Answer:
(a). y'(1)=0 and y'(2) = 3
(b). [tex]$y'(t)=kb2t\cos(bt^2)$[/tex]
(c). [tex]$ b = \frac{\pi}{2} \text{ and}\ k = \frac{3}{2\pi}$[/tex]
Step-by-step explanation:
(a). Let the curve is,
[tex]$y(t)=k \sin (bt^2)$[/tex]
So the stationary point or the critical point of the differential function of a single real variable , f(x) is the value [tex]x_{0}[/tex] which lies in the domain of f where the derivative is 0.
Therefore, y'(1)=0
Also given that the derivative of the function y(t) is 3 at t = 2.
Therefore, y'(2) = 3.
(b).
Given function, [tex]$y(t)=k \sin (bt^2)$[/tex]
Differentiating the above equation with respect to x, we get
[tex]y'(t)=\frac{d}{dt}[k \sin (bt^2)]\\ y'(t)=k\frac{d}{dt}[\sin (bt^2)][/tex]
Applying chain rule,
[tex]y'(t)=k \cos (bt^2)(\frac{d}{dt}[bt^2])\\ y'(t)=k\cos(bt^2)(b2t)\\ y'(t)= kb2t\cos(bt^2)[/tex]
(c).
Finding the exact values of k and b.
As per the above parts in (a) and (b), the initial conditions are
y'(1) = 0 and y'(2) = 3
And the equations were
[tex]$y(t)=k \sin (bt^2)$[/tex]
[tex]$y'(t)=kb2t\cos (bt^2)$[/tex]
Now putting the initial conditions in the equation y'(1)=0
[tex]$kb2(1)\cos(b(1)^2)=0$[/tex]
2kbcos(b) = 0
cos b = 0 (Since, k and b cannot be zero)
[tex]$b=\frac{\pi}{2}$[/tex]
And
y'(2) = 3
[tex]$\therefore kb2(2)\cos [b(2)^2]=3$[/tex]
[tex]$4kb\cos (4b)=3$[/tex]
[tex]$4k(\frac{\pi}{2})\cos(\frac{4 \pi}{2})=3$[/tex]
[tex]$2k\pi\cos 2 \pi=3$[/tex]
[tex]2k\pi(1) = 3$[/tex]
[tex]$k=\frac{3}{2\pi}$[/tex]
[tex]$\therefore b = \frac{\pi}{2} \text{ and}\ k = \frac{3}{2\pi}$[/tex]
The y'(1) =0, y'(2) = 3, and the [tex]\rm y'(t) = kb2t \ cos(bt^2)[/tex] and value of b and k are [tex]\pi/2[/tex] and [tex]3/2\pi[/tex] respectively.
It is given that the curve [tex]\rm y(t) = ksin(bt^2)[/tex]
It is required to find the critical point, first derivative, and smallest value of b.
What is a function?It is defined as a special type of relationship and they have a predefined domain and range according to the function.
We have a curve:
[tex]\rm y(t) = ksin(bt^2)[/tex]
Given that the first critical point of y(t) for positive t occurs at t = 1
First, we have to find the first derivative of the function or curve:
[tex]\rm y'(t) = \frac{d}{dt} (ksin(bt^2))[/tex]
[tex]\rm y'(t) = k\times2bt\times cos(bt^2)[/tex] [ using chain rule]
[tex]\rm y'(t) = kb2t \ cos(bt^2)[/tex]
y(0) = 0
y'(0) = 0
The critical point is the point where the derivative of the function becomes 0 at that point in the domain of a function.
