = 6 + 2y[/tex]
Substitute the given value of x for the equation 3 + y = 8[tex]3(6 + 2y) + y = 8[/tex]
solve the equation for y[tex]y = - \frac{10}{7} [/tex]
substitute the given value of y into the equation x = 6 + 2[tex]x = 6 + 2 \times ( - \frac{10}{7} )[/tex]
solve the equation for x[tex]x = \frac{22}{7} [/tex]
The possible solution of the system is the ordered pair (x,y)[tex] (\frac{22}{7} . - \frac{10}{7} )[/tex]
The dot (.) in the center is supposed to be a comma but the scientific keyboard does not support a comma[tex](x.y) \: \: ( \frac{22}{7} . - \frac{10}{7} )[/tex]
This is the solution Marnie out!A football team gained 9 yards on one play and then lost 22 yards on the next. Write a sum of integers to find the overall change in field position. Explain your answer
Answer:
+9-22=-13
Step-by-step explanation:
Its 13 yrds lost
A 2.5 ft wide circular track for a camera dolly is set up for a movie scene. The two rails of the track form concentric circles. The radius of the inner circle is ft. How much farther does a wheel on the outer rail travel than a wheel on the inner rail of the track in one turn?
Answer:
15.71 ft
Step-by-step explanation:
Given that:
width of the circular track = 2.5ft
Suppose the radius of the inner circle is 57 ft since it is not given
Then the radius of the outer circle = (2.5 + 57) ft = 59.5 ft
The circumference of a circle = 2πr
For inner circle now, the circumference = 2 × π × 57 ft
For inner circle now, the circumference = 358.14 ft
For the outer circle, the circumference = 2 × π × 59.5 ft
For the outer circle, the circumference = 373.85 ft
The difference between the circumference of the outer wheel from the inner wheel shows how farther does a wheel on the outer rail travel than a wheel on the inner rail of the track in one turn
∴
= ( 373.85 - 358.14 ) ft
= 15.71 ft
For what values of a and b does a - b = b - a?
how can a+b=0?
is a+b=0 a single word followed by the question mark ? the sentence is not complete if “a+b=0” is the subject, it’s like: how can cat?
is the sentence rather: how can a+b be equal to 0 ( meaning zero) ? in that case, supposing we are talking of the usual sum of two elements of an additive group : how can the sum of a and b, written a+b, can be equal to zero, then this seems more like a question about what powers do have any two elements of a group to, by association through addition, to obtain a zero value. Like “how can my brother and me get one of these chocolates ?”
MORE
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Now, in your question, maybe a and b are not any two elements of said group but elements well identified before,
suppose you know a is 1 and b is -1 for instance. Then how can 1–1=0? is a very good question : it marvels at the fact that the addition does what it is supposed to do. Lots of things don’t, and lots of people take it for granted that things do what they are supposed to de, like speeds add up, etc.
let’s suppose for example, a is 1 and b is 2.
Then your question is very justified : how can 1+2 be equal to 0 ? it’s a scandal, either the computer is broken, or my mind is , and if anywhere in the world 1+2 =0, there is something wrong with the world.
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Hope this helps!! - Maddy
(if this helps please make brainliest, rate, and thank so I know how I did!)
╰(*°▽°*)╯
15 inches of snow fell in 12 hours. At this rate, how many inches of snow will fall in 3 days.
Answer:
90 in
Step-by-step explanation:
15 x 6 = 90 in
This is because
6 x 12 hrs = 3 days
Answer:
90 inches total
Step-by-step explanation:
1 day= 24 hours
12x2=24
15x2=30
30x3=90
3o inches of snow in a full day, and 3 days of snow so 90 inches total
How many (5in. by 5in. by 5in) cubes will occupy a classroom 9ft by 8ft by 7ft in dimension?
Answer:
Step-by-step explanation:
first convert feet to inches because the measure of cubes is in inches
( 12 inches=1 foot)
9 ft = 12*9=108 inches
8 ft=12*8=96 inches
7 ft= 12*7=84
the volume of the one cube= 5*5*5=125
volume of the classroom: 108*96*84=870912
divide : 870912/125=6967 cubes
What combination of transformations is shown below?
A) translation, then rotation
B) translation, then reflection
C) rotation, then reflection
D) rotation, then translation
Explanation:
Going from figure (1) to figure (2) has us rotate 90 degrees counterclockwise. Note the smallest side of the green figure how it is horizontal, and it corresponds to the smallest side of the blue figure and it is vertical. The center of rotation is the top right corner of the green figure.
Then we apply a translation to go from figure (2) to figure (3). This is another way of saying we shifted the figure some distance left/right and up/down. In this case, we shifted 1 unit to the right and 4 units down.
10 points for anyone that can help me on this PRE-ALGEBRA QUESTION SEE ATTACHMENT BELOW
Answer:
Step-by-step explanation:
on a trip to canada you may wish to convert the local temperature from celsius to fahrenheit.
