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]
Jenny is in charge of ordering T-shirts for the math club at her school. If she paid $322 for 23 T-shirts, which of the following statements are true?
A. Jenny paid $322 for 23 T-shirts, which is a rate of $37 per T-shirt.
B. Jenny paid $322 for 23 T-shirts, which is a rate of $14 per T-shirt.
C. Jenny paid $322 for 23 T-shirts, which is a rate of $299 per T-shirt.
D. Jenny paid $322 for 23 T-shirts, which is a rate of $23 per T-shirt.
Answer:
B. Jenny paid $322 for 23 T-shirts, which is a rate of $14 per T-shirt.
Step-by-step explanation:
To find the rate per shirt, divide the cost by the number of shirts:
322/14
= 14
So, she paid $322 at a rate of $14 per shirt.
Therefore, B is correct.
Can someone please help me with 4+5 and 6 pleaseeeee
Answer:
Answer to (4+5): (0,0)
Answer to 6: 0
Step-by-step explanation:
(4+5 Explanation):
We can start to imagine the graph of [tex]y=|x|[/tex] in our head.
If we have a positive value of x, then y will be equal to x.
If we have a negative value of x, then y will be the opposite of x (since the absolute value of a negative is a positive).
This means that the graph will look a bit like this, changing at the point (0,0).
\/, it would look like a downward facing arrow. This means the vertex is at (0,0).
6 Explanation:
If we know the value of [tex]w[/tex], we can substitute it into the expression [tex]2w+w-15[/tex] as 5.
[tex]2(5) + 5 - 15\\\\10 + 5 - 15\\\\15-15\\\\0[/tex]
Hope this helped!
Answer:
6: 3w-15
Step-by-step explanation:
you can put all the W's together and just add the -15 at the end.
how do I get the correct answer?
Answer:
1989.674m³
Step-by-step explanation:
It’s difficult to see the picture, and I can’t read the question. Are you looking for the volume of the composite shape? If so:
Cylinder: V=[tex]\pi[/tex]r²h =
Cone: V=[tex]\pi[/tex]r²h/3 =
Hemisphere: V=2/3[tex]\pi[/tex]r³ = 2/3
TOTAL: 1570.796+157.079+261.799=1989.674m³
The dimension of the rectangle prism show are given in centimeters 4 cm 3 cm 1.4 cm what is the volume of the rectangular prism in the cubic centimeter
Answer:
16.8 cubic centimeter
Step-by-step explanation:
Dimensions of rectangular prism are:
[tex]4\ cm, 3\ cm , 1.4\ cm[/tex]
To find:
The volume of rectangular prism in cubic cm ?
Solution:
The formula for volume of prism is given as:
[tex]V=l\times w\times h[/tex]
Where [tex]l[/tex] is the length of rectangular prism
[tex]w[/tex] is the width of rectangular prism
[tex]h[/tex] is the height of rectangular prism
Here we are given the three dimensions of prism as:
Length, [tex]l[/tex] = 4 cm
Width, [tex]w[/tex] = 3 cm
Height, [tex]h[/tex] = 1.4 cm
Putting the values in formula for volume:
[tex]V=4\times 3\times 1.4\\\Rightarrow \bold{V =16.8\ cm^3}[/tex]
So, volume is 16.8 cubic centimeter.
Answer:
16.8
Step-by-step explanation
(4 cm times 3 cm) = 12 cm times 1.4 = 16.8
hope i got it correct :)
Complete the following statement. Write your answer as a decimal or whole number
% of $96 = $72
Answer:
75%
Step-by-step explanation:
let the unknown percent be x.
[tex]\frac{x}{100}*96=72\\\frac{96x}{100}=72\\ 96x=72*100\\96x=7200\\\frac{96x}{96}=\frac{7200}{96}\\ x=75%[/tex]
Answer:
Step-by-step explanation:
x/100 * 96 = 72
96x = 7200
x = 75
1. Select all the triangles that can be rotated to match up with Triangle 1. Triangle 1 A B D C С
Answer:it should be B and D
Step-by-step explanation:
B could be rotated clockwise and D could be rotated clockwise as well.
6. Give an example of an irrational number that is greater than 10.
Hi can someone please,please,please help me
Answer:
29. 3
30. 11
31. 4
32. 124˚
so I am in algebra 1 and I need help with A+B=C but it says solve for A and I wanted to see if you can show how to do it for more questions in the future
Answer:
A = C-B
Step-by-step explanation:
A+B=C
Subtract B from each side
A+B-B=C-B
A = C-B
what is 624/1000 in lowest terms
Answer:
Hey there!
624/1000=78/125.
We can get this by dividing the numerator and denominator by 8.
Hope this helps :)
The half-life of carbon-14 is 5600 years. If a piece of charcoal made from the wood of a tree shows only 72% of the carbon-14 expected in living matter, when did the tree die?
