`find the equatifindon of tangent and normal of parabola y²=16ax at point whose coordinate is -5a.
Answers
Answer:
[tex] \rm \displaystyle y _{ \rm tangent} = - \frac{8}{5} x - \frac{5}{2} a[/tex]
[tex] \rm \displaystyle y _{ \rm normal} = \frac{5}{8} x - \frac{765}{128} a[/tex]
Step-by-step explanation:
we are given a equation of parabola and we want to find the equation of tangent and normal lines of the Parabola
finding the tangent line
equation of a line given by:
[tex] \displaystyle y = mx + b[/tex]
where:
m is the slopeb is the y-interceptto find m take derivative In both sides of the equation of parabola
[tex] \displaystyle \frac{d}{dx} {y}^{2} = \frac{d}{dx} 16ax [/tex]
[tex] \displaystyle 2y\frac{dy}{dx}= 16a[/tex]
divide both sides by 2y:
[tex] \displaystyle \frac{dy}{dx}= \frac{16a}{2y}[/tex]
substitute the given value of y:
[tex] \displaystyle \frac{dy}{dx}= \frac{16a}{2( - 5a)}[/tex]
simplify:
[tex] \displaystyle \frac{dy}{dx}= - \frac{8}{5}[/tex]
therefore
[tex] \displaystyle m_{ \rm tangent} = - \frac{8}{5}[/tex]
now we need to figure out the x coordinate to do so we can use the Parabola equation
[tex] \displaystyle ( - 5a {)}^{2} = 16ax [/tex]
simplify:
[tex] \displaystyle x = \frac{25}{16} a[/tex]
we'll use point-slope form of linear equation to get the equation and to get so substitute what we got
[tex] \rm \displaystyle y - ( - 5a)= - \frac{8}{5} (x - \frac{25}{16} a)[/tex]
simplify which yields:
[tex] \rm \displaystyle y = - \frac{8}{5} x - \frac{5}{2} a[/tex]
finding the equation of the normal line
normal line has negative reciprocal slope of tangent line therefore
[tex] \displaystyle m_{ \rm normal} = \frac{5}{8}[/tex]
once again we'll use point-slope form of linear equation to get the equation and to get so substitute what we got
[tex] \rm \displaystyle y - ( - 5a)= \frac{5}{8} (x - \frac{25}{16} a)[/tex]
simplify which yields:
[tex] \rm \displaystyle y = \frac{5}{8} x - \frac{765}{128} a[/tex]
and we're done!
( please note that "a" can't be specified and for any value of "a" the equations fulfill the conditions)
Answer:
In attachment
Step-by-step explanation:
For answer refer to attachment .
Related Questions
In the diagram below of RST. L is a point on RS, and M is a point on RT, such that LM parallel to ST
If RL = 3 LS= 12 LM=7. and ST=x+ 2, what is the length of ST?
Answers
Answer:
ST is 28
Step-by-step explanation:
Using the similarity formla
RL/LS = LM/ST
3/12 = 7/x+2
3(x+2)=84
x +2= 84/3
x+2 = 28
x= 28-2
x = 26
ST = x+2
ST = 26+2
ST = 28
Hence the length of ST is 28
a driver travelled a distance of 864 km in 12 hours what is the speed of car
Answers
answer:
speed= 72 km - per • hour
Answer:
Speed of car = 72 km per hour
PLease help me with this math qestion
Answers
Answer:
n+3 = 15 ; n = 12
3n -6 = 12; n=6
Step-by-step explanation:
more than means it comes after
a number
n
3 more than
n+3
is 15
n+3 = 15
Subtract 3 from each side
n+3-3 = 15-3
n = 12
Subtract from comes after
three times a number
3n
six subtracted from
3n -6
is 12 means equal to
3n -6 = 12
To solve add 6 to each side
3n -6+6 =12+6
3n = 18
Divide by 3
3n/3 =18/3
n =6
Answer:
A = 3 - x = 15 B = 6 - 3 times x = 12
Step-by-step explanation:
Martin deposits $200 in a savings account that earns 5% annual interest. Four years later, Cary deposits $200 in an account earning the same interest. Let M represent the balance in Martin’s account and let C represent the amount of money in Cary’s account.
