Answer:
[tex]\frac{dy}{dx} =-\sqrt[3]{\frac{y}{x} }[/tex]
Step-by-step explanation:
Recall that using the chain rule we can state:
[tex]\frac{dy}{dt} =\frac{dy}{dx}*\frac{dx}{dt}[/tex]
and therefore solve for dy/dx as long as dx/dt is different from zero.
Then we find dy/dt and dx/dt,
Given that
[tex]x=sin^3(t)\\dx/dt = 3 sin^2(t)* cos(t)[/tex]
And similarly:
[tex]y=cos^3(t)\\dy/dt=-3\,cos^2(t)*sin(t)[/tex]
Therefore, dy/dx can be determined by the quotient of the expressions we just found:
[tex]\frac{dy}{dx} =\frac{dy/dt}{dx/dt} =\frac{-3\,cos^2(t)*sin(t)}{3\,sin^2(t)*cos(t)} =-\frac{cos(t)}{sin(t)}[/tex]
now notice that we can find [tex]cos(t) = \sqrt[3]{y}[/tex] from the expression for y,
and [tex]sin(t) = \sqrt[3]{x}[/tex] from its expression for x.
Therefore dy/dx can be written in terms of x and y as:
[tex]\frac{dy}{dx} =-\frac{cos(t)}{sin(t)}=-\sqrt[3]{\frac{y}{x} }[/tex]
What is the value of the function at x=−2?
Answer:
y = 3
General Formulas and Concepts:
Reading a Cartesian PlaneReading and labeling coordinatesStep-by-step explanation:
The question is asking us what the y-value is when x = -2.
According to the graph, when x = -2, y = 3.
Therefore, y = 3.
The price of one share of a stock fell 4 dollars each day for 8 days. How much value did one share of the stock lose after 8 days?
Answer:
After 8 days, the stock lost 32 dollars.
Step-by-step explanation:
If 4 dollars fell every day for 8 days, it would be 32 dollars because 4*8 is 32.
Find all solutions to the system:
5x-3y=2,
15x+6y=6
Answer:
2/5 0
Step-by-step explanation:
HELP PLEASE IM BEGGING YOU
Which equation is a point slope form equation for line AB?
Oy-3=2(x - 2)
Oy-6=2(x - 5)
Oy-5=2(x - 6)
Oy+2=2(x+3)
Answer:
y-6=2(x-5)
I hope this is good enough:
Find the amount that results from investing $5000 at 3% compounded continuously for 5 years. Round your
answer to two decimal places.
Answer:
The amount that results from investing $5000 at 3% compounded continuously for 5 years is $5800
Step-by-step explanation:
We are given:
Principal Amount (P) = $5000
Years (t) = 5
Rate (r) = 3% or 0.03
We need to find New Amount (A)
The formula used is: [tex]A=P(1+\frac{r}{n})^{nt}[/tex]
Since amount is compounded continuously so n=1
Putting values and finding A
[tex]A=P(1+\frac{r}{n})^{nt}\\A=5000(1+\frac{0.03}{1})^{1*5}\\A=5000(1+0.03)^5\\A=5000(1.03)^5\\A=5000(1.16)\\A=5800[/tex]
So, New Amount (A) = $5800
The amount that results from investing $5000 at 3% compounded continuously for 5 years is $5800
168 students enrolled in a freshman-level chemistry class. By the end of the semester, 5 times the number of students passed as failed. Find the number of students who passed.
Answer:
33.6
Step-by-step explanation:
Find the general solution of the given system. Use a computer system or graphing calculator to construct a direction field and typical solution curves for the system
Answer:
hello your question is incomplete attached below is the complete question and solution
answer : general solution ( X ) = [tex]C_{1} e^{3t} \left \{ {{1} \atop {-1}} \right. + C_{2} e^{3t} \left \{ {{1} \atop {-1}} \right.[/tex]
Step-by-step explanation:
attached below is the detailed solution to determine the general solution of the given system
general solution ( X ) = [tex]C_{1} e^{3t} \left \{ {{1} \atop {-1}} \right. + C_{2} e^{3t} \left \{ {{1} \atop {-1}} \right.[/tex]
Please help me with this.