Answer:
t =2654.01465 year
Step-by-step explanation:
Given that the half-life of carbon-14 is 5600 years and if a piece of charcoal made from the wood of a tree shows only 72% of the carbon-14 expected in living matter.
we know
[tex]y=a(b)^{t/h}[/tex]
where y= final amount
a= initial amount
b= growth/decay
t= time elapsed
h= half time
plugging the values we get
[tex]0.72 =(\frac{1}{2})^{t/5600}\\[/tex]
taking log on both side
log 0.72 = t/5600 log(1/2)
solving we get t =2654.01465 year
Solve each system of inequalties by graphing.
y< 3x+2
y<_-2x+1
↑ the second equation is y smaller than or equal to but i wont let me type that so :) PLZ help! ty!!♡
Start by graphing each line.
• Because the first inequality is smaller than, it will have a dotted (- - -) line.
• Because the second inequality is smaller than or equal to, it will have a solid line (---).
Then, plug in points to see where your shading will go. If the statement is true (x = x), you will shade that area along the line.
[tex]y < 3x + 2[/tex]
[tex](0) < 3(0) + 2[/tex]
[tex]0 < 2[/tex]
0 is less than 2.
Do the same step for the other equation. Your solution to the problem is any point that lies between the shading from both inequalities (where the blue and red meet).
convert 56 inches to centimeters pleaseee show steps
Answer:
142.24 centimeters
Step-by-step explanation:
To convert from inches to centimeters, you multiply the inches value by 2.54 and that will give you its equivalent in centimeters.
56 * 2.54 = 142.24
Please mark brainliest and hope this helped.
3k - 2c + 8
use k = 7 and c = 4
Answer:
21
Step-by-step explanation:
3 (7) - 2(4) + 8
21 - 8 + 8
13 + 8
21
Answer:
21
Step-by-step explanation:
3k - 2c + 8
k = 7 and c = 4
Substitute the values of k and c in the algebraic expression
3(7) - 2(4) + 8 = 21 - 8 + 8 = 21
Bernard's bird feeder holds 4 1/2 cups of birdseed. Bernard is filling the bird feeder with a scoop that holds 9/10 of a cup. How many scoops of birdseed will Bernard put into the feeder? Write your answer as a fraction or as a whole or mixed number.
Answer:
5 scoops
Step-by-step explanation:
Given
[tex]Feeder = 4\frac{1}{2}[/tex]
[tex]Scoop = \frac{9}{10}[/tex]
Required
Determine the number of scoop in a feeder
To do this, we simply divide the size of the feeder by the size of the scoop as follows;
[tex]Number = \frac{Feeder}{Scoop}[/tex]
[tex]Number = 4\frac{1}{2}/\frac{9}{10}[/tex]
Convert Fractions to improper
[tex]Number = \frac{9}{2}/\frac{9}{10}[/tex]
[tex]Number = \frac{9}{2}*\frac{10}{9}[/tex]
[tex]Number = \frac{9 * 10}{2 * 9}[/tex]
[tex]Number = \frac{90}{18}[/tex]
[tex]Number = 5[/tex]
Hence, there are 5 scoops in a feeder
Select all of the following scenarios below that contain nonbiased samples.
Select all that apply:
✓ To estimate the political party distribution of residents in his state, Frank collects data from a large group of
randomly selected residents of his city.
✓ To estimate the mean number of classes that students take at his university, Samuel collects data from a
randomly selected proportionate number of students from each grade level.
David wants to estimate the mean grade point average of students at his school. He collects data by recording the
grade point average of every 25th student on the list of students after a randomly selected first student
Helen wants to estimate the male to female ratio of the residents of her city. She collects data by recording the sex
of every 50th resident after selecting a random starting point on a list of residents,
Answer:
b.) To estimate the mean number of classes that students take at his university, Samuel collects data from a randomly selected proportionate number of students from each grade level.
c.) David wants to estimate the mean grade point average of students at his school. He collects data by recording the grade point average of every 25th student on the list of students after a randomly selected first student.
d.) Helen wants to estimate the male to female ratio of the residents of her city. She collects data by recording the sex of every 50th resident after selecting a random starting point on a list of residents.
Why? Because a sample is only biased if some individuals of the population are more or less likely to be chosen than others.
The sample from choice B isn't biased because every student has the same opportunity of being selected. It's the same predicament with choice C; it's also non-biased because again, each student has a chance of being in it, there is no preference.
And finally, the sample from option D is non-biased, because every resident that is being selected has an equally fair chance of being selected at random.
Hope this helps ;)
Answer:
Step-by-step explanation:
To estimate the mean number of classes that students take at his university, Samuel collects data from a randomly selected proportionate number of students from each grade level.
David wants to estimate the mean grade point average of students at his school. He collects data by recording the grade point average of every 25th student on the list of students after a randomly selecting first student.
