==========================================================
Explanation:
You'll need the chain rule for this one.
[tex]y = 3x^3 + 4x\\\\\frac{d}{dt}(y) = \frac{d}{dt}\left(3x^3 + 4x\right)\\\\\frac{dy}{dt} = \frac{d}{dt}\left(3x^3\right) + \frac{d}{dt}\left(4x\right)\\\\\frac{dy}{dt} = 3\frac{d}{dt}\left(x^3\right) + 4\frac{d}{dt}\left(x\right)\\\\\frac{dy}{dt} = 3*3\left(x^2\right)*\frac{dx}{dt} + 4\frac{dx}{dt}\\\\\frac{dy}{dt} = 9x^2\frac{dx}{dt} + 4\frac{dx}{dt}\\\\\frac{dy}{dt} = (9x^2+4)\frac{dx}{dt}\\\\[/tex]
Now apply substitution
[tex]\frac{dy}{dt} = (9x^2+4)\frac{dx}{dt}\\\\\frac{dy}{dt} = (9*4^2+4)*2\\\\\frac{dy}{dt} = 296\\\\[/tex]
Answer:
296
Step-by-step explanation:
I just did the math and I also got 296.
Categorize the graph as linear increasing, linear decreasing, exponential growth, or exponential decay
Answer:
D. Exponential growth
Step-by-step explanation:
Hope this helps
Function that is similar to exponential.
Option (A) is correct.
What is exponential decay?Exponential decay describes the process of reducing an amount by a consistent percentage rate over a period of time. It can be expressed by the formula [tex]y=a(1-b)^{x}[/tex] wherein y is the final amount, a is the original amount, b is the decay factor, and x is the amount of time that has passed.
We can observe that
First, y increases as x increases
Last it is a function that is similar to exponential.
Function is an exponential decay.
Option (A) is correct.
Find out more information about exponential decay here
https://brainly.com/question/14355665
#SPJ2
Does this graph show a function? Explain how you know.
A. No; the graph fails the vertical line test.
• B. No; there are y-values that have more than one x-value.
• C. Yes; the graph passes the vertical line test.
D. Yes; there are no y-values that have more than one x-value.
Answer:
C. Yes; the graph passes the vertical line test.
Step-by-step explanation:
Reasons the others are wrong:
A. It does pass the vertical line test.
B. Y-values can have any x values. It is x-values that can't have multiple y-values.
D. There are y-values with more than one x-value on this graph so that's just false. Even if it were true, that still doesn't invalidate it due to the reasons given in Answer B.
Sammy and Hannah are finalists in a cooking competition. For the final round, each of them will randomly select a card without replacement that will reveal what their star ingredient must be. Here are the available cards:
Cabbage
Spinach
Kale
Leeks
Carrots
Turnips
Cabbage
Leeks
Spinach
Carrots
Kale
Turnips
Sammy and Hannah both want to get leeks as their star ingredient. Sammy will draw first, followed by Hannah.
What is the probability that NEITHER contestant draws leeks?
Round your answer to two decimal places.
The probability that neither of them draws the Leeks card is P = 4/6 = 0.667
Here we can assume that all the cards have the same probability of being randomly drawn.
The cards are:
Cabbage Spinach Kale Leeks Carrots TurnipsSo we have 6 cards. We want to find the probability that neither contestant draws the "Leeks" card.
Sammy draws first, the probability of drawing the Leeks card will be equal to the quotient between the number of Leeks cards (one) and the total number of cards (6).
Then the probability of drawing the leeks card is p = 1/6
This means that the probability of NOT drawing the leeks card is:
q = 1 - 1/6 = 5/6.
Now draws Hanna, now there are 5 cards in the deck (because one was already drawn). With the same approach as before, the probability of drawing the Leeks card is p = 1/5, then the probability of NOT drawing the card is:
q = 1 - 1/5 = 4/5.
The joint probability (this is, the probability of both of these events to happen together) is just the product of the individual probabilities.
Then the probability that neither of them draws the Leeks card is:
P = (4/5)*(5/6) = 4/6 = 0.667
If you want to learn more about probability, you can read:
https://brainly.com/question/24349426
I really need an answer as soon as possible. 10 pts worth it
Answer:
A. Correct: When we plug in g(x) for the x in f(x), we get H(x).
B. Correct: When we plug in g(x) for the x in f(x), we get H(x).
C. Correct: When we plug in g(x) for the x in f(x), we get H(x).
D. Correct: When we plug in g(x) for the x in f(x), we get H(x).
Step-by-step explanation:
Brainliest, please!
Find the measure of <3. 90 50 40 130
=============================================================
Explanation:
This figure is a kite since we have two pairs of adjacent sides that are congruent, but not all sides are the same length.
One property of kites is that the diagonals are always perpendicular (this applies to rhombuses as well). This means angle 3 is 90 degrees.
