Differentiate both sides implicitly:
[tex]\dfrac{\mathrm d}{\mathrm dt}[e^y+x^3y^2+\ln x]=\dfrac{\mathrm d[1]}{\mathrm dt}[/tex]
[tex]e^y\dfrac{\mathrm dy}{\mathrm dt}+3x^2y^2\dfrac{\mathrm dx}{\mathrm dt}+2x^3y\dfrac{\mathrm dy}{\mathrm dt}+\dfrac1x\dfrac{\mathrm dx}{\mathrm dt}=0[/tex]
Solve for [tex]\frac{\mathrm dx}{\mathrm dt}[/tex]:
[tex]\left(3x^2y^2+\dfrac1x\right)\dfrac{\mathrm dx}{\mathrm dt}=-(e^y+2x^3y)\dfrac{\mathrm dy}{\mathrm dt}[/tex]
[tex]\dfrac{\mathrm dx}{\mathrm dt}=-\dfrac{e^y+2x^3y}{3x^2y^2+\frac1x}\dfrac{\mathrm dy}{\mathrm dt}[/tex]
[tex]\dfrac{\mathrm dx}{\mathrm dt}=-\dfrac{xe^y+2x^4y}{3x^3y^2+1}\dfrac{\mathrm dy}{\mathrm dt}[/tex]
Plug in [tex]x=1[/tex], [tex]y=0[/tex], and [tex]\frac{\mathrm dy}{\mathrm dt}=2[/tex]:
[tex]\dfrac{\mathrm dx}{\mathrm dt}=\boxed{-2}[/tex]
A magnitude 6.7 earthquake struck the SanFernando valley region of Los Angeles in 1994, causing widespread damage. Suppose another region with more active earthquakes and the number of earthquakes in this region is a random variable (binomial) distribution. Use a normal distribution approximation to find standard deviation if the probability is 0.87 that there will be at least 15 earthquakes with mean=17.6.
Answer: 2.308 .
Step-by-step explanation:
Let X denotes the number of earthquakes in SanFernando valley region of Los Angeles in 1994.
Given: [tex]\mu=17.6[/tex]
Probability is 0.87 that there will be at least 15 earthquakes .
i.e. [tex]P(X\geq15)=0.87[/tex]
[tex]\Rightarrow\ P(\dfrac{X-\mu}{\sigma}\geq\dfrac{15-17.6}{\sigma})=0.87\\\\ \Rightarrow\ P(Z\geq\dfrac{-2.6}{\sigma})=0.87\ \ \ [Z=\dfrac{X-\mu}{\sigma}][/tex]
Z-value corresponding to p-value 0.87 is -1.1263 .
So, [tex]\dfrac{-2.6}{\sigma}=-1.1263[/tex]
[tex]\sigma= \dfrac{-2.6}{-1.1263}\approx2.308[/tex]
Hence, the required standard deviation = 2.308 .
A student measures the mass of an 8 cm 3 block of brown sugar to be 12.9 g. What is the density of the brown sugar?
Answer:
[tex]\huge\boxed{\rho=1.6125\dfrac{g}{cm^3}}[/tex]
Step-by-step explanation:
The formula of a density:
[tex]\text{density}=\dfrac{mass}{volume}\Rightarrow\rho=\dfrac{m}{V}[/tex]
We have
[tex]\text{mass}\ m=12.9g\\\\\text{volume}\ V=8cm^3[/tex]
Substitute:
[tex]\rho=\dfrac{12.9g}{8cm^3}=\dfrac{12.9\cdot10}{8\cdot10}\dfrac{g}{cm^3}=\dfrac{129}{80}\dfrac{g}{cm^3}=1.6125\dfrac{g}{cm^3}[/tex]
The the density of the brown sugar is equal to [tex]1.6125 \;g/cm^3[/tex]
Given the following data:
Volume = 8 [tex]cm^3[/tex]Mass = 12.9 gramsTo find the density of the brown sugar;
Density can be defined as mass all over the volume of an object.
Simply stated, density is mass per unit volume of an object.
Mathematically, the density of a substance is given by the formula;
[tex]Density = \frac{Mass}{Volume}[/tex]
Substituting the values into the formula, we have;
[tex]Density = \frac{12.9}{8}[/tex]
Density = [tex]1.6125 \;g/cm^3[/tex]
Therefore, the the density of the brown sugar is equal to [tex]1.6125 \;g/cm^3[/tex]
Find more information: brainly.com/question/5995838
3.87 m to kilometers
Answer:
0.00387
To convert from meters to kilometers, you must divide the number pf meters by 1000.
3.87 ÷ 1000 = 0.00387.
So, that is the answer. Hope it helps!
Please help ASAP. Worth 50 points
Answer:
the anser is 9.5+1.5n and the second ansr is 48x+16
Answer:
a
Step-by-step explanation:
Translate the figure 1 unit left and 2 units up.
Draw a vector from the origin 1 unit left and 2 units up.
I need help asap
Answer:
Hey there!
The correct answer would be a line from (0, 0) to (-1, 2)
Let me know if this helps :)
x^2 -9 divided by x+3
Answer:
x-3
Step-by-step explanation:
x²-9÷x+3=x-3
How are I supposed to do this ?
Answer:
Step-by-step explanation:
1. binomial polynomial
2. 2 terms
3. 4 is the constant term
4. - 1/10 x^3 is the leading term
5. -1/10 is the leading coefficient.
Classify the number 0 by listing all the sets of numbers to which it belongs
Answer:
0 belongs to the set of whole number,set of rational numbers,set of real numbers and integers
Step-by-step explanation:
Rhonda is building a rectangular patio. The perimeter of the patio is to be 96 feet. Determine the dimension of the patio if the length is to be 6 feet less than twice the width
Answer:
Length= 30 ft
Width= 18ft
Step-by-step explanation:
The perimeter of the rectangular patio is to be 96 feet.
the length is to be 6 feet less than twice the width
Perimeter=2(length+width)
But
Length= 2(width)-6
Substituting in perimeter equation
Perimeter=2(length+width)
Perimeter=2((2(width)-6)+width)
Perimeter= 96 feet
Let width= x
Perimeter=2((2(width)-6)+width
96=2((2(x)-6)+x)
96= 4x-12+2x
108= 6x
18= x
Width= 18ft
Length= 2(width)-6
Length= 2(18)-6
Length= 36-6
Length= 30 ft
HELP PLEASE ASAP !!!!
-3h -6(5h/3 + 7/2) +9h = -53
Find the value for h.
Answer: h= 8
Step-by-step explanation:
-3h - 6(5h/3 + 7/2) + 9h = -53 Distribute on the left
-3h - 10h - 21 + 9h = -53 combine like terms on the left side
-4h -21 = -53 Now add 21 to both sides
+21 +21
-4h = -32 Divide both sides by -4
h = 8
Enter the number in two other forms. six million, ninety thousand, thirty-six
Standard form and expanded form
Answer:
Standard form:
Simplify the words.
6,090,036
Expanded form:
Take the standard number and expand it.
6000000 + 90000 + 30 + 6
I'm sorry if I misunderstood.
Good luck though! :)
Please add Brainliest if you'd like, not that it matters.
The measures of the angles of a triangle are in the ratio 2 : 3 : 4. The simplified ratio of the measures of the exterior angles of the triangle is a : b : c. Find a + b + c.
Answer:
Step-by-step explanation:
2x+3x+4x=180 degrees
9x=180 fdegrees
x=180/9
x=20
2x=40
3x=60
4x=80
Answer:
18
Step-by-step explanation:
The measures of the angles of a triangle are in the ratio 2:3:4 means we have one interior angle measuring 2x, another measuring 3x, and the last one measuring 4x. We know the sum of the measures of the interior angles of a triangle is 180 degrees.
We need to solve the following equation to find first x, and then find the measurement of each interior angle of the triangle.
2x+3x+4x=180
(2+3+4)x=180
(9)x=180
x=180/9
x=20
So one interior angle measures 2x=2(20)=40.
Another measures 3x=3(20)=60.
The last measuring 4x=4(20)=80.
The exterior angles of this triangle therefore measure the following:
180-40=140
180-60=120
180-80=100
So the un-simplified ratio of the measures of the exterior angles is as follows:
140:120:100.
Let's simplify that.
It is easy to see each number is divisible by 10.
Let's reduce it by dividing each by 10:
14:12:10
Let's simplify more (as we want the most simplified ratio).
Each number is divisible by 2 since they are all even.
Let's reduce again but not by dividing by 2:
7:6:5
So the simplified ratio of the measures of the exterior angles of the triangle is a:b:c=7:6:5 and so a+b+c=7+6+5=18.
Answer is 18.
PLease help i dont know how to do this please explain too!!
Answer:
6.25
Step-by-step explanation:
The perimeter is the sum of the lengths of the sides.
For a rectangle, it's the two widths plus the two heights.
P = 2W + 2H
Plugging in values:
52 = 2(3x − 1) + 2(x + 2)
52 = 6x − 2 + 2x + 4
52 = 8x + 2
50 = 8x
x = 6.25
Find the value of x.
Formula used:-Perimeter of rectangle = 2 ( l + b )
Solution:-We know that,
Perimeter of rectangle = 52 [ Given ]
⇒ 2 ( l + b ) = 52
⇒ 2 ( 3x - 1 + x + 2 ) = 52
⇒ 2 ( 4x + 1 ) = 52
⇒ 8x + 2 = 52
⇒8x = 52 - 2
⇒ 8x = 50
⇒ x = 50/8
⇒ x = 6.25 inches
Evaluate the expression. 202 + 6(9 + 3)
Answer:
= 274
Step-by-step explanation:
202 + 6(9 + 3)
= 202 + 9 * 12
= 202 + 72
= 274
Answer:
Its is actually 472
Step-by-step explanation:
If 7x + 4 = -19 + 5x, then 2x – 14 equals
A-23
B 23
C-37
D-14
Answer:
C
Step-by-step explanation:
Here we have the question,
7x+4 = -19 + 5x
Now we add 19 to both sides,
7x + 4 + 19 = -19 + 19 + 5x
7x + 23 = 5x
Now we subtract 7x from both sides,
23 = -2x
We divide -2 from both sides,
x = -23/2
Now we plug this in into 2x - 14,
2(-23/2) - 14 = -23-14 = -37
Our answer is C
2-(3x2)➗6 solve this asap pls (I just need the number) ty <3
Answer:
1
Step-by-step explanation:
Assume that the Poisson distribution applies and that the mean number of hurricanes in a certain area is 6.2 per year. a. Find the probability that, in a year, there will be 5 hurricanes. b. In a 35-year period, how many years are expected to have 5 hurricanes? c. How does the result from part (b) compare to a recent period of years in which years had hurricanes? Does the Poisson distribution work well here?
Answer: Try to use socratic
Step-by-step explanation:
can some one plzz answer this fastttttt plzzz
Answer:
Please see attached picture
hope it helped you:)
Solve the equation 3(x + 1) − 2 = x + 5.
Answer:
X=2
Step-by-step explanation:
First, distribute the 3 to get
3x+3-2=x+5
Solve for 3-2 to get
3x+1=x+5
subtract 1 from both sides to get
3x=x+4
subtract x from both sides to get
2x=4
divide both sides by 2 to finalily get
x=2
A highway sign in Canada gives the speed limit as 100 kilometers per hour. If you are driving 62 miles per hour are you driving under the speed limit? (1mi=1.6km)
As we know that 1 mile=1.6km
then,
62 miles=62*1.6km
=99.2km/hour
so, yes we are driving under the speed limit.
Answer:
Yes
Step-by-step explanation:
Convert 62 mph to kph by multiplying it by 1.6
62(1.6)
= 99.2
Yes, you are driving under the speed limit
Lori is picking up lunch for herself and her coworkers. Some of her coworkers ordered the salad which costs $7.50, and some of her coworkers ordered the soup which costs $6.25. When Lori gets to the restaurant, she had lost the paper where she had written down who ordered which. She recalls that twice as many people ordered the salad than the soup, and she has a total of $63.75 to pay for the orders. How many people must have ordered the soup?
Answer: 3 people ordered soup.
Step-by-step explanation:
Let x be the number of people ordered salad and y be the number of people ordered soup.
As per given,
x=2y (i)
7.50x+6.25y= 63.75 (ii)
Substitute value of c =2y in (ii) , we get
7.50(2y)+6.25y= 63.75
⇒ 15y+6.25y = 63.75
⇒21.25y = 63.75
⇒ y= 3 [divide both sides by 21.25]
Then, x= 2(3) =6
So 6 people ordered salad and 3 people ordered soup.
PLEASE HELP MEEEEE!!!!
Answer:
5
Step-by-step explanation:
The leading coefficient is the coefficient with a variable with the greatest exponent.The exponent is the number you would say "the power to". What I mean is let's say you have this number: [tex]3^{2}[/tex] . The exponent would be 2 in this equation because it's saying what power 3 is too. Therefore, 5 is the leading coefficient.
In an election between two candidates,a candidate secured 47% of the votes polled and the lost the election by 8700 votes . Find the total number of votes polled and the votes secured by winning candidate
Answer:
Total number of votes- 145,000
Votes secured by winning candidate- 76,850
Step-by-step explanation:
Candidate A- 47%
Candidate B- 53%
6% difference or 8700 votes so
6%=8700
1%=1450
100%=145,000
53%= 76,850
The length of the shadow of a pole on level ground increases by 90m when the angle of elevation of the sun changes from 58° to 36° find the height of the pole
Answer:
119.45 m
Step-by-step explanation:
Given:
When angle of elevation of the sun changes from 58° to 36° the length of shadow of a pole increases by 90 m.
To find:
Length of pole = ?
Solution:
Kindly refer to the attached image.
[tex]\triangle ABC[/tex] represents the 1st angle of elevation of sun i.e. 58°
[tex]\triangle ABD[/tex] represents the 2nd angle of elevation of sun i.e. 36°
Change in shadow is represented by CD = 90 m
Let height of pole, AB = [tex]h[/tex] m
Let side BC = [tex]x[/tex] m
Now, let us apply tangent rules in [tex]\triangle ABC, \triangle ABD[/tex] one by one:
[tex]tan\theta = \dfrac{Perpendicular}{Base}\\\Rightarrow tan58^\circ=\dfrac{AB}{BC}\\\Rightarrow tan58^\circ=\dfrac{h}{x}\\\Rightarrow x = 0.624h ..... (1)[/tex]
[tex]tan36^\circ = \dfrac{h}{x+90}[/tex]
Putting value of [tex]x[/tex] using equation (1):
[tex]tan36^\circ = \dfrac{h}{0.624h+90}\\\Rightarrow 0.726\times 0.624h+0.726\times 90 = h\\\Rightarrow h-0.453h =65.34\\\Rightarrow \bold{h = 119.45\ m}[/tex]
119.45 m is the height of pole.
my last question please help
Step-by-step explanation:
(2) (x+2)^2 + (-15x -3)
I hope this will be helpful for you.
Answer:
[tex]2(x + 2)^{2} + (-15x - 3)[/tex]
The guy above is correct
Proof :
[tex]2(x + 2)^{2} - 15x - 3 \\ 2((x + 2)(x + 2) - 15x - 3 \\ 2( {x}^{2} + 4x + 4) - 15x - 3[/tex]
[tex]2 {x}^{2} + 8x - 15x + 8 - 3 \\ 2 {x}^{2} - 7x + 5[/tex]
My workings are in the picture
My asnwer was 5/2 and -1
Will GIVE 75 POINTS PLZ HELP!!!
Joey owns a small bakery and today Phoebe has ordered 100 cookies. If Joey boxes the cookies by the dozen, which of the following equations describes how many boxes of cookies Phoebe will have? Let b represent the number of boxes. (HINT: All of the cookie boxes are not necessarily full.)
A. 100 = b/12
B. 12b + 4 = 100
C. 12b = 100 – 4
D. 100/b = 12
E. (100-4)/12=b-1
F. 12 + b = 100
Answer:
A
Step-by-step explanation:
Complete the following table using the equation:
y = 2x^2
Plot the points on a graph and determine which graph best represents the equation.
Graph A
Answer:8,2,0,2,8; Graph A
Step-by-step explanation:
The graph of the given equation best represents a parabola.
What is the graph of an equation?A graph represents the nature of the equation graphically by plotting the points of it.
Given, y = 2x²
For x = - 2, y = 2(- 2)² = 8
For x = - 1, y = 2(- 1)² = 2
For x = 0, y = 2(0)² = 0
For x = 1, y = 2(1)² = 2
For x = 2, y = 2(2)² = 8
Therefore, the given table will be:
x - 2 - 1 0 1 2
y 8 2 0 2 8
By plotting the graph, it is clear that, the graph best represents a parabola.
Learn more about the graph of an equation here: https://brainly.com/question/4047677
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I WILL GIVE BRAINLIEIST!!
Answer:
y= -7
Step-by-step explanation:
This line is a horizontal line.
Horizontal lines all have the same form of y=k (where k is the y-intercept of the horizontal line).
The y-intercept is the point where the line meets the y-axis (the vertical axis). For this line, the y-intercept is in between -6 and -8, making it: (0,-7) or just -7.
Let's return to the form for horizontal lines.
y= k
The y-intercept is -7. Substitute -7 in for k.
y= -7
The equation of the line is y= -7
14+-6 what is the answer answer
Answer:
the answer is 8. just think of it as subtraction. subtract +6 from +14. then you get the answer for +14+-6.
Solve 5g = 20
Please and thank u
Answer:
g = 4
Step-by-step explanation:
5g = 20
Divide each side by 5
5g/5 = 20/5
g = 4
Answer:
g= 4
Step-by-step explanation:
5g = 20
5g /5 = 20 /5
g =4