`show that the normal to the parabola y²=8x at (2 4)meets the parabola again in(18, -12)`
Answers
Answer:
See Below.
Step-by-step explanation:
We want to show that the normal line to the parabola:
[tex]y^2=8x[/tex]
At the point (2, 4) meets the parabola again at (18, -12).
First, find the tangent line to the parabola at the point (2, 4). We can take the derivative of both sides with respect to x:
[tex]\displaystyle \frac{d}{dx}\left[ y^2\right]=\frac{d}{dx}\left[8x\right][/tex]
Implicit differentiation:
[tex]\displaystyle 2y\frac{dy}{dx}=8[/tex]
Therefore:
[tex]\displaystyle \frac{dy}{dx}=\frac{8}{2y}=\frac{4}{y}[/tex]
Then the slope of the tangent line to the point (2, 4) is:
[tex]\displaystyle \frac{dy}{dx}\Big|_{y=4}=\frac{4}{(4)}=1[/tex]
Thus, the slope of the normal line is -1.
And since it passes through the point (2, 4), by the point-slope form:
[tex]y-(4)=-1(x-2)[/tex]
Simplify:
[tex]y=-(x-2)+4[/tex]
By letting x = 18:
[tex]y=-(18-2)+4=-16+4=-12[/tex]
So, the normal line indeed passes through (18, -12).
Answer:
answer is in the picture.
Related Questions
Simplify -4 + (-3) + 6.
Answers
Answer:3/6 in simplest fraction form is 1/2.
Step-by-step explanation:EASY and my chanel is FireFlameZero if u can check dat out
Evaluate the function at the given values of x. Round to 4 decimal places, if necessary. =fx7x
Answers
Step-by-step explanation:
what are the given values of x ?
there is nothing visible.
and what is the function itself ? f(x) = 7x ?
it is not clear.
Solve the homogeneous linear system corresponding to the given coefficient matrix. (If there is no solution, enter NO SOLUTION. If the system has an infinite number of solutions, set x4 = t and x2 = s and solve for x1 and x3 in terms of t and s.)
[1 0 0 1]
[0 0 1 0]
[0 0 0 0]
(x1, x2, x3, x4) = _________
Answers
Answer:
[tex]x_1 = -t[/tex]
[tex]x_2 = s[/tex]
[tex]x_3 = 0[/tex]
[tex]x_4 = t[/tex]
Step-by-step explanation:
Given
[tex]\left[\begin{array}{cccc}1&0&0&1\\0&0&1&0\\0&0&0&0\end{array}\right][/tex]
Required
Determine x1 to x4
First, we write the augmented matrix
[tex]\left[\begin{array}{cccc}1&0&0&1\\0&0&1&0\\0&0&0&0\end{array}\right] = \left[\begin{array}{c}0&0&0\end{array}\right][/tex]
Taking the position of each column, we have:
[tex]x_1 + 0 + 0 +x_4 = 0[/tex]
[tex]0 + 0 + x_3 +0 = 0[/tex]
[tex]0 + 0 + 0 + 0 = 0[/tex]
There is no explicit equation for [tex]x_2[/tex]
So: [tex]x_2 = s[/tex] ----- arbitrary variable
[tex]x_1 + 0 + 0 +x_4 = 0[/tex] implies that:
[tex]x_1 + x_4 = 0[/tex]
[tex]0 + 0 + x_3 +0 = 0[/tex] implies that
[tex]x_3 = 0[/tex]
[tex]0 + 0 + 0 + 0 = 0[/tex] implies that
[tex]0 = 0[/tex]
So, we have:
[tex]x_1 + x_4 = 0[/tex]
[tex]x_3 = 0[/tex]
[tex]x_1 + x_4 = 0[/tex] becomes
[tex]x_1 = -x_4[/tex]
Let
[tex]x_4 = t[/tex]
So:
[tex]x_1 = -x_4[/tex]
[tex]x_1 = -t[/tex]
Where t , s are real numbers
On a
paper, graph y < -2x Then determine which answer matches
the graph you drew.
Answers
Answer:
theres the graph
Step-by-step explanation:
Examine the geometric relationships in the diagram below which option shows the correct value of x and y?
Answers
Answer:all of them
Step-by-step explanation:
Calculate the interest rate with a deposit $27,580.00 in an interest-bearing account. After one year, your accrued interest is $1,442.43.