Answers
Complete question :
Martin deposits $200 in a savings account that earns 5% annual interest. four years later, cary deposits $200 in an account earning the same interest. let m represent the balance in martins account and let c represent the amount of money in carys account. choose the pair of expressions that describe the accounts y years after martin opened his account. martin: 200(1.05)y cary: 200(1.05)y+4 martin: 200(1.05)y+4 cary: 200(1.05)y4 martin: 200(0.05)y cary: 200(0.05)y4 martin: 200(1.05)y cary: 200(1.05)y4 choose the equation that relates the balances in the accounts y years after martin opened his account. c = m(1.05)4y m = c(1.05)4y c = 1.22m m = 1.22c
Answer:
m = m = 200(1.05)^y+4
c = m = 200(1.05)^y
m = 1.22c
Step-by-step explanation:
The future value can be represented as :
Future value, F = P(1 + r)^n
r = interest rate = 5% = 0.05 , n = number of years ;
For Martin :
m = 200(1 + 0.05)^n
For cyan :
c = 200(1 + 0.05)^n
y years after Martin
Cyan opened 4 years after Martin :
Representing in terms of y
Cyan = y ; Martin = y +4
m = m = 200(1.05)^y+4
c = m = 200(1.05)^y
From. Indices :
(1.05)^y+4 = 1.05^y * 1.05^4
Hence,
m = 200 * 1.05^y * 1.05^4
c = 200 * 1.05)^y
Hence,
m = c * 1.05^4
m = c * 1.2155
m = c * 1.22
m = 1.22c
Answer:
the first question is d and so is the second one
Which is a factor of 10?
OA. 40
B. 10
C. 30
D. 20
Answers
Answer: B. 10
Explanation: Any number is a factor of itself.
We can rule out choices A, C and D because those values are larger than 10. They are multiples of 10, but not factors of 10.
PLEASE HELP. Last 3 times I asked people put spam, please do not this is urgent.
WILL MARK BRAINLIEST
Answers
Answer:
A) 2^12
Step-by-step explanation:
3x - y = 12
3(5) - 3 = 12
15 - 3 = 12
12 = 12
[tex]\frac{8^x}{2^y}[/tex]
[tex]\frac{8^5}{2^3}[/tex]
[tex]\frac{32768}{8}[/tex]
4096
2^12
Short Response
Shantelle wants to rent a mid-size car for one day. Value Rent-a-Car charges $20 a day plus $0.20 per
mile, and Best Rent-a-Car charges $30 a day plus $0.10 per mile for rental of the same mid-size car.
Part A) Write an equation in slope intercept form, y=mx+b, for each car:
Value Rent-a-Car: y=0.20x+20
Best Rent-a-Car: y=0.10x+30
Part B: Determine the mileage where the rental charges are the same.
Answers
9514 1404 393
Answer:
100 miles
Step-by-step explanation:
A. The answers shown are correct
__
B. Equate the values of y and solve for x.
0.20x +20 = 0.10x +30
0.10x = 10 . . . . . . . subtract (20+0.10x)
x = 100 . . . . . . . . divide by 0.10
The rental charges are the same for 100 miles.
The cost of a piece of furniture is calculated as follows:
Wood: Rs.300, Paint: Rs.200 and wages Rs.200
If the cost of the wood and paint are increased by 12% and 7% respectively, find the new cost of the furniture.