From the critical point y'(1) = 0 ⇒ [tex]\rm kb2 \ cos(b) =0[/tex]
k and b can not be zero
[tex]\rm cos(b) = 0[/tex]
b = [tex]\rm \frac{\pi}{2}[/tex]
and y'(2) =3
[tex]\rm y'(2) = kb2\times 2 \times cos(b\times2^2) =3\\\\\rm 4kb \ cos(4b) =3[/tex](b =[tex]\rm \frac{\pi}{2}[/tex])
[tex]\rm 4k\frac{\pi}{2} \ cos(4\frac{\pi}{2} ) =3\\\\\rm2 \pi kcos(2\pi) = 3[/tex]
[tex]\rm2 \pi k\times1) = 3\\\rm k = \frac{3}{2\pi}[/tex]
Thus, y'(1) =0, y'(2) = 3, and the [tex]\rm y'(t) = kb2t \ cos(bt^2)[/tex] and value of b and k are [tex]\pi/2[/tex] and [tex]3/2\pi[/tex] respectively.
Learn more about the function here:
brainly.com/question/5245372
Last week Betty practiced her guitar for 45 minutes on Monday, 25 minutes on Tuesday, 35 minutes on Wednesday, 20 minutes on Thursday, and 40 minutes on Friday. What was the mean number of minutes that she spent practicing each day?
Answer:
33 minutes
Step-by-step explanation:
To find the mean, you first must add up the values given.
45 + 25 + 35 + 20 + 40 = 165
Now, divide the sum by the number of values you have.
165/5 = 33
The mean number of minutes she spent practicing is 33.
solve systems by substitution method x + y = 12 3x - y = 20
Step-by-step explanation:
x+y=12
3×+y=20
×=12-y
3 (12-y)+y=20
36-3y+y=20
36-4y=20
-4y=20-36
-4y= -16
y =16÷4
y=4
×+y=12
×+4=12
×=12-4
×=8
therefoer;y=4,x=8
Consider a regular pyramid A with a square base and a right circular cone B.
It is given that the length of a side of the square base of pyramid A is the same as the base radius of cone B.
If the two solids have the same volume, which solid will have a greater height? Explain your answer.
Please help me solve this question with steps!orz
Answer:
Pyramid
Step-by-step explanation:
[tex]\text{Volume of a Square Pyramid }=\frac{1}{3} \times l^2 \times Height\\\\ \text{Volume of a Cone }=\frac{1}{3} \pi r^2 \times Height[/tex]
Given that the two solids have the same volume
[tex]\frac{1}{3} \times l^2 \times Height=\frac{1}{3} \pi r^2 \times Height[/tex]
If the length of a side of the square base of pyramid A is the same as the base radius of cone B. i.e l=r
[tex]\frac{1}{3} \times l^2 \times $Height of Pyramid=$\frac{1}{3} \pi l^2 \times $Height of cone$\\\\$Cancel out $ \frac{1}{3} \times l^2$ on both sides\\\\Height of Pyramid= \pi \times $ Height of cone$[/tex]
If the height of the cone is 1
[tex]H$eight of Pyramid= \pi \times 1 \approx 3.14$ units[/tex]
Therefore, the pyramid has a greater height.
Find the value of each trigonometric ratio.
Will give brainliest
Answer:
3.36:45=0,8
4.40:32=1,25
536:45=0,8
6.48:50=0,96
Hope it helps and likes it
Step-by-step explanation:
3- sin Z = opp/hyp
sin Z = 27/45
Z = sin-¹(27/45)
Z = 37
4- tan C = opp/adjacent
tanC = 24/32
C = tan -¹ ( 24/32)
C = 36.87 ( or 37)
5- cos X = adj/hyp
cos X= 36/45
X = cos-¹ (36/45)
X = 37
6- sin C = opp/hyp
sin C = 14/48
C = sin -¹ (14/48)
C= 17 (or 16.96)
HELP MAJOR ASSIGNMENT PLEASE HELP pls?
Answer:
1: V:56.52 SA:94.2 Ratio: 3:5
2: V:113.04 SA:62.8 Ratio: 9:5
3: V:113.04 SA:138.16 Ratio: 9:11
4: V:113.04 SA:131.88 Ratio: 6:7
Step-by-step explanation:
Hey there!