Answer:
-4 ≤ x ≤ 4
Step-by-step explanation:
The domain is essentially the range of values x can take. In the figure, the highest value is 4 and the lowest is -4.
1. Solve 2x < 10. Explain how to find the solution set. I need help with this question.
Which of the following equations could be used to solve the given equation?
9x + 26 + 7x - 17 = 2x + (-3x) + 5x
16x + 9 = 4x
16x + 11 = 4x
16x + 9 = 0
Answer:
16x + 9 = 4x
Step-by-step explanation:
9x+7x+26-17=2x-3x+5x
16x+9=4x
can someone help me plsssss :( 20 ᴘᴏɪɴᴛs !
a.) m = -1
b.) m = 0
c.) m = undefined
d.) m = 1/2
Answer (bolded part is slope):
a.) y = -x + 2 (slope = -1)
b.) y = -2 (slope = 0)
c.) x = 3 (slope = undefined)
d.) y = [tex]\frac{2}{3}[/tex]x + [tex]\frac{3}{2}[/tex] (slope = 2/3)
What is the base in the expression 4 superscript 5?
A)4 B)5 C)9 D)20
Answer:
A)4
Step-by-step explanation:
Expression 4 superscript pt 5=4^5
Answer:
A
Step-by-step explanation:
HELP PLS A carnival charges $2.50 per ride after an entrance fee.You paid a total of $22.50 after 6 rides.Find the total cost for 15 rides.
Simplify (6x ^ 2 + 11x - 3) + (2x ^ 2 - 17x - 4) . (1 point)
1 ) 8x ^ 2 + 6x - 1
2) 8x ^ 2 - 6x - 7
3 ) 8x ^ 2 + 6x + 1
4 ) 8x ^ 2 - 6x + 7
Answer:
2) 8x^2 -6x-7 hope this helps
Which represents a function? Edge 2020.
A recent study reported that the prevalence of hyperlipidemia (defined as total cholesterol over 200) is 30% in children 2-6 years of age. If 12 children are analyzed.
Required:
a. What is the probability that at least 3 are hyperlipidemic?
b. What is the probability that exactly 3 are hyperlipidemic?
c. How many would be expected to meet the criteria for hyperlipidemia?
Answer:
(a) 0.7472
(b) 0.2397
(c) 3.6
Step-by-step explanation:
Let X denote the number of children who are hyperlipidemic.
The proportion of children who are hyperlipidemic is, p = 0.30.
A random sample of n = 12 children are analyzed.
Every child is independent of the others to be expected to meet the criteria for hyperlipidemia.
The random variable X follows a binomial distribution with parameters n = 12 and p = 0.30.
(a)
Compute the probability that at least 3 are hyperlipidemic as follows:
[tex]P(X\geq 3)=1-P(X<3)\\\\=1-\sum\limits^{2}_{0}{{12\choose x}(0.30)^{x}(0.70)^{12-x}}\\\\=1-0.25282\\\\=0.74718\\\\\approx 0.7472[/tex]
Thus, the probability that at least 3 are hyperlipidemic is 0.7472.
(b)
Compute the probability that exactly 3 are hyperlipidemic as follows:
[tex]P(X=3)={12\choose 3}(0.30)^{3}(0.70)^{12-3}\\\\=220\times 0.027\times 0.040353607\\\\=0.23970042558\\\\\approx 0.2397[/tex]
Thus, the probability that exactly 3 are hyperlipidemic is 0.2397.
(c)
Compute the expected number of children who would meet the criteria for hyperlipidemia as follows:
[tex]E(X)=np=12\times 0.30=3.6[/tex]
Thus, 3.6 children would be expected to meet the criteria for hyperlipidemia.