Answers
Answer:
Examining whole-body center of mass (COM) motion is one of method being used to quantify dynamic balance and energy during gait. One common method for estimating the COM position is to apply an anthropometric model to a marker set and calculate the weighted sum from known segmental COM positions. Several anthropometric models are available to perform such a calculation. However, to date there has been no study of how the anthropometric model affects whole-body COM calculations during gait. This information is pertinent to researchers because the choice of anthropometric model may influence gait research findings and currently the trend is to consistently use a single model. In this study we analyzed a single stride of gait data from 103 young adult participants. We compared the whole-body COM motion calculated from 4 different anthropometric models (Plagenhoef et al., 1983; Winter, 1990; de Leva, 1996; Pavol et al., 2002). We found that anterior-posterior motion calculations are relatively unaffected by the anthropometric model. However, medial-lateral and vertical motions are significantly affected by the use of different anthropometric models. Our findings suggest that the researcher carefully choose an anthropometric model to fit their study populations when interested in medial-lateral or vertical motions of the COM. Our data can provide researchers a priori information on the model determination depending on the particular variable and how conservative they may want to be with COM comparisons between groups. Copyright © 2017 Elsevier Ltd. All rights reserved.
Step-by-step explanation:
What is the value of z in the equation 3z+9=z?
Answers
Can I have help I am stuck on this problem It would mean the world if u helped me and tysm!! =-)
Answers
The area of a rectangle is length x width:
14.26 cm x 9.28 cm = 132.3328
Area is measured in square centimeters, in this case
FINAL ANSWER:
132.3328 square centimeters
HOPE THIS HELPS!
Answer:
132.3328 or 132.33 if you round do the nearest hundredth
Step-by-step explanation:
To find area, just multiply length by width. 14.26x9.28=132.3328
6 +7 ( □ +7 5) = 1
help me pls
Answers
Answer:
Can't be possible.
Step-by-step explanation:
Given:
6+7(x+75)=1
So according to given equation it can't be possible because when we add some value in 6 their result will be always greater than 1.
Crawling Crayfish!
Big Claw, the crayfish, challenged Flicker to a 60 em race. Since Big Claw is much
larger, he offered to give Flicker a 10 cm head start Flicker agreed and the race
began. After 5 seconds, Big Claw had crawled 6 cm and Flicker had crawled 4 cm.
If they continue at this rate, who do you predict will win the race? justify your
prediction
How many seconds have elapsed when Big Claw and Flicker are tied?
Answers
Answer: Crayfish, 25 s
Step-by-step explanation:
Given
The length of race is 60 cm
Flicker gets a 10 cm head-start
Cray fish covers 6 cm in 5 s i.e. its speed is
[tex]\Rightarrow \dfrac{6}{5}=1.2\ cm/s[/tex]
Flicker covers 4 cm in 5 s, its speed is
[tex]\Rightarrow \dfrac{4}{5}=0.8\ cm/s[/tex]
Time taken by Cray fish to cover the race is
[tex]\Rightarrow t_1=\dfrac{60}{1.2}\\\\\Rightarrow t_1=50\ s[/tex]
Time taken by flicker to cover race with 10 cm head start
[tex]\Rightarrow t_2=\dfrac{60-10}{0.8}\\\\\Rightarrow t_2=62.5\ s[/tex]
Time taken by crayfish is less. Hence, crayfish wins the race
When they both covers the same distance, they tied momentarily i.e.
[tex]\Rightarrow 1.2t=10+0.8t\\\Rightarrow 0.4t=10\\\\\Rightarrow t=\dfrac{10}{0.4}\\\\\Rightarrow t=25\ s[/tex]
After 25 s, they tied the race.
Which equation best matches the graph shown below?
Answers
Answer:
y=0.5(x+6)(x+5)
Step-by-step explanation:
Since the parabola goes upwards as it expands from the vertex, the "a" value is definitely positive so the answer must be either the top-left or bottom-right. Next, use the roots to find the final answer. The roots are on the left side of the y-axis which indicates that they are negative. Now you know that the answer is the bottom-right answer because if both roots are negative, then the expressions must include addition to create 0 which is the y-value at the bases.
in order for the parallelogram to be a rhombus x=?