By using the following formula for volume of a cylinder I got,
[tex](3.14) r^2h[/tex]
1: 56.52
2: 113.04
3: 113.04
4: 113.04
Now to find SA we'll use the following formula,
1: 94.2
2: 62.8
3: 138.16
4: 131.88
Now for the ratio,
56.52:94.2 - 3:5
113.04:62.8 - 9:5
113.04:138.16 - 9:11
113.04:131.88 - 6:7
Hope this helps :)
does the table represent a function why or why not?
Answer:
Yes, because each x-value corresponds to one y value.
Step-by-step explanation:
If you look at the table, you notice that there is one output (y) for every input (x). This means that it is a function. It would NOT be a function if you had two outputs for an input. For example, there are two x values that are 6. For one coordinate pair, the table says (6,9) and (6,8). Since there are two values for the same input- it wouldn't be a function. In this case, there is an input of 4 and 5 with the same output. That is okay! Even though they have the same y value, those inputs still only have ONE output.
-2x(x+3)-(x+1)(x-2) please help me solve this
Answer:
u have to multiply these.
it's too easy .
see I will tell you the answer.
-2x²-6x-(x²-2x+x-2)
Now the signs of the underlined terms will change because negative sign is outside it.
-2x²-6x-x²+ 2x-x + 2
Now we have to solve it simply
-2x²-x²-6x+ 2x-x + 2
-3x²-5x+2
so here is ur answer.
for Indians it is soo simple question bro
I am Indian
if u need any help plz let me know.
0.719 to the nearest hundredth
Answer:
.72
Step-by-step explanation:
9 rounds up because 1-4 stay the same and 5-9 round up
Answer: 0.719 to the nearest hundredth is 0.72
x and x+1 are the two continuous natural numbers, then (i) Write the next two natural numbers. (ii) Find the product of first and the fourth number. (iii) Find the product of second and the third number. (iv) Find the relation between these products.
Answer:
(i) X+2 and x+3;
(ii) x( x+4)= X^2 +4x;
(iii) x( x+4)=a
(x+1)(x+3)= a+3
Step-by-step explanation:
(i) X+2 and x+3;
(ii) x( x+4)= X^2 +4x;
(iii) (x+1)(x+3)=x^2+3X+X+3=x^2+4x+3;
x(x+4)=a
(x+1)(x+3)= a+3
Step-by-step explanation:
x is followed by x+1 so each time we add one
our sequence goes like this:
xx+1 x+1+1⇒ x+2 x+2+1⇒x+3the first number is x and the fourth one is x+3
x*(x+3) x²+3xthe second number is x+1 and the third one is x+2
(x+1)(x+2)x²+2x+x+2 x²+3x+2the first product is x²+3x and the second one is x²+3x+2
Let P be x²+3x and P' be x²+3x+2
P'-P = 2P' = P+2Suppose a company needs temporary passwords for the trial of a new time management software. Each password will have one digit, followed by one letter, followed by two digits. The digit 7 will not be used. So, there are 26 letters and 9 digits that will be used. Assume that the digits can be repeated. How many passwords can be created using this format?
Answer: 18954
Step-by-step explanation:
The given format for password : Each password will have one digit, followed by one letter, followed by two digits. The digit 7 will not be used. So, there are 26 letters and 9 digits that will be used.
We assume that the digits can be repeated.
Then by using fundamental principle of counting,
Number of passwords can be created = (Number of digits) x (Number of letters) x (Number of digits)x(Number of digits)
= 9 x 26 x 9 x 9
= 18954
Hence, Number of passwords can be created= 18954
One of these is not an aquatic swimming A. canoeing B. shooting C. swimming D. diving
The answer is B. Shooting. Shooting is a sport on dry land, while the other three are aquatic sports, that is, they are on or in the water.
Which of these is the absolute value parent function?