Answer:
59
Step-by-step explanation:
A submarine is 450 feet below sea level. It descends 300 feet. What is its new position?
Answer:
750 feet below sea level
Step-by-step explanation:
This submarine is now 750 feet below sea level because:
450 + 300 = 750.
So, the answer is 750.
Hope this helps you!
sherry had $125.05 in her checking account She made deposit of $28.35 and $78.88 how much money was in sherry account after the deposit
Answer:
$17.82
Step-by-step explanation:
[tex]125.05 - 28.35 = 96.7 \\ 96.7 - 78.88 = 17.82[/tex]
Answer: $232.48
Step-by-step explanation: an equation you could use would be:
125.25+(28.35+78.88)
Add parentheses: 28.35+78.88= 107.23
Add the rest: 125.25+107.23= 232.48
Which function has an inverse that is a function?
b(x) = x^2 + 3
d(x) = -9
m(x) = -7x
p(x) = |x|
Answer: m(x) = -7x
Step-by-step explanation:
egen2020
The which function has an inverse that is a function is m(x) = -7x
How can we know if a function has an inverse?
let f be a Function. If any horizontal line intersects the graph of f extra than once, then f does now not have an inverse. If no horizontal line intersects the graph of f greater than once, then f does have an inverse. The belongings of getting an inverse may be very vital in arithmetic, and it has a call.
There are one-of-a-kind forms of inverse function just like the inverse of trigonometric functions, the inverse rational capabilities, inverse hyperbolic features, and inverse log capabilities.
Learn more about Function here https://brainly.com/question/10439235
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A national survey of middle-school students asks which subject is most challenging. Which of these samples is a representative sample?
Answer:
The correct option is D.
Hoped I helped
Answer:D
Step-by-step explanation:
5/16 as a decimal..?
Answer:
0.3125
Step-by-step explanation:
type that into a calculator
Hudson bought a plant and planted it in a pot near a window in his house. The initial height of the plant was 8 inches and it grew at a rate of 3 inches per month. Write an equation for H,H, in terms of t,t, representing the height, in inches, of the plant tt months after Hudson bought the plant.
Answer:
H = 3t + 8
Step-by-step explanation:
Since the plant has an initial height of 8 inches, this will be added to the amount it grows each month.
3t will represent how much it grows t months after he bought the plant, since it grows 3 inches each month.
So, the equation will be H = 3t + 8
PLSSSS HELLLPPP WILL GIVE BRAINLIESTTT!!!!!!!!!
Answer:
-2
Step-by-step explanation:
between each point on the graph, the line goes down two and over one. 2/1 = 2. the slope is negative because it goes downwards
Answer:
slope could be -2/1. or -2
Step-by-step explanation:
if you do rise and run/ look at the change
rise: 2_____change in y:-2
run: 1______change in x:1
HOPE THIS HELPS!
Subtract:
30−2.11
8.80
27.89
27.99
32.11
Answer:
27.89
Step-by-step explanation:
It is 27.89 because if you subtract 2 from 30 you get 28 and 28- 0.11 is 27.89
Which sequence of transformations creates a similar, but not congruent, triangle? (4 points) 1) Rotation and translation 2) Reflection and rotation 3) Dilation and rotation 4) Translation and reflection
Answer:
3) Dilation and rotation
Step-by-step explanation:
Rotation, translation, and reflection are rigid motions. They always result in congruent figures. If you don't want a congruent figure, you need to have dilation by a factor other than 1.
Similar, but not congruent, figures will be created by ...
Dilation and Rotation
Answer:Dilation and rotation
Step-by-step explanation:
Greta draws one side of equilateral △PQR on the coordinate plane at points P(−2, 2) and Q(6, 2). Which ordered pair is a possible coordinate of vertex R?
Answer:
1,8.9
Step-by-step explanation:
Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint. (Hint: Let (x,y) be the unknown endpoint. Apply the midpoint formula, and solve the two equations for x and y.) midpoint (-4,13) endpoint-(0,5)
Answer:
end point of a segment X₂ = - 8 ; Y₂ = 21
Step-by-step explanation:
given;
midpoint = ( Mx = -4 , My = 13 )
endpoint ₁ = ( X₁ = 0 , Y₁ = 5 )
find the other endpoint ₂ ( X₂ , Y₂)
use the mid point formula to get the other endpoint:
Mx = ( X₁ + X₂ ) / 2 My = ( Y₁ + Y₂ ) / 2
- 4 = (0 + X₂) / 2 13 = (5 + Y₂) / 2
-8 = 0 + X₂ 26 = 5 + Y₂
X₂ = -8 Y₂ = 21
12 percent of 4000 is what
Answer:
480
Step-by-step explanation:
4000 * 0.12 = 480
Answer:
the answer is 480
Step-by-step explanation:
Write 12% as
12
100
Since, finding the fraction of a number is same as multiplying the fraction with the number, we have
12/100 of 4000
12/100 × 4000
which statement is true? all whole numbers are rational numbers all integer's are whole numbers are rational numbers are integer's or none of the above
Answer:
a
Step-by-step explanation:
hope this helps
1. One number is 11 more than 3 times another number. Their sum is 71. Find the smaller number. 2. Two angles are complementary. One angle measures 22 degrees more than the other angle. Find the measure of the larger angle. 3. Two angles are supplementary. One angle measures 40 degrees more than the other angle. Find the measure of the larger angle. 4. The sum of three consecutive even integers is -36. Determine the largest integer of the three.