The measure of ∠3 is 90°
Because in a kite the diagonals bisects at 90°
Therefore ∠3 is 90°
Answered by Gauthmath must click thanks and mark brainliest
What is the vertex of g(x) = 3x2 − 12x + 7?
(−6, −5)
(−2, −5)
(2, −5)
(6, −5)
(h ,k) —> (2 , –5)
g(x)=3x²-12x+7 —> y= 3(x-2)²-5
y=a(x–h)²+k —> a= 3 , h=2 , k= –5
(h ,k ) —> (2, –5)
I hope I helped you^_^
Answer:
C, Option 2, or (2,-5)
Step-by-step explanation:
edge 2021
can anyone help with this? im confused
CP = Rs 720 and SP = Rs 810
Answer:
Bro what to do in this question. Hope you understand me
Find the measure of
Answer:
74 degrees
.................
Answer:
74
Step-by-step explanation:
BEC and CED form a straight line so they add to 180
BEC+CED = 180
106+ CED = 180
CED = 180-106
CED = 74
Select the correct answer (for Edmentum/PLATO).
Which expression represents the series 1 + 5 + 25 + 125 + 625?
Answers attached in photo.
Answer:
Correct answer is A. Trust me
Step-by-step explanation:
Select the correct answer.
Simplify the following expression.
(3x^2 - 11x - 4) – (x – 2) (2x + 3)
Answer choices
5x^2 - 12x - 10
x^2 - 10x + 2
x^2 + 10x - 2
x^2 – 12x – 10
Answer:
x^2 -10x+2
Step-by-step explanation:
(3x^2 - 11x - 4) – (x – 2) (2x + 3)
FOIL
(3x^2 - 11x - 4) – (2x^2-4x+3x-6)
Combine like terms
(3x^2 - 11x - 4) – (2x^2 -x-6)
Distribute the minus sign
3x^2 - 11x - 4 – 2x^2 +x+6
Combine like terms
x^2 -10x+2
Please help solve x and round all answers to the nearest tenth
Please hell the question is in the photo ^^
May be this.. you may find all the math answers in the app known as Gauth math so I would suggest you to download it .Thank you
ASAP!! Photo attached
Answer:
FG = 120 cm
Step-by-step explanation:
The explanation is in the picture!
write two properties of right angled triangle
Answer:
The properties of right angle triangle are as follows
the hypotenuse is the longest sideone angle is 90 degree then other angle will be also 90 degree.Look at the figure. Which step should be taken next to construct a line through point R that is perpendicular to ST ?
Answer:
where is the figure without figure how to find out
Each coffee pot hold 6 cups of coffee we sell 10 cups of coffee every fifteen minutes how many pots of coffee do I need to make in an hour?
Answer:
7 pots of coffee (If you want to be precise its 6 2/3)
Step-by-step explanation:
So basically you need 10 cups of coffe in fifteen minutes, so 60/15=4 then time 10. so 40 is how much coffee you need in a hour, but we are solving the pot so 40/6= 6 2/3. but it says how many pots so we round it up so its 7. (Unless you wanna be precise)
SOMEONE PLEASE HELP ME OUT ON THIS. PLEASE!
n= 1. then a1= 7+3(1)
How to solve it.
Answer:
I think this is right for the 2nd problem
Step-by-step explanation:
a1=7+(3)(1)
Step 1: Simplify both sides of the equation.
a1=7+(3)(1)
a=7+3
a=(7+3)(Combine Like Terms)
a=10
a=10
Answer:
a=10
PLEASE ANSWER ASAP
Write an inequality and show on a number line all numbers: greater than (-3) but less than or equal to 3
Answer:
The inequality is -3<x<3
Step-by-step explanation:
(-3,3)
Find the measure of FG.
Answer:
8
Step-by-step explanation:
By power of a point, (x-2)(x+13) = (x-3)(x+16). Solving, we find that x=11, so FG= 11-3 = 8
Explain how to solve the equation
.
b – 7 = 12
Answer:
19
Step-by-step explanation:
Add 7 onto 12 to find answer.
Answer:
b = 19
Step-by-step explanation:
b = 12 + 7
Simplify 12+7 to 19.
Add.
(-2+6x3 – 3x_) + (4x3 – 5 + x²)
Express the answer in standard form.
Enter your answer in the box.
Write a simplified polynomial expression in standard form to represent the area of the rectangle below:
(See photo)
A. 2x^2 + 3x - 20
B. 2x^2 + 13x - 1
C. 2x^2 + 13x - 20
D. 2x^2 + 3x - 1
Answer:
A
Step-by-step explanation:
The area (A) of a rectangle is calculated as
A = length × breadth
= (2x - 5)(x + 4) ← expand using FOIL
= 2x² + 8x - 5x - 20
= 2x² + 3x - 20 → A
PLEASEEE HELP!!
___ + 42= -18
and
-56+___=-84
i will give brainlist plus 50 points!!!!!
Answer:
-60 and -28
Step-by-step explanation:
-60 + 42= -18
CHECK:
-42-18=-60
-56+-28=-84
CHECK:
-84+28=-56
Hope this helps <3 Need thanks? Comment /hearthelp
Answer:
-60
-28
Step-by-step explanation:
x +42 = -18
Subtract 42 from each side
x+42-42 = -18-42
x = -60
-56 +y = -84
Add 56 to each side
y = -84+56
y = -28
HELP! TRIGONOMETRY QUESTION!!
Use the law of cosines, which says
189² = 215² + 123² - 2×215×123 cos(∠P)
==> cos(∠P) = 25,633/52,890
==> ∠P ≈ 61.06°
How do you simplify 3 times the square root 13?
Answer:
3√13
Step-by-step explanation:
3√13
This expression cannot be simplified because you cannot take any common factor outside the root.
Can someone plz help me
Answer:
37500
Step-by-step explanation:
pattern is multiplying by -5.
-7,500*-5 = 37,500
Have a nice day! :-)
PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER PLS GIVE ME A STEP BY STEP EXPLANATION!!
The students in Shawn's class got to choose whether to visit the zoo or the aquarium. 3 students went to the zoo and 15 students went to the aquarium. What is the ratio of the number of students who went to the zoo to the number of students who did not go to the zoo?
A. 1:6
B. 1:1
C. 1:3
D. 1:5
Answer:
1 : 5
Step-by-step explanation:
3 students zoo
15 students aquarium
zoo : not zoo
3: 15
Divide each side by 3
3/3 : 15/3
1 : 5
when x=1,2,3,.... find limit x->infinity
choice
a. 0
b. 1
c. 2
d. 3
f. 4
help me!!!
Let y = √x, so the limit can be rewritten as
[tex]\displaystyle \lim_{y\to\infty}\left(\frac{\sqrt{y^6+y^2}}{y^2+3} - \frac{\sqrt{y^4+1}}{y+4}\right)[/tex]
Now,
[tex]\sqrt{y^6+y^2} = \sqrt{y^2\left(y^4+1\right)} = y\sqrt{y^4+1}[/tex]
so we can rewrite the limit further as
[tex]\displaystyle \lim_{y\to\infty}\left(\frac{y}{y^2+3} - \frac1{y+4}\right)\sqrt{y^4+1}[/tex]
Combine the rational terms:
[tex]\dfrac y{y^2+3} - \dfrac1{y+4} = \dfrac{y(y+4)-(y^2+3)}{(y^2+3)(y+4)} = \dfrac{4y-3}{(y^2+3)(y+4)}[/tex]
Then in the limit, we get
[tex]\displaystyle \lim_{y\to\infty}\frac{(4y-3)\sqrt{y^4+1}}{(y^2+3)(y+4)} = \lim_{y\to\infty}\frac{(4y^3-3y^2)\sqrt{1+\dfrac1{y^4}}}{y^3+4y^2+3y+12} \\\\ = \lim_{y\to\infty}\frac{\left(4-\dfrac3y\right)\sqrt{1+\dfrac1{y^4}}}{1+\dfrac4y+\dfrac3{y^2}+\dfrac{12}{y^3}} = \boxed{4}[/tex]
20 The nth term of an arithmetic series is Un where un > 0 for all n.
The sum to n terms of the series is Sn
Given that u4 = 6 and that S11 = (u6)2 + 18
Find the value of u20
Answer:
Hi,
[tex]u_{20}=30[/tex]
Step-by-step explanation:
[tex]u_n=u_1+(n-1)*r, \ r= commun\ ratio.\\u_4=u_1+3*r=6\\u_6=u_1+5r\\(u_6)^2=u_1^2+10ru_1+25r^2\\s_n=u_1+u_1+r+u_1+2r+...+u_1+10r=11*u_1+55r\\s_{11}=(u_6)^2+18\ \\\Longrightarrow\ u_1^2+10ru_1+25r^2+18=11u_1+55r\\\Longrightarrow\ 4r^2+2r-12=0\\\Longrightarrow\ 2r^2+r-6=0\\r=\dfrac{3}{2} \ or\ r=-2\ (excluded)\\\\u_1=6-3r=\dfrac{3}{2} \\\\\\\boxed{u_{20}=u_1+19*r=30}\\[/tex]
The value of the 20th term of the arithmetic series will be 30
What is arithmetic progression?An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.
Un = u₁+(n-1) x r
u₄ = u₁ +(3 x r)=6
u₆ = u₁ +5r
u₆²=u₁²+10ru₁+25r²+18=11u₁+55r
Sn= u₁+u₁+r+u₁+2r+.............u₁+10r= (11 x u₁) +55 r
4r²+2r-12=0
2r²+r-6=0
r=3/2
u₁=6-3r=3/2
u₂₀=u₁+(19 x r)= 30
Hence the value of the 20th term of the arithmetic series will be 30
To know more about arithmetic progression follow
https://brainly.com/question/6561461
#SPJ2