Answers
Answer:
x = 12
Step-by-step explanation:
In a rhombus, the diagonal is also the bisector of the angle, so the two vlaue must be congruent
2x + 35 = 8x- 37
6x = 72
x = 12
wegnerkolmp2741o can you please answer this I will mark brainliest
An isosceles triangle has two 5.5 cm sides and two 32.4° angles. Explain how to determine the perimeter of the triangle. Include a diagram in your solution. You do NOT need to solve.
Answers
Answer:
see below
Step-by-step explanation:
The drawing in blue is what we are told in the problem.
We are given two sides and two angles. It is an isosceles triangle with two equal sides and two equal angles. Draw a perpendicular bisector ( it makes a 90 degree angle. Now we have two identical right triangles. We can use trig functions to find x
cos theta = adj/ hyp
cos 32.4 = x / 5.5
Solving for x
5.5 cos 32.4 =x
Now we have 2x for the third side of the triangle
2( 5.5 cos 32.4) is the third side
P = 5.5 + 5.5 + 2( 5.5 cos 32.4)
Answer:
See the Below
Step-by-step explanation:
Draw a circle with a radius of 5.5 and center at A.Take any point B on the circle and join AB.Draw a line thru B making an angle 32.4 with AB which intersects the circle at D. Extend AD on both sides.Draw two circles with a radius of 5.5cm and centers B and D which intersect the line BD at E and F.Measure length EF, which is the perimeter of triangle ABD.=20.3 cm.Method 2. Assume that base of the triangle =x cm.x/2= 5.5 cos 32.4 and x=11*cos 32.4 =11*0.844=9.287Perimeter = 20.287please help me find the area
Answers
Answer:
17,290 yd2
Step-by-step explanation:
I rlly don't know how u were taught to solve it but what I did was multiply all the sides
5(a^6+2a^5)-6a(5a^4-7a^3)
Answers
Answer:
a4(5a2−20a+42)
Step-by-step explanation:
Factor 5(a6+2a5)−6a(5a4−7a3)
5a6−20a5+42a4
=a4(5a2−20a+42)
Make me brainliest!
You start driving for 3 miles, turn right, and drive north for another 13 miles. At the end of driving, what is your straight line distance from your starting point? Round to the nearest tenth of a mile.
Answers
Answer:
13.34
Step-by-step explanation
Pythagorean Theorem: c= sqrt(a^2+b^2) or a^2=+b^2=sqrt(c)
3^2+13^2= sqrt(178) = 13.34166= 13.34
simplify the expression (c^7)^9(c^0)^5
Answers
Answer:
c^63 Your welcome !!
Step-by-step explanation:
How many ounces in 31/2 pounds
Answers
Answer:
248 ounces
Step-by-step explanation:
I hope this helps :D
Answer:
248 ounces is the correct answer hope you will like it and Mark me as BRAINLIEST!!!!
How do you know the absolute value of a number?
Answers
Step-by-step explanation:
It is very simple
Any number's absolute value should be positive
Let's say absolute value of 3 - >answer is 3
But absolute value of - 3 - > is also 3
Hope you understood it.
Answer:
Step-by-step explanation: In order to find the absolute value all you do is see what number you have and turn into an positive, say "what is the absolute value" of -5" it would just be 5,
Hope this helps :)
if Tom had 78 apples and he gave to the shop for 80% and he put it on sale for another 10% what many apples would Tom get in the end?
Answers
Answer:
he has to many apples
Step-by-step explanation:
Never gonna give you up
Never gonna let you down
Never gonna run around and desert you
Never gonna make you cry
Never gonna say goodbye
Never gonna tell a lie and hurt you
Find the volume of the prism or pyramid below
Answers
Answer:
6.3 Cubic cm
Step-by-step explanation:
[tex]V=A*h=(1.8*1.2+.5*1.1*1.8)*2=6.3cm^{3}[/tex]
If x = 0 and y > 0, where is the point (x, y) located?
