Answer:
Hello,
P=(30,6)
Step-by-step explanation:
[tex]x=6t^2+6\\y=t^3-2\\\\\dfrac{dx}{dt}= 12t\\\dfrac{dy}{dt}= 3t^2\\\\\dfrac{dy}{dx} =\dfrac{\dfrac{dy}{dt} }{\dfrac{dx}{dt} } =\dfrac{3t^2}{12t} =\dfrac{t}{4} \\\\\dfrac{t}{4} =\dfrac{1}{2} \Longrightarrow t=2\\\\\\x=6t^2+6=6*2^2+6=30\\\\y=t^3-2=2^2-2=8-2=6\\\\\\Tangence\ point=(30,6)\\[/tex]
The point on the curve x = 6t² + 6, y = t³ - 2 where the tangent line have slope 1/2 is (30, 6).
How to depict the point on the curve?From the information given, x = 6t² + 6, y = t³ - 2. We'll find the first order derivative of x and y which will be:
dx/dt = 12t
dy/dt = 3t²
Therefore, 3t²/12t = t/4, t = 2.
We'll put the value of t back into the equations.
x = 6t² + 6,
x = 6(2)² + 6
x = 24 + 6 = 30
y = t³ - 2.
y = (2)³ - 2
y = 8 - 2 = 6
In conclusion, the correct options is (30, 6).
Learn more about slope on:
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Find a formula for a function f that satisfies the following conditions. lim x→±∞ f(x) = 0, lim x→0 f(x) = −∞, f(2) = 0 lim x→7− f(x) = ∞, lim x→7+ f(x) = −∞
9514 1404 393
Answer:
f(x) = (x -2)/(x²(7-x))
Step-by-step explanation:
The horizontal asymptotes of zero mean the denominator degree needs to be greater than the numerator degree. The zero at x=2 means (x-2) will be a factor in the numerator. The limit at x=0 means there will be a factor of x² in the denominator. Since the numerator term is negative at x=0, the signs of the terms so far do not need modification.
The vertical asymptote at x=7 means there will be a factor of (x-7) in the denominator. In order for the limits to be correct, it must have a negative sign:
-(x -7) = (7 -x)
Then the function with these characteristics can be written ...
f(x) = (x -2)/(x²(7 -x))
Approximately how many times greater is
7.4 x 10^8
than
2.5 x 10^7
0.3
3
30
300
Answer:
30
Step-by-step explanation:
To compare the numbers, divide the first number by the second number.
(7.4 x 10^8)/(2.5 x 10^7) = (74 x 10^7)/(2.5 x 10^7) = 74/2.5 = 29.6
Answer: 30
Mila wants to buy a scooter for Rs 62,000 . She has only Rs 19,000 with her, so she decides to take a loan from a bank for the remaining amount. The bank offers Mini three loan schemes as shown below. Mini has to return the loan amount with interest in equal monthly instalments
1) How much money does mila take as loan from the bank?
a) Rs 62,000
b) Rs 44,000
c) Rs 45,000
d) Rs 43,000
Answer:
Scheme a 45000 is the answer
The sum of 3 times a number and 4 is 9.
Answer: x = 5/3
Step-by-step explanation:
Let the number be x
Then
3x + 4 = 9
3x = 9-4
3x = 5
x = 5/3
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Which polynomial expressions are in standard form?
x2 - x - 72
(x + 3)(x - 7)
-8x + 56
05
5x(2x)
Answer:
PLATO ANSWER
Step-by-step explanation:
x2 − x − 72
-8x + 56
5
those are the correct answers
What is the conjugate of 3 + 6i?
A -3 - 61
B 3 - 6i
C 3 + 6i
D 9i
Answer:
C.3-6
Step-by-step explanation:
Every complex number has a complex conjugate.
Examples is a+bi the conjugate is a-bi,if your adding the two conjugate its going to be 2a and if your subtracting the result is 2bi.And if multiplied it is seen as complex number which are a²+b²
evaluate the function f(x)=4x^2-7x+7 find f(7)
please I need the answer soon!
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Answer:
f(7) = 154
Step-by-step explanation:
The basic idea is you put 7 where x is and do the arithmetic.
Polynomial evaluation is sometimes easier if you rewrite it to Horner form.
f(x) = (4x -7)x +7
f(7) = (4·7 -7)(7) +7 = 21(7) +7 = 147 +7
f(7) = 154
Which of the following is an example of a sample that would NOT be random?