O A f(x) = 12x1
O B. f(x) = (x + 1
O c. f(x) = [xl - 2
O D. f(x) = [X]
Answer:
D. f(x) = |x|
Step-by-step explanation:
The absolute value parent function has nothing added or subtracted or multiplied. It is simply ...
f(x) = |x|
Simplify
[tex]\ \textless \ br /\ \textgreater \ \sqrt[4]{16a^- 12}\ \textless \ br /\ \textgreater \ [/tex]
Answer:
[tex]\huge\boxed{\sqrt[4]{16a^{-12}}=2a^{-3}=\dfrac{2}{a^3}}[/tex]
Step-by-step explanation:
[tex]16=2^4\\\\a^{-12}=a^{(-3)(4)}=\left(a^{-3}\right)^4\qquad\text{used}\ (a^n)^m=a^{nm}\\\\\sqrt[4]{16a^{-12}}=\bigg(16a^{-12}\bigg)^\frac{1}{4}\qquad\text{used}\ a^\frac{1}{n}=\sqrt[n]{a}\\\\=\bigg(2^4(a^{-3})^4\bigg)^\frac{1}{4}\qquad\text{use}\ (ab)^n=a^nb^n\\\\=\bigg(2^4\bigg)^\frac{1}{4}\bigg[(a^{-3})^4\bigg]^\frac{1}{4}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=2^{(4)(\frac{1}{4})}(a^{-3})^{(4)(\frac{1}{4})}=2^1(a^{-3})^1=2a^{-3}\qquad\text{use}\ a^{-n}=\dfrac{1}{a^n}[/tex]
[tex]=2\left(\dfrac{1}{a^3}\right)=\dfrac{2}{a^3}[/tex]
À television ser costs $350 cash. When
bought on hire purchase, a deposit of $35 is
required, followed by 12 monthly payments
of $30. How much is saved by paying cash
Answer:
$45.
Step-by-step explanation:
When the TV is bought on hire purchase, you deposit $35 and pay $30 monthly. There are 12 payments. 12 * 30 = $360. 360 + 35 = $395.
Since cash would've cost $350, the amount of money saved by paying cash is 395 - 350 = $45.
Hope this helps!
What is the y-intercept of the function y=4-5x?
Answer:
4
Step-by-step explanation:
y=mx+b
b=y-intercept.
In this case...
mx=-5<-- this is the slope of the line.
b=4<-- y intercept.
Hope this helps, any further questions, please feel free to ask.
suppose that consumer usage time of computers in the public library is uniformly distributed with a minimum of 20 minutes and a maximum of 80 minutes. what is the standard deviation of the distribution
Answer:
17.32 minutes
Step-by-step explanation:
The standard deviation for a uniform distribution is:
[tex]\sigma =\frac{b-a}{\sqrt12}[/tex]
If a = 20 minutes and b = 80 minutes, the standard deviation is:
[tex]\sigma =\frac{80-20}{\sqrt12} \\\sigma=17.32\ minutes[/tex]
The standard deviation of the distribution of consumer usage time of computers in the public library is 17.32 minutes.
248 miles per hour = x meters per second. Round to the nearest hundredth.
Answer:
110.87 m/sStep-by-step explanation:
This problem is based on unit conversion from miles per hour to meter per second.'
From tables 1 mph= 0.44704 m/s
Given 248 mph to be converted to meters per second.
hence we have
1 mph= 0.44704 m/s
248 mph= x
cross multiplying we have
x= 110.86592 m/s
to the nearest hundreth we have
110.87 m/sPlease help, ty if you do
Answer:
C
Step-by-step explanation:
4,800 times 7% is 336, and 1200 times 14% is 168, and 168 is half as much as 336, so the correct answer is c
Answer:
C
Step-by-step explanation:
Multiply .7 to 6000 and solve
the square root of 5 is
Step-by-step explanation:
The square root of 5 can be approximately found by doing the square root of 4 to get 2, and the square root of 9 to get 3. Then, because 5 is closer to 4 than 9, the square root of 5 is about 2.2.
Otherwise, simply do sqrt(5) in a calculator to get 2.23606798
Hope it helps <3
NEEEED HELPPPPP PLEASEEEEEE Use long division to find the quotient below.