Answer:
1. The two numbers are 56 and 15
2. The two angles are 56 and 34 degrees
3. The two angles are 110 and 70 degrees
4.The largest number is -10
Step-by-step explanation:
Solving (1):
Represent both numbers with x and y
[tex]x = 11 + 3y[/tex]
[tex]x + y = 71[/tex]
Solving for x and y
Substitute [tex]11 + 3y[/tex] for x in the second equation
[tex]11 + 3y + y = 71[/tex]
Collect Like Terms
[tex]3y + y =71 - 11[/tex]
[tex]4y = 60[/tex]
Divide both sides by 4
[tex]y = 15[/tex]
Recall that
[tex]x = 11 + 3y[/tex]
[tex]x = 11 + 3 * 15[/tex]
[tex]x = 56[/tex]
Hence, the two numbers are 56 and 15
Solving (2)
Represent the two angles with x and y
[tex]x = 22 + y[/tex]
Since they are complementary;
[tex]x + y = 90[/tex]
Substitute 22 + y for x in [tex]x + y = 90[/tex]
[tex]22 + y +y= 90[/tex]
[tex]22 + 2y =9 0[/tex]
Collect Like Terms
[tex]2y = 90 - 22[/tex]
[tex]2y = 68[/tex]
Divide both sides by 2
[tex]y = 34[/tex]
Recall that [tex]x = 22 + y[/tex]
[tex]x = 22 + 34[/tex]
[tex]x = 56[/tex]
Solving (3):
Represent the two angles with x and y
[tex]x = 40 + y[/tex]
Since they are supplementary;
[tex]x + y = 180[/tex]
Substitute 40 + y for x in [tex]x + y = 180[/tex]
[tex]40 + y + y = 180[/tex]
[tex]40 + 2y = 180[/tex]
Collect Like Terms
[tex]2y = 180 - 40[/tex]
[tex]2y = 140[/tex]
Divide both sides by 2
[tex]y = 70[/tex]
Recall that [tex]x = 40 + y[/tex]
[tex]x = 40 + 70[/tex]
[tex]x = 110[/tex]
Solving (4):
Let the smallest number be x
[tex]x + x + 2 + x + 4 = -36[/tex]
Collect Like Terms
[tex]x + x + x = -36 - 2 - 4[/tex]
[tex]3x =-42[/tex]
Divide through by 3
[tex]x = -14[/tex]
The largest number; x + 4 is
[tex]x + 4 = -14 + 4[/tex]
[tex]x + 4 = -10[/tex]
Hence, the largest number is -10
does anybody know this ???
Answer:
(a) angle ACB is not proper way
Answer:
A.
Step-by-step explanation:
We can read the angle with the labels found in answers B, C and D.
On a field trip, the school bus drove five more than twice as many miles in the afternoon as in the morning. If the whole trip was 125 miles, how many miles did the bus travel in the morning and how many in the afternoon?
Answer:
morning - 40
afternoon - 85
Step-by-step explanation:
The bus traveled 40 miles in the morning and 85 miles in the afternoon.
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
The school bus traveled five miles more on a field trip in the afternoon than it did in the morning. If the journey was 125 kilometers long
Let x the distance traveled by bus in the morning.
As per the given condition, we can get the equation shown below:
⇒ x + 2x + 5 = 125
⇒ 3x + 5 = 125
⇒ 3x = 120
⇒ x = 40
In the afternoon, the bus traveled 2x + 5 miles.
Now substitute the value of x in the equation for the afternoon miles to include:
⇒ 2 × 40 +5 = 85
Therefore, the bus traveled 40 miles in the morning and 85 miles in the afternoon.
Learn more about the equation here:
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can you help me find slope and y intercept
Answer:
it's right in front of you actually. the y intercept is negative 1/7 and the slope is 1/7
Answer:
your slope 1/7x and your y-int is -1/7. Hope this helps!
Step-by-step explanation:
Tamika is reserving a room in a hotel in France were they use euros. The room charge is €75. Suppose the conversation rate is €1=$1.298. What is the cost of the room in dollars?
Answer:
$93.75
Step-by-step explanation:
Multiply the conversion equation by 75:
€1 × 75 = $1.298 × 75
€75 = $93.75