A. Going through the list and choosing the first 25 names on the list.
B. Writing each student’s name on a card and then drawing out 25 names without looking.
C. Choosing one student at random from the list and going through the list and choosing every fifth student until she has 25 names.
D. Separating the students on the list into boys and girls and choosing a sample from each group that is proportional to the size of the group.
Answer: D
"Separating the students on the list into boys and girls and choosing a sample from each group that is proportional to the size of the group."
Step-by-step explanation:
You are sampling an equal amount of boys and girls since your getting an equal sample of each gender. (Not random)
The option that is not a random sample is:
Separating the students on the list into boys and girls and choosing a sample from each group that is proportional to the size of the group.
Option D is the correct answer.
What is random sampling?It is the way of choosing a number of required items from a population given.
Each item has an equal probability of being chosen.
We have,
We will see which option is a sample that is not random.
A. Going through the list and choosing the first 25 names on the list.
Going through the list means every name has an equal chance of getting chosen.
This is a random sample.
B. Writing each student’s name on a card and then drawing out 25 names without looking.
Since we are drawing out 25 names without looking, all the students' names have an equal chance of getting drawn.
This is a random sample.
C. Choosing one student at random from the list and going through the list and choosing every fifth student until she has 25 names.
Choosing one student at random means every student has an equal chance of getting chosen.
This is a random sampling.
D. Separating the students on the list into boys and girls and choosing a sample from each group that is proportional to the size of the group.
The students are separated into boys and girls and the sample is chosen from each group so we are selecting the sample from the separated group.
This can not be a random sampling.
Thus,
The option that is not a random sample is:
Separating the students on the list into boys and girls and choosing a sample from each group that is proportional to the size of the group.
Option D is the correct answer.
Learn more about random sampling here:
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The sum of a number and its inverse is 3 29 / 52. Find the number?
Select the correct answer from each drop-down menu. Complete the statement. The solutions of sin2x= √3/2
are : 30 / 120 / 150 / 330
and
45 / 60 / 105 / 135
What are the correct solutions?
Answer:
henc X = 30°
Step-by-step explanation:
here is the proof
when X=30° then
sin2x = sin2×30
=sin 60°
= √3/2
or else,
putting value of X = 30° then
sin2x= 2sinxcosx
= 2×sin30°×cos30°
=2×1/2×√3/2
= 2√3/4
= √3/2
hence proved sin2x= √3/2.
Solve each equation for the given variable
1.3(2x+4)=54
2.4+(5x+5)54
Please
Answer:
1. x = 7
2. 270x+274
Explanation:
see attached filed for step by step reasoning
solve 3/4(2/3m)=24. use the properties of equality first. justify each step.
pls help urgent
Answer:
m = 48
Step-by-step explanation:
3/4(2/3m)=24
Multiply each side by 4/3 using the multiplication property of equality
4/3*3/4(2/3m)=24*4/3
2/3m = 32
Multiply each side by 3/2 using the multiplication property of equality
3/2*2/3m = 32*3/2
m = 48
−5x−9y=3 added to 5x−9y=−2
Answer:
the 5s cancel out the -9s become -18y and 3-2 is 1
Step-by-step explanation:
so -18y=1
Answer From Gauth Math
5. Determine the formula for the following arithmetic sequence: 4, 7, 10, 13, ...
Answer:
[tex]a_{n}[/tex] = n + 3Step-by-step explanation:
Each number increases by 3. Therefore, n+3.
A recipe says to use 2/3 cup milk to make 4/5 serving of pudding. How many cups of milk are in one serving?
Answer:
[tex]\frac56[/tex] cups
Step-by-step explanation:
The serving size is proportional to the amount of milk used, so we have
[tex]\frac{2/3}{4/5}=\frac x1[/tex]
where [tex]x[/tex] is the amount of milk needed for 1 serving. The right side is simply [tex]x[/tex]. We now simplify
[tex]x=\frac23\cdot\frac54=\frac{10}{12}=\frac56[/tex]
Therefore [tex]\frac56[/tex] cups of milk are needed for 1 serving.
The highest attendance at this stadium was in 2007 when 91,547 people attended. The average cost of a ticket was $57. How much money was made on ticket sales for that game?
Answer:57*91547
Step-by-step explanation:
Solve each equation.