Describe 3 types of maps
Answer:
population-amount of people per sq ft
climate- the average climate in that are
physical- elevation, landmarks,
Step-by-step explanation:
Turkey A: $10.35 for a 15lb
Turkey B: $11.80 for 20lb
Turkey C: $9.48 for 12lb
Determine which turkey would be best for you to buy. Find the unit price of each, then pick a turkey and explain why you choose that turkey.
light stand for knowledge in the poem
Answer:
light stand for knowledge in the poem
Step-by-step explanation:
What are 25 times by the same number then divide it by sixty
HELP PLZZZ i need it plz
A sample of n = 16 scores has a mean of M = 40 and a variance of s2 = 64. What is the estimated standard error for the sample mean?
Answer:
[tex]S.E = 2[/tex]
Step-by-step explanation:
Given
[tex]Mean = 40[/tex]
[tex]s^2 = 64[/tex] ----- variance
[tex]n = 16[/tex] ------------ sample
Required
Determine the S.E
The estimated standard error (S.E) for the sample mean is calculated using the following formula:
[tex]S.E = \frac{SD}{\sqrt n}[/tex]
Where
[tex]SD = Standard\ Deviation[/tex]
[tex]SD = \sqrt {s^2}[/tex]
[tex]SD = \sqrt {64}[/tex]
[tex]SD = 8[/tex]
So:
[tex]S.E = \frac{SD}{\sqrt n}[/tex]
[tex]S.E = \frac{8}{\sqrt{16}}[/tex]
[tex]S.E = \frac{8}{4}[/tex]
[tex]S.E = 2[/tex]
Hence: the estimated standard error for the sample mean is 2
Anyone???
Mathematics
Could you form a triangle either side lengths of 1 inch 2 inch and 3 inch
Answer:
no
Step-by-step explanation:
No, a triangle cannot be constructed with sides of 2 in., 3 in., and 6 in. For three line segments to be able to form any triangle you must be able to take any two sides, add their length and this sum be greater than the remaining side.
1. A local pizzeria sold 70 pizzas yesterday.
(a) The owner offers the employees a bonus if the number of pizzas sold increases by 30% today. How many pizzas must the pizzeria sell for employees to receive the bonus?
2. A certain TV can be purchased from the manufacturer for $150. A certain online retailer has a standard markup of 30%, and a certain superstore has a standard markup of 40%.
(a) What is the price of the TV when purchased online?
(b) What is the price of the TV when purchased at the superstore?
3. You have saved $140 for a new pair of skis. They have a regular price of $189. They have been reduced by 30%. There is a 13% tax as well.
a. What is the discount?
b. What is the new price?
c. What is the tax?
d. What was the total price of the shoes, after the discount and tax?
e. Do you have enough money? Please explain in a complete sentence
Answer:
1. 91 = 70*1.30
2a. 195= 150*1.30
2b. 210 = 150*1.40
3a. 56.70 = 156* .30
3b. 132.30 = 156-56.70
3c. 17.20 = 132.30 *0.13
3d. 149.50 = 132.30+17.20
3e. You do not have enough money, because you need $9.50 more.
Step-by-step explanation:
good luck
Question 1:
70 x 1.30 is 91 - 70 is equal to 21 pizzas, they would have to sell 91 total pizzas, which is 21 more than what was sold the previous day
Question 2:
Both parts are solved below:
Step-by-step explanation:
Given:
Purchase price = 150
Part A
As the online trailer marks up 30% so the price would be:
= 150 + 30% of 150
=150 + 0.3(150)
= 150 + 45
Price online= $195
° ♡ ₒ ♡ °
Part B
As the superstore marks up the price by 40% so the price would be:
= 150 + 40% of 150
=150 + 0.4(150)
= 150 + 60
Price at superstore = $210
° ♡ ₒ ♡ °
Difference
Difference = price at superstore - price online
Difference = 210 - 195
Difference = $15
Difference in markup = 40% - 30% = 10%
So a 10% difference leads to the difference of $15 in price.
Ashley can run 12 miles in 2 hours. At this rate, how many minutes does it take Ashley to run 1 mile?
Answer:
10 minutes
Step-by-step explanation:
If you divide both sides by 2 you get 6 miles and 1 hour.
Divide it again by 2 and you get 3 miles and 30 minutes.
Divide that by 3 and you get 1 mile in 10 minutes.
Given: TriangleSTU with Line segment S T is parallel to line segment X Y Prove: StartFraction S X Over X U EndFraction = StartFraction T Y Over Y U EndFraction Triangle S T U is cut by line segment X Y. Line segment X Y goes from side U S to side U T. Angle U Y X is 1, angle Y X U is 3, angle U T S is 2, and angle T S U is 4. Complete the steps of the proof. ♣: ♦:
Answer:
1:C Triangle STU is similar to triangle XYU
2:B subtraction property
Step-by-step explanation:
i just did the test
Applying the AA similarity theorem, the missing parts of the proof are:
Triangle STU is similar to triangle XYUSubtraction property What is the AA Similarity Theorem?According to the AA similarity theorem, if two triangles have two corresponding congruent angles, then both triangles are similar.
In the proof given, triangles STU and XYU have two pairs of corresponding angles that are congruent, therefore, triangle STU is similar to triangle XYU by AA similarity theorem.
Also, subtraction property was applied in the proof. Thus, the missing parts of the proof are:
Triangle STU is similar to triangle XYUSubtraction propertyLearn more about the AA similarity theorem on:
https://brainly.com/question/21247688
#SPJ9
whats 2+2 brainliest
Answer:
4
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
I neeed help plz 30 points
Quadrilateral NATS has coordinates N(-4, -3), A(1, 2), T(8, 1), and S(3, -4). Prove that quadrilateral NATS is a rhombus. Give your statement with the equal distances. Remember to identify the sides.
Answer:
Step-by-step explanation:
NA = √[(- 4 - 1 )² + (- 3 - 2)²] = 5√2
AT = √[(8 - 1 )² + (1 - 2)²] = 5√2
TS = √[(3 - 8 )² + (- 4 - 1)²] = 5√2
NS = √[(- 4 - 3 )² + (- 3 + 4)²] = 5√2
NA = AT = TS = NS = 5√2
[tex]m_{NA}[/tex] = (- 3 - 2) / (- 4 - 1) = 1 ........ (1)
[tex]m_{TS}[/tex] = (- 4 - 1) / (3 - 8 ) = 1 ......... (2)
From (1) and (2) ⇒ NA║TS
[tex]m_{AT}[/tex] = ( 1 - 2) / ( 8 - 1) = - 1 / 7 .......... (3)
[tex]m_{NS}[/tex] = ( - 4 + 3) / ( 3 + 4) = - 1 / 7 .... (4)
From (3) and (4) ⇒ AT║NS
Thus, NATS is rhombus.
Michelle works in the mall and her hours increase during busy shopping times of the year. Michelle has a plan to
save $45 each week for 7 weeks, and then increase that amount by $30 for the next 8 weeks during the busy time,
then go back to $45 per week. If Michelle's plan is to save $1185, how many weeks total will she need to save?
Show your work
12
II
Answer:
The total number of weeks Michelle needs to save is 29.
Step-by-step explanation:
Michelle plans to save $1185 in a number of weeks to determine later.
In the first 7 weeks, she will save $45 each week for a total of
$45 * 7 = $315
In the next 8 weeks, she will save $30 each week for a total of:
$30 * 8 = $240
During these 15 weeks, she has saved
$315 + $240 = $555
She still has a remaining $1185 - $555 = $630 to save.
Those $630 will be saved in a number of weeks at $45 per week, thus the number of weeks is:
$630 / $45 = 14 weeks
Total weeks = 15 + 14 = 29
The total number of weeks Michelle needs to save is 29.
Factor by Grouping
2y2 + 7yz + 5z2