Answers
Answer:
5.23%
Step-by-step explanation:
See Image below:)
order of operation problem who two operations inside parentheses and two ex outside ( using all add, subtract, multiply and divide)
PLEASE SHOW ALL WORK
Answers
Answer:
17 + 123 (4 - 1) + (36 / 18) 52 =
17 + 123 x 3 + 2 x 52 =
17 + 369 + 104 =
17 + 473 =
490
Step-by-step explanation:
hope this helps! i made up everything so i hope its okay!
Suppose a certain state university's college of business obtained the following results on the salaries of a recent graduating class:
Finance Majors Business Analytics Majors
n1 = 140 n2 = 30
x1 = $48,237 x2 = $55,417
s1 = $19,000 s2 = $10,000
Required:
a. Formulate hypotheses so that, if the null hypothesis is rejected, we can conclude that salaries for Finance majors are significantly lower than the salaries of Business Analytics majors. Use α = 0.05. (Let μ1 = the population mean salary for Finance majors, and let μ2 = the population mean salary for Business Analytics majors.
b. What is the value of the test statistic?
c. What is the p-value? (Round your answer to four decimal places.)
d. What is your conclusion?
Answers
Answer:
Following are the responses to the given choice:
Step-by-step explanation:
For point a:
[tex]H_0: \mu_1 - \mu_2 = 0\\\\ H_1: \mu_1 - \mu_2 < 0[/tex]
For point b:
[tex]t = -2.953[/tex]
For point c:
[tex]\to p- value = 0.0021[/tex]
For point d:
Reject [tex]H_o[/tex]. It could deduce that the pay of higher banking is considerably lower than the pay of higher project management.
Is -40/8 positive or negative?
Answers
Answer:
Negative. The answer gives - 5
Answer:
Negative
Step-by-step explanation:
-40/8 is equivalent to -5. Since -5 or "negative five" is negative (as it states), the equation is negative.
Choose the conditional statement that can be used with its converse to form the following biconditional statement: "It is a leap year if and only if the year has 366 days."
A. If it is not a leap year, then it does not have 366 days.
B. If it is a leap year, then the year has 366 days.
C. If a leap year has 366 days, then this is a leap year. D. If a year does not have 366 days, then it is not a leap year
Answers
Given the biconditional statement: "It is a leap year if and only if the year has 366 days.", the converse to form it is "If the year has 366 days, then this is a leap year". (Right choice: C)
How to determine the propositional form of a sentence
According to logics, propostions are truth bearers that makes sentences true or false. In linguistics, propositions are the meaning of declarative sentences. There are simple and composite propositions, the latter are formed by one simple proposition at least and logic connectors. There are five logic connectors:
Conjuction X ∧ Y ("and" operator)Disjunction X ∨ Y ("or" operator)Negation ¬ X ("not" operator)Implication/Conditional X ⇒ Y ("if-then" operator)Double implication/Biconditional X ⇔ Y ("if-only if" operator)By logic rules we know that the double implication/biconditional is commutative operator:
(X ⇔ Y) ⇔ (Y ⇔ X)
In addition, a double implication/biconditional has the following equivalence:
(X ⇒ Y) ∧ (Y ⇒ X)
Where Y ⇒ X is the converse of X ⇒ Y.
Therefore, the converse to form the statement "It is a leap year if and only if the year has 366 days" is Y ⇒ X: "If the year has 366 days, then this is a leap year".
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Express square root 4x – 7 as a power .
Answers
Answer:
It's answer is 4x-7^1/2
Explain how to translate the phrase into an algebraic
expression
a number squared decreased by ten
Answers
Answer:
I think the answer is 1^2 - 10
PLEASE HELP!!! IM ALMOST DONE WITH THIS SEMESTER
Answers
You can calculate it out or you can see that it's the only answer in slope intercept form
Calculate the mean and the standard deviation of the age of individuals that purchased skateboarding shoes. Use 10 as the midpoint of the first class. (Do not round intermediate calculations. Round your answers to 2 decimal places.)
Answers
Answer:
Mean = 19.84
Standard deviation = 11.12
Step-by-step explanation:
Note: This question is not complete. The complete question is therefore provided before answering the question. See the attached pdf file for the complete question.
The explanation of the answer is now given as follows:
Note: See the attached excel file for the calculation of the total of fx and total of f*x^2.
N = Number of individuals sampled = 200
From the attached excel file, we have:
Total of fx = 3,967
Total of f*x^2 = 103,425.50
Therefore, we have:
Mean = Total of fx / N = 3,967 / 200 = 19.84
Variance = (Total of f*x^2 / N) - Mean^2 = (103,425.50 / 200) - 19.84^2 = 517.13 - 393.43 = 123.70
Standard deviation = Variance^0.5 = 123.70^0.5 = 11.12
Gina wants to take dance classes. She compares two dance studios to determine which has the best deal for her. Dance World charges a rate for each class. Toe Tappers charges a rate for each class plus a one-time registration fee. The system of equations shown models the total costs for taking x classes at each.
Dance World: y = 15x
Toe Tappers: y = 25 + 12.5x
How many classes would Gina need to take for the total cost to be the same at both dance studios?
Answers
Answer:
Gina would need to take 10 classes.
Step-by-step explanation:
Cost of x classes at dance studio:
[tex]y_d(x) = 15x[/tex]
Cost of x classes at toe tappers:
[tex]y_t(x) = 25 + 12.5x[/tex]
How many classes would Gina need to take for the total cost to be the same at both dance studios?
This is x for which:
[tex]y_d(x) = y_t(x)[/tex]
So
[tex]15x = 25 + 12.5x[/tex]
[tex]2.5x = 25[/tex]
[tex]x = \frac{25}{2.5}[/tex]
[tex]x = 10[/tex]
Gina would need to take 10 classes.
Answer:
10 just took it on edge
Please help me answer e, f and number 3. See the image below
Answers
Answer:
Prat two of e) 6/12 Both the numerator and denominator were multipled by three, the number of boxes we split each box into.
F) we can multiply both the numerator and denominator without changing the values, so 2a/2b or 10a/10b
What are the three plot points and is it over the x-axis or y-axis
Answers
Answer:
(-2,1), (0,1), and (2,0). its over the y axis
Step-by-step explanation:
Answer:
shift it 3 values right and 2 units up
Step-by-step explanation:
moving x-axis and moving y-axis
Simply please hurry!! Thank you also please ignore my answer I had to click something
Answers
9514 1404 393
Answer:
(b) 3h^-8·k^10
Step-by-step explanation:
The applicable rule of exponents is ...
(a^b)/(a^c) = a^(b-c)
__
[tex]\dfrac{15h^{-4}k^{15}}{5h^4k^5}=\dfrac{15}{5}h^{-4-4}k^{15-5}=\boxed{3h^{-8}k^{10}}[/tex]
A jug is 80% full of water. After 360 millimeters of water are poured out, the jug is 60% filled with water. What is the capacity of the jug?
15 POINTS!!
Answers
Answer:
1800ml
Step-by-step explanation:
Given data
let the capacity of the Jug be x millimeters
from 80% to 60% = 20%
Since 20% of the capacity is equivalent to 360ml
the 100% will be x ml
cross multiply we have
360*100= 20*x
x= 36000/20
x= 1800ml
Hence the capacity of the jug is 1800ml
HELP ANYONE OUT THERE WITH MY MATH
Answers
Answer:
x is 37.,.,.,.,.,.,.,.,.,.,.,.,.,.,.,.
Answer:
x = 37
Step-by-step explanation:
Interior angles of a square is 90 each.
∠JKL = 90°
Given ∠JKL = 3x - 21
Therefore, 3x - 21 = 90
3x = 90 + 21
3x = 111
x = 37
Can I get the awnsers for these two? Any help is appreciated.
Answers
Answer:
y = 4x - 5
Step-by-step explanation:
for slope intercept form
y = mx + c
where m is the slop so
M = 4
point = (1, -1)
a point on the line must satisfy the equation so replacing y and x by -1 and 1 respectively to get to c.
-1 = 4 × 1 + c
-1 - 4 = c
-5 = c
placing these values in y = mx + c
y = 4x - 5
Answer:
y = 4x - 5.
Step-by-step explanation:
First write it in point-slope form:
y - y1 = m(x - x1)
y - (-1) = 4(x - 1)
y + 1 = 4x - 4
y = 4x - 4 - 1
y = 4x - 5. <------- Slope-intercept.
Find the missing term given below.
14,916,2536,?
Answers
if this helps pls give brainliest thank youuuu
Question 5
Refer to the data that you recorded in part D. In each row, compare the slope of ABto the slope of the perpendicular line. What is the
relationship between the two slopes? What conclusion can you draw about the relationship between the slopes of any two perpendicular lines?
Ok
Answers
Answer:
Step-by-step explanation:
Answer:
The product of the slopes of and the line perpendicular to through C is -1 in all cases. So, I can conclude that any two perpendicular lines have slopes that are negative reciprocals of each other.
Step-by-step explanation:
its correct
bine like terms.
7 – 64 – 5x3 – 1 + x3 – 7 – 2y
PLS HURRY
Answers
Answer:
-4x³ - 8y - 1
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Terms/CoefficientsStep-by-step explanation:
Step 1: Define
Identify
7 - 6y - 5x³ - 1 + x³ - 7 - 2y
Step 2: Simplify
[Addition] Combine like terms (x³): -4x³ + 7 - 6y - 1 - 7 - 2y[Subtraction] Combine like terms (y): -4x³ - 8y + 7 - 1 - 7[Subtraction] Combine like terms: -4x³ - 8y - 1Which polygons have at least one pair of parallel sides but are not parallelograms? Choose all that apply.
Answers
The correct option is polygon E.
What are polygons?A polygon is a plane figure that is described by a finite number of straight line segments connected to form a closed polygonal chain.
Given that, Which polygons have at least one pair of parallel sides but are not parallelograms,
Such polygons are called trapezoid.
A trapezoid, also known as a trapezium, is a flat-closed shape having 4 straight sides, with one pair of parallel sides.
Hence, the correct polygon is E.
Learn more about polygons, click;
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State the domain of the graphed function, using interval notation. The domain is ______
Answers
Answer:
[-10,-2) U (-2,2) U [2, 5) U (5, infinity)
Step-by-step explanation:
p/s: I don't have the infinity symbol on my keyboard but you know what it is. Hope this help
In rectangle ABCD shown below, CD = 24 and m angle ABD = 35º. Determine the length of diagonal line BD to the nearest tenth. Show the work that leads to your answer.
Answers
Answer:
BD = 29.3
Step-by-step explanation:
Each half of the rectangle is a right triangle.
The diagonal is the hypotenuse of each right triangle.
Let's focus on right triangle ABD
Reference angle = m<ABD = 35°
AB = CD = 24
Adjacent length = AB = 24
Diagonal = Hypotenuse = BD
To find BD, apply CAH:
Cos 35° = Adj/Hyp
Substitute
Cos 35° = 24/BD
BD × Cos 35° = 24
BD = 24/Cos 35°
BD = 29.3 (nearest tenth)
A cargo plane has a maximum take off weight of 910000 pounds which expression can be used to determine the maximum take off weight in tons?
Answers
Answer:
910,000 ÷ 2,000
Step-by-step explanation:
1 ton = 2000 pounds
therefor divide pounds by 2000 to get tons
910,000 ÷ 2,000
Which of the following inequalities represents all values of X for which the quotient below is defined?
Answers
Answer:
[tex]x \ge 1[/tex]
Step-by-step explanation:
Given
[tex]\sqrt{6(x - 1)} \div \sqrt{3x^2[/tex]
Required
x for [tex]which[/tex] the function is [tex]de fi ned[/tex]
To do this, we set the numerator root [tex]\ge 0[/tex]
So, we have:
[tex]6(x - 1) \ge 0[/tex]
Divide by 6
[tex](x - 1) \ge 0[/tex]
Solve for x
[tex]x \ge 1[/tex]
Also, we set the denominator greater than 0:
[tex]3x^2 > 0[/tex]
Divide by 3
[tex]x^2 > 0[/tex]
Take square roots
[tex]x > 0[/tex]
So, we have:
[tex]x > 0[/tex] and [tex]x \ge 1[/tex]
Combine both to give:
[tex]x \ge 1[/tex]
Find angle X in the angle diagram.
Answers
Answer:
80*
Step-by-step explanation:
Angle x + 80* add up to the vertical angle of 160*
So, 160* = x + 80*
80* = x
Answer:
80°
Step-by-step explanation:
160 is vertically opposite the x and 80, which means they have the same value. This makes x+80=160.
This can be solved to x=80.