(8x^2 + 4x^2 + 100) - (2x + 5)
Answer:
[tex]4x^2 - 8x + 20[/tex]
Step-by-step explanation:
The correct equation is:
[tex]8x^3 + 4x^2 + 100[/tex]
We want to divide that by (2x + 5)
To do the long division, divide each term by 2x and then subtract the product of the result and (2x + 5) from the remaining part of the equation.
When you get to 0, you have reached the end of the division.
Whatever term you get from each step of division is part of the quotient.
Go over the steps above carefully while following them below:
Step 1:
Divide [tex]8x^3[/tex] by 2x. You get [tex]4x^2[/tex].
Step 2
Multiply [tex]4x^2[/tex] by (2x + 5) and subtract from [tex]8x^3 + 4x^2 + 100[/tex]:
[tex]8x^3 + 4x^2 + 100[/tex] - ([tex]8x^3 + 20x^2[/tex]) = [tex]-16x^2 + 100[/tex]
Step 3
Divide [tex]-16x^2[/tex] by 2x. You get [tex]-8x[/tex].
Step 4
Multiply -8x by (2x + 5) and subtract from [tex]-16x^2 + 100[/tex]:
[tex]-16x^2 + 100[/tex] - ([tex]-16x^2 - 40x[/tex]) = 40x + 100
Step 5
Divide 40x by 2x. You get 20.
Step 6
Multiply 20 by (2x + 5) and subtract from 40x + 100:
40x + 100 - (40x + 100) = 0
From the three steps of the division, we got [tex]4x^2[/tex], -8x and 20.
Therefore, the quotient is [tex]4x^2 - 8x + 20[/tex]
The table shows the number of flowers in four bouquets and the total cost of each bouquet. A 2-column table with 4 rows. The first column is labeled number of flowers in the bouquet with entries 8, 12, 6, 20. The second column is labeled total cost (in dollars) with entries 12, 40, 15, 20. What is the correlation coefficient for the data in the table? –0.57 –0.28 0.28 0.57
Answer:
The correct option is;
0.28
Step-by-step explanation:
The given data values are;
x, f(x)
8, 12
12, 40
6, 15
20, 20
Where;
x = The number of flowers in the bouquet
f(x) = The total cost (in dollars)
The equation for linear regression is of the form, Y = a + bX
The formula for the intercept, a, and the slope, b, are;
[tex]b = \dfrac{N\sum XY - \left (\sum X \right )\left (\sum Y \right )}{N\sum X^{2} - \left (\sum X \right )^{2}}[/tex]
[tex]a = \dfrac{\sum Y - b\sum X}{N}[/tex]
Where:
N = 4
∑XY = 1066
∑X = 46
∑Y = 87
∑X² = 644
(∑X)² = 2116
b = (4*1066 - 46*87)/(4*644 - 2116) = 0.5696
a = (87 - 0.5696*46)/4 = 15.1996
The standard deviation of the x- values
[tex]S_X = \sqrt{\dfrac{\sum (x_i - \mu)^2}{N} }[/tex]
[tex]\sum (x_i - \mu)^2}[/tex] = 115
N = 4
Sx =√(115/4)
Sx = 5.36
[tex]S_Y = \sqrt{\dfrac{\sum (y_i - \mu_y)^2}{N} }[/tex]
[tex]\sum (y_i - \mu_y)^2}[/tex] = 476.75
N = 4
Sy =√(476.75/4)
Sy= 10.92
b = r × Sy/Sx
Where:
r = The correlation coefficient
r = b × Sx/Sy = 0.5696*5.36/10.92 = 0.2796 ≈ 0.28
The correct option is 0.28.
Answer:
C on edge
Step-by-step explanation:
g(x)=5-2x what is domain
Answer:
all real numbers
Step-by-step explanation:
The domain of any polynomial function is "all real numbers."
please solve it 100 POINTS please help- PLEASE HELP its Identify the following for the quadratic relations please slove it all please if you can save the picture and do it on the page
Answer:
[tex]\boxed{\mathrm{view \: attachments}}[/tex]
Step-by-step explanation:
Vertex is the highest or lowest point of a parabola.