Helen wants to estimate the male to female ratio of the residents of her city. She collects data by recording the sex of every 50th resident after selecting a random starting point on a list of residents.
188= 45 - v = please help solve for v
Answer:
v=-143
Step-by-step explanation:
45-v=188
-v=188-45
-v=143
v=-143
Answer:
Step-by-step explanation:
45 - v = 188
-v = 188 - 45
-v = 143
v = -143
Simplify 12 to the 16th power over 12 to the 4th power.
Answer:
12 power 12
Step-by-step explanation:
Since the have the same base 16-4=12
So its 12 to the twelfth power
Answer:
12 Power of 12
Step-by-step explanation:
i forgor
Help please inverse / direct variations problem
Answer:
y = 30
Step-by-step explanation:
y ∝ 1/x
y = k/x → y = 60/x
12 = k/5 y = 60/2
60 = k y = 30
I hope this helped you :)
Simplify each of the following:
2
1. (3+4i ) + ( 19 - 5i)
I hope this helps you
(3+19)+(4i-5i)
22-i
Find the mean distance (○｀ 3′○)
Answer:
189.571428571 miles or km
Step-by-step explanation:
Just deduct the last odometer reading with the first one and divide by the number of days,
(11,477-10,150)/7 = 189.571428571
The problem has been started for you. 670 StartLongDivisionSymbol 2345.0 EndLongDivisionSymbol minus 2010 to get a remainder of 3350 and a quotient of 3.blank.
Answer:
The answer is 3.5
Step-by-step explanation:
I just got it right on the instruction.
The graph shows Ms. Collin's driving speed during 10 minutes of her commute. Driving Speed 70 60+ 50 40 Speed (miles per hour) 30 20 10 0 1 2 9 10 3 4 5 6 7 8 Time (minutes) Between which times did Ms. Collin drive at a constant speed? A. O and 2 minutes B. 2 and 4 minutes O c. 4 and 6 minutes D. 6 and 8 minutes
Answer:
B. 2 and 4 minutes
Step-by-step explanation:
Between 2 and 4 minutes on the graph on the x axis, Ms Collin's driving speed was 50 m/h
PLEASE HELP! 20 question
Answer:
C
Step-by-step explanation:
So we have the following sequence:
-7, -3, 1, 5...
As given, the (direct) formula for any arithmetic sequence is:
[tex]a_n=a_1+d(n-1)[/tex]
Where aₙ is the value of the nth term, a₁ is the value of the first term, and d is the common difference.
From the sequence, we can see that the initial/first term is -7. Thus, a₁ is -7.
And we can see that each subsequent number if 4 greater than the previous one. Thus, the common difference is +4.
Therefore, plugging these into our equation, we have:
[tex]a_n=-7+4(n-1)[/tex]
The answer is C.
Need help pls help if u can
what is the answer to the following question choices: 1)9 2)0 3)2/3 4)3
I hope this helps you...
1 point
A video game tournament, in which gamers compete in multiple games
and accumulate an overall score, pays the top 20 finishers. First place
receives $5000, second place receives $4800, third place receives $4600
and so on until the 20th finisher receive $1200 and then no more prize
money is awarded. How much total prize money is awarded? *
Answer:
$62,000
Step-by-step explanation:
There are 20 people.
You have to add $5000 and $1200, which equals $6,200.
You have to multiply that by 10 to get the answer.
Krysten is having some friends over and is buying some drinks. She buys a 4 pack of canned sodas for $12.00. What is the unit rate for the soda in can?
Answer:
3 dollars per can
Step-by-step explanation:
12/4
12 divided by 4=3
4 divided by 4=1
3/1=3
Evaluate the following function for f(x)=−3 f(x)=2x+5
Answer:
x = -4
Step-by-step explanation:
Step 1: Write out given
f(x) = -3
f(x) = 2x + 5
Step 2: Substitute f(x)
-3 = 2x + 5
Step 3: Solve for x
-3 - 5 = 2x + 5 - 5
-8 = 2x
-8/2 = 2x/2
-4 = x
Answer:
x = - 4Step-by-step explanation:
f(x)=2x+5
To find f(x)=−3 equate f(x) to - 3 and evaluate
That's
2x + 5 = - 3
Subtract 5 from both sides
That's
2x + 5 - 5 = - 3 - 5
2x = - 8
Divide both sides by 2
[tex] \frac{2x}{2} = - \frac{8}{2} [/tex]
We have the final answer as
x = - 4Hope this helps you
8x + 2 + 4y; x = 9, y = 2
Answer:
82
Step-by-step explanation:
plug in and multiply
Answer:
Step-by-step explanation:
8x + 2 + 4y
Let x = 9 and y = 2
8*9 + 2 + 4*2
72 + 2+ 8
82