1) -133 = 7(-3 + 4v)
Answer:
-4
Step-by-step explanation:
-133 = -21 + 28v
-133 + 21 = 28v
-112 = 28v
v = -4
A rectangular prism has volume 1,088 ft3 and height 8 ft. What is the area of the base of the prism?
a. 146 ft2
c. 136 ft2
b. 1,080 ft2
d. 1,096 ft2
We know
[tex]\boxed{\sf Volume=Area\:of\:Base\times Height}[/tex]
[tex]\\ \sf\longmapsto Area\:of\:Base=\dfrac{Volume}{Height}[/tex]
[tex]\\ \sf\longmapsto Area\:of\:Base=\dfrac{1088}{8}[/tex]
[tex]\\ \sf\longmapsto Area\;of\:base=136ft^2[/tex]
find the measure of the indicated angle
Answer:
Step-by-step explanation:
36°
What is the equation of the line that passes through (4,3) and (2, -1)?
y = 4x -13
y = 6x+4
y = 2x-5
y = 1/2 x -2
Answer:
y=2x-5
Step-by-step explanation:
By using two-points form:
y-y1/y2-y1=x-x1/x2-x1
p(x1,y1)=(4,3)
p(x2,y2)=(2,-1)
Subtitute points in formula:
y-3/-1-3=x-4/2-4
y-3/-4=x-4/-2
y-3/-2=x-4/-1
1(y-3)=2(x-4)
y-3=2x-8
y=2x-8+3
y=2x-5
Note:if you need to ask any question please let me know.
for the vector (-9,3), find 1/2V, -V, and 4V
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Answer:
1/2V = <-9/2, 3/2>-V = <9, -3>4V = <-36, 12>Step-by-step explanation:
The scalar multiplier multiplies each of the components.
1/2V = <-9×1/2, 3×1/2> = <-9/2, 3/2>
-V = <(-9)(-1), (3)(-1)> = <9, -3>
4V = <-9×4, 3×4> = <-36, 12>
PLEASE HELP!! WHOEVER HELPS FIRST AND GETS IT CORRECT GETS BRAILIEST!!
Answer:
16 rotations
Step-by-step explanation:
500/32 = 15.625
15.625 rounded = 16
hope it helps!
Need help answer plz help
Answer:
BONANA MY NANA
Step-by-step explanation:
Which of the following statements accurately describes the period of a trigonometric function?
Answer:
b
Step-by-step explanation:
b is correct.
A) -0.25(O)=-1.753 +2.25
Answer:
If you are trying to find O, then O would be
-1.988
Step-by-step explanation:
First, add -1.754 and 2.25, then divide by -0.25 which results in O=-1.988
Plz help quick quick quick
Step-by-step explanation:
[tex]\angle 3[/tex] and [tex]\angle 16[/tex] are alternate exterior angles so they are equal to each other, which means
[tex]5x - 30 = 3x + 10 \Rightarrow x = 20[/tex]
Solving for the measure of [tex]\angle 16[/tex], we get
[tex]m\angle 16 = 5(20) - 30 = 70°[/tex]
Since [tex]\angle 12[/tex] and [tex]\angle 16[/tex] are supplementary,
[tex]m\angle 12 = 180° - 70° = 110°[/tex]
Answer:
ur image wont load
Step-by-step explanation:
I need help with this question please
Answer:
Step-by-step explanation:
30t - 5t² = 10
5t² - 30t + 10 = 0
t = [30 ± √(30² - 4 ⋅ 5 ⋅ 10)] / [2 ⋅ 5]
= [30 ± √700] / 10
= [30 ± 10√7] / 10
= 3 ± √7
≈ 0.35 seconds and 5.65 seconds
12/1,000 into decimal
0.012 is the answer!
I hope this helps you out! :D
[tex]\\ \sf\longmapsto \dfrac{12}{1000}[/tex]
1000 has 3zeros hence decimal will go 3 points left[tex]\\ \sf\longmapsto 0.012[/tex]
More:-
[tex]\\ \sf\longmapsto \dfrac{1}{10}=0.1[/tex]
[tex]\\ \sf\longmapsto \dfrac{1}{100}=0.01[/tex]
rewrite the following statements into algebraic expression
the sum of x and y
5 is subtracted from y
Devaughn is 6 years older than Sydney. The sum of their ages is 56 . What is Sydney's age?
Answer:
Devaughn = 31, Sydney = 25
Step-by-step explanation:
(56-6)÷2= 25
So they would both be 25 if they were the same age but Devaughn is 6 years older so 25+6=31
ATQ
[tex]\\ \sf\longmapsto x+x+6=56[/tex]
[tex]\\ \sf\longmapsto 2x+6=56[/tex]
[tex]\\ \sf\longmapsto 2x=56-6[/tex]
[tex]\\ \sf\longmapsto 2x=50[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{50}{2}[/tex]
[tex]\\ \sf\longmapsto x=25[/tex]