Axis of symmetry is the line that cuts the parabola in half.
y-intercept is the point where the parabola touches the y-axis.
The maximum or minimum values are the highest or lowest values the parabola can reach.
x-intercepts are the points where the parabola touches the x-axis.
Why the order of a succession is important
Answer:
Step-by-step explanation:
The order of a succession is a way that the terms (the first, the second, the third, etc.) can be distinguished according to a certain formation law or order criterion.
Example:
a¹/a²/a³/a⁴ And successively
In the order of a sequence you can assign any letter.
can someone help me with this?
Answer:
-5z^3-z^4+4z^5
which measure is of an angle that is conterminal with a 95 degree angle
Answer: Choice B
95 - 1080n for any integer n
=================================================
Explanation:
Notice how 1080 is a multiple of 360 since 360*3 = 1080. The other values 1450, 780 and 340 are not multiples of 360. For example 1450/360 = 4.02777 approximately. We need a whole number result to show it is a multiple.
Therefore, choice B shows subtracting off a multiple of 360 from the original angle 95. In my opinion, it would be better to write 95+360n or 95-360n to make it more clear we are adding or subtracting multiples of 360.
Choice B will find coterminal angles, but there will be missing gaps. One missing coterminal angle is 95-360 = -265 degrees. So again, 95-360n is a more complete picture. I can see what your teacher is going for though.
A chef uses 12 cup of cheese for a small pizza. There are 6 grams of fat in 14 cup of cheese. Drag one expression next to each question. The correct expression for each row is a way to answer that question.
Answer:
I guess that we want to find how many grams of fat we have in a small pizza.
In a small pizza, we use 12 cups of cheese.
in 14 cups of cheese, we have 6 grams of fat.
Then, in 12 cups of cheese, we have x grams of fat.
We want to find the value of x.
We know that the ratio between the number of cups must be the same as the ratio between the grams of fat then:
12cups/14cups = x/6grams
x = (12/14)*6grams = 5.14 grams
Then in the 12 cups of cheese, we have 5.14 grams of fat.
1. A box without a top is to be made from a rectangular piece of cardboard, with dimensions 8 in. by 10 in., by cutting out square corners with side length x and folding up the sides. (a) Write an equation for the volume V of the box in terms of x. (b) Use technology to estimate the value of x, to the nearest tenth, that gives the greatest volume. Explain your process.
Step-by-step explanation:
The dimensions are (8-2x) and (10-2x) We will say the depth of the box is x. The equation we use for the volume of the box is V=x(8-2x)(10-2x)
Answer:
part b of the answer is x=1.5 inches
Step-by-step explanation:
The area of the rectangle below is __sq. units.
5
16
Answer:
C.
Step-by-step explanation:
To find the area of a rectangle, times the length and the breadth together. So, it would be 16×5=80. option C is 80.
Answer:
80 sq.units
Step-by-step explanation:
A of rectangle = L×B
L= 16 units
B=5 units
A of rectangle = L×B
=16×5 units
=80 sq.units
The side length of each square is 6 units. Find the areas of the inscribed shapes.
Answer:
a) 18
b) 20
c) 12
d) 12
Step-by-step explanation:
a) The triangle is half of the square, so you can find the area of the square(36) and divide by 2: so 18
b) There are 4 same sized blank triangles with area of 4 ( (2*4)/2 ) so 4 * 4 is 16. 16 is the blank area so the area of the shaded is 36 - 16: 20
c) There are 2 blank triangles which areas are 6, and 18, so you subtract those numbers from 36: 36 - (6+18) = 12
d) Another 2 same blank triangles with areas of 12 ( (6 *4)/2 )so you subtract them from 36 too: 36 - (12*2) = 36 - 24 = 12