Answers
Answer:
upper half y axis
Step-by-step explanation:
If x = 0 we are on the y axis. If y >0 we are on the upper half of the y axis
What is the awnsers helppppp
Answers
Answer: 0.77
Step-by-step explanation:
Answer:
0.23
Step-by-step explanation:
the chart adds up to 1 as a whole so 23% chose football and there is a 23% chance the next person will also choose football.
Bill can hit a bucket of 323 golf balls in 17 hours.
How many golf balls can Bill hit in 23 hours?
Answers
Explanation:
Bill’s unit rate of golf balls per hour is:
323 ÷ 17 = 19
19 golf balls per hour
To find how many golf balls Bill can hit in 23 hours, multiply:
19 • 23 = 437
Therefore, Bill can hit 437 golf balls in 23 hours.
Please, say if my answer is right
If its, glad to help!
-SpaceMarsh
Which of the following expressions are equivalent to 63? Check all that are true.
Answers
Answer:
A & E
Step-by-step explanation:
Main equation: [tex]6^{3} = 216[/tex]
A. [tex]\frac{6^{7} }{6^{4}} = 6^{3} = 216[/tex]
B. 18
C. [tex](6^{1})^{2} = 36[/tex]
D. 81
E. 6 * 6 * 6 = 216
F. [tex]6^{2} + 6^{1} = 36 + 6 = 42[/tex]
Hope this helps!
Please mark as the Brainliest!
To find the constant vector C, we use the given initial condition v(0) = k, we also know that at t = 0, the general equation for v() i:s Comparing both equations for V(0) and solving for C, we have C = k. Substituting it back into the general equation, we have
V(t) = 4ti + 5tj + c = ______.
Answers
Answer:
4ti + 5tj + k
Step-by-step explanation:
Initial condition V(0) = k
at t = 0
general equation for v(t )
V(0) = 0i + 0j + c = k
when we compare V(0) and solve for c , c = k
back to general equation
V(t) = 4ti + 5tj + c = 4ti + 5tj + k
A force of 4 pounds is required to hold a spring stretched 0.4 feet beyond its natural length. How much work (in foot-pounds) is done in stretching the spring from its natural length to 0.6 feet beyond its natural length
Answers
Answer:
the work done in stretching the spring from its natural length is -1.8 ft.lb
Step-by-step explanation:
Given the data in the question;
From Hook's law, the magnitude of force applied on a spring is expressed as follows;
|F| = k|x|
where F is the force applied the spring, k is the spring constant, x is the length extension
Now, given that; F = 4 pounds = 4 lb and x = 0.4 ft
we substitute
4 = k × 0.4
k = 4 / 0.4
k = 10 lb/ft
Also, Hook's law can be expressed as follows;
F = -kx ---------- let this be equation 1
Now, work done by a force applied between two points is expressed as follows;
dW = Fdx ----------- let this be equation 2
substitute equation 1 into equation 2
dW = (-kx )dx
we integrate both side
∫(dW) = ∫((-kx )dx)
W = -k∫xdx
W = -k[tex]\frac{x^2}{2}[/tex]
w = -[tex]\frac{1}{2}[/tex]kx²
we substitute 10 lb/ft for k and 0.6 ft for x
w = -[tex]\frac{1}{2}[/tex] × 10 lb/ft × (0.6 ft)²
w = -[tex]\frac{1}{2}[/tex] × 10 lb/ft × 0.36 ft²
w = -1.8 ft.lb
Therefore, the work done in stretching the spring from its natural length is -1.8 ft.lb
How do I solve this math problem? The answer is: x = a^2/a-3
Answers
Answer:
I love algebra anyways
the ans is in the picture with the steps
(hope it helps can i plz have brainlist :D hehe)
Step-by-step explanation:
