Answer:
[tex]y = 6x + C[/tex]
Step-by-step explanation:
Given the system of equations
dx/dt = 6x − y ............. 1
dy/dt = 36x − 6y ............ 2
Divide equation 2 by 1;
[tex]\dfrac{dy/dt}{dx/dt} = \dfrac{36x-6y}{6x-y} \\\\\dfrac{dy/dt}{dx/dt} = \dfrac{6(6x-y)}{6x-y}\\ \\\dfrac{dy/dt}{dx/dt} = 6\\\\\dfrac{dy}{dt}* \dfrac{dt}{dx} = 6\\\dfrac{dy}{dx} = 6[/tex]
cross multiply
[tex]dy = 6dx\\[/tex]
integrate both sides of the expression
[tex]\int\limits {dy} = \int\limits {6} \, dx \\\\y = 6x + C[/tex]
Hence the general solution to the system of equation is [tex]y = 6x + C[/tex]
Which of the following expressions is in simplified form?
Write the equation of a line that is parallel to 4x-2y=3 and is passing through the point (2,1)
Answer:
y= 2x -3
Step-by-step explanation:
Let's rewrite the given equation into the form of y=mx+c, so that we can find the gradient of the line. In this form, m (coefficient of x) is the gradient.
4x -2y= 3
2y= 4x -3
Divide by 2 throughout:
[tex]y = 2x - 1 \frac{1}{2} [/tex]
Thus the gradient is 2.
Parallel lines have the same gradient thus the line would also have a gradient of 2.
Substitute m=2 into the equation:
y= 2x +c
To find the value of c, substitute a pair of coordinates.
When x=2, y=1,
1= 2(2) +c
1= 4 +c
c= 1 -4
c= -3
Thus, the equation of the line is y= 2x -3.
A particular zebra runs 40 miles per hour. Select the animals who run at a faster unit
rate per hour than the zebra. Mark all that apply.
O reindeer: 70 miles in 3 hours
O greyhound 120 miles in 3 hours
O lion 100 miles in 2 hours
O Pig 33 miles in 3 hours
4 radians
А
2 cm
B
What is the length of the arc subtended by the angle measuring 4 radians?
A.
4 cm
B.
2 cm
C
16 cm
D
8 cm
Answer:
D. 8 cm
Step-by-step explanation:
Given :
Let the length of the arc be = l
radius of the arc, r = 2 cm
degree of angle subtended at the center by the arc, θ = 4 radian
Now we know that the angle subtended by an arc at the center of the circle whose radius is 2 cm will be,
θ = l/r
Therefore, we can write,
l = θ x r
l = 4 x 2
= 8 cm
So the length of the arc is 8 cm.
how do I put on 0.54 as a fraction number 2 how do I write 4.18 as a mixed number number 3 how do I write 0.51 as a fraction
Answer:
0.54 as a fraction is 54/100
4.18 as a mixed number is 4 18/100
0.51 as a fraction is 51/100
it would be really cool if you could mark me as brainliest :)
Step-by-step explanation:
solve the absolute value equation and check your answer for extraneous solution. I-4xI=32
Answer:
x=8
Step-by-step explanation:
I-4xI=32
4x=32
4x÷4 → 32÷4
=8 →x=8
the formula for the area of a triangle is a=1/2bh in which b represents the length of the base and h represents the height. If a triangel has an area of 287 mm and the height is 18 mm, what is the b=meausre of the base?
Answer:
287/9
Step-by-step explanation:
so the formula is a=1/2bh
A=287
B=?
H=18
:287=1/2b*18
287=b*9
b=287/9
Which statement about the image pictured is true?
Which car is accelerating?
Answer:
What care is accelerating? I can't even see the answer choices-_-
Step-by-step explanation:
Find the value of x for which the lines rand s are parallel.
Answer:
x = 12
Step-by-step explanation:
<1 and the 142-deg angle are vertical, so m<1 = 142 deg
The angle measuring 3x + 2 and <1 are same-side interior angles. If the lines are parallel, then those two angles are supplementary.
3x + 2 + 142 = 180
3x + 144 = 180
3x = 36
x = 12
can someone help me please.
Answer:
D
Step-by-step explanation:
Its 5x (on bottom row, its the simplest way to put it), and 625 x 5 = 3125, then 3215 x 5 = 15625. So its D.
Answer:
D
Step-by-step explanation:
If you look closely, you may see a pattern in the denominators.
the 1st one is 5,
the 2nd one is 5²
the 3rd one is 5³
so it is only reasonable that the next 2 are 5^4 and 5^5
If I had 4 eggs
A thief gave me 3 eggs
My farm rooster lays 5 eggs
How many eggs do I have?
Using basic operations, it is found that you have 12 eggs.
----------------------------------
Initially, you had 4 eggs.When the thief gave you 3 eggs, these 3 eggs were added to your amount, thus, you had 4 + 3 = 7 eggs.When the farm rooster laid 5 eggs, these 5 eggs were added to your amount, thus, at the end, you ended up having 7 + 5 = 12 eggs.A similar problem is given at https://brainly.com/question/24459209
Solve 5x - 6y = 13 for y.
Answer:
13 + 5 into 6 Y equal y10 6 into 5 equal why into 13
The femur or thigh bone of an average human is 480 millimeters long. The spinal cord of an average human is 45 centimeters long. What is the total length of a spinal cord and a femur in meters
PLEASE NEED HELP
Answer:
0.93m
Step-by-step explanation:
Convert 480 mm to m
480mm x (1m/1000mm) = 0.48m
Convert 45 cm to m
45cm x (1m/100cm) = 0.45m
Add the two numbers up
0.48m + 0.45 m = 0.93 m
If the height of a parallelogram is 11m and the
base is 6.9m, what is the area of the parallelogram?
Answer:
[tex] \huge{ \boxed{ \tt{75.9}\sf \: {m}^{2} }}[/tex]
Step-by-step explanation:
[tex] \underline{ \sf{Given}} : [/tex]
[tex] \star{ \sf{ \: Height \: of \: a \: parallelogram \: (h) \: = 11m}}[/tex]
[tex] \star{ \sf{ \: Base \: of \: a \: parallelogram \: (b) \: = 6.9m}}[/tex]
[tex] \underline{ \sf{Finding \: the \: area \: of \: the \: parallelogram \: having \: height \: of \: 11m \: and \: base \: of \: 6.9m}} : [/tex]
[tex] \boxed{ \sf{Area \: of \: parallelogram = base \: ∗ \: height}}[/tex]
[tex] \mapsto{ \sf{Area \: of \: parallelogram = 6.9m \: ∗ \: 11m}}[/tex]
[tex] \mapsto{ \sf{Area \: of \: a \: parallelogram = 75.9 \: {m}^{2} }}[/tex]
Hope I helped!
Best regards! :D
~[tex] \sf{TheAnimeGirl}[/tex]
[tex] \huge\sf {\dag Question} [/tex]
If the height of a parallelogram is 11m and the base is 6.9m, what is the area of the parallelogram?
[tex] \huge\sf {\dag Solution } [/tex]
[tex] {\underline {\underline {\rm { Given:}}}} [/tex]
h ( height of the parallelogram ) = 11mb ( base of the parallelogram ) = 6.9m[tex] {\underline {\underline {\rm { To \: find :}}}} [/tex]
Area of the parallelogram
[tex] {\underline {\underline {\rm { Calculation :}}}} [/tex]
We know that,
[tex] {\underline {\underline {\rm {\red { Ar. \: of \: parallelogram = h \times b}}}}} [/tex]
Substituting values-
[tex] \sf {\implies Ar. \: of \: parallelogram = 11 \times 6.9}[/tex]
[tex] \sf {\implies Ar\: of \: parallelogram = 75.9{m}^{2}}[/tex]
_________________________________b. Find the equation of the line through (-3, 3) with slope 4.
Answer:
Step-by-step explanation:
use the formula y=mx+b. the first number in the parenthesis is -3 so that is x. 3 is y and the slope is m
so it is 3=4(-3)+b
Data will be collected on the following variables. Which variable can be considered discrete? A. The height of a person B . The weight of a person C. The length of a person’s arm span D The time it takes for a person to solve a puzzle E The number of books a person finished reading last month
Answer: E: The number of books a person finished reading last month
Step-by-step explanation:
First, a discrete variable is a variable that only can take some given values in a set, the discrete variables are usually not dense, and a continuous variable is a variable that can take any value in a range (where the accepted values are dense).
So, for example, the set of the natural numbers is discrete, and the set of the real numbers can represent a continuous variable.
Here the only option that is really discrete will be the number of books that a person finished reading last month because here only positive whole numbers are accepted (you can not finish a 0.454 of a book)
The other options are continuous because all are classical measures.
For example, the weight of a person can jump between:
75.6kg and 75.7kg.
So you could think that this is discrete because the values between 75.6kg and 75.7g are not shown with our measuring device, but those will be added in the error of the measure because the weights between 75.6kg and 75.7kg are actually possible, so they must be accepted.
Option E is right.
A. The height of a person. Height is a continuous variable.
B . The weight of a person. Weight is a continuous variable.
C. The length of a person’s arm span. Length is a continuous variable.
D. The time it takes for a person to solve a puzzle. Time is a continuous variable.
E. The number of books a person finished reading last month. The number of books is discrete variable.
Learn more: https://brainly.com/question/11315571
what is 0.76 +9.786
Answer:10.546
Step-by-step explanation:
0.76+9.786=10.546
What is the length of side AC as shown on the coordinate plane?
0 1 units
O 3 units
O 4 units.
O 6 units
Answer:
Easy, 4 units
Step-by-step explanation:
what decimal is equilvalent to 3/8
Answer:
0.375
Step-by-step explanation:
Answer:
0.375.....................
Find the z score that corresponds to P30 (the 30th percentile).
Answer:
Step-by-step explanation:
From the standard normal distribution tables it is -0.524.
The value of Z score for P 30 is - 0.524
What is Z score ?Z score is the value that relates the data with the mean of the data , A ,0 , Z score means the data point is equal to the mean.
It is given to find
the z score that corresponds to P 30%
From the standard normal distribution table the value corresponding to 30 % is -0.524.
Therefore the value of Z score for P 30 is - 0.524
To know more about Z Score
https://brainly.com/question/15016913
#SPJ2
Landon mixes 6 parts yellow paint with 3 part blue paint to make green she adds 1 more part of yellow to change the shade of green. What is the new ratio of yellow to blue?
A. 3 to 7
B. 4 to 7
C. 6 to 4
D. 7 to 3
Answer:
d
Step-by-step explanation:
_______ will produce a rational answer when multiplied by 0.9
Answer:
10
Step-by-step explanation:
A rational number is 9.
When you multiply 0.9x10 you get the sum of 9.
9 is a rational number because it is a perfect square and an integer.
I hope this helps you understand :)
Predict the number of pancakes that would have 48 chocolate chips
Answer:
You can’t determine that.
Step-by-step explanation:
За – 6а + 2 = 8а + 20 – 5а
Answer:
a = -3
Step-by-step explanation:
3a - 6a + 2 = 8a + 20 - 5a
Combine Like Terms
-3a + 2 = 3a + 20
-2 -2
-------------------------------------
-3a = 3a + 18
-3a -3a
-------------------------------------
-6a = 18
---- ----
-6 -6
a = -3
6. Mary and Steve each travel 845 miles. Mary drove an average of 5 mph faster than Steve and completed the trip in one hour's less time
than Steve. What was each person's average speed?
Answer:
Steve had an average speed of 62.55 mph while Mary had an average speed of 67.55 mph
Step-by-step explanation:
Here, we want to calculate the average speed of each of the two.
From the question, we are told that Mary drove an average of 5 mph faster than steve.
So, let the average speed of Steve be x mph, this means that the average speed of Mary will be (x + 5) mph
Mathematically;
Time = distance/speed
Time taken by Steve = 845/x hours
Time taken by Mary = 845/(x + 5)
But Mary took an hour less to complete her own trip;
This means that;
if we add one hour to the time spent by Mary, then we will have the time spent by Steve
845/(x + 5) + 1 = 845/x
845/(x + 5) = 845/x -1
845/(x + 5) = (845 - x)/x
Cross multiply;
845(x) = (x + 5)(845-x)
845x = x(845-x) + 5(845-x)
845x = 845x-x^2 + 4225 - 5x
x^2 + 5x - 4225 = 0
We can solve this using the quadratic formula;
x = -b ± √(b^2 - 4ac)/2a
where a = 1 , b = 5 , c = -4225
x = -5 ± √(5^2 - 4(1)(-4225)/2(1)
x = -5 ± √(25 + 16,900)/2
x = -5 ± √(16,925)/2
x = (-5 + 130.1)/2 or (-5-130.1)/2
We ignore the negative side as speed cannot be negative
x = (-5 + 130.1)/2 = 62.548 which is approximately 62.55 mph
So steve’s speed is 62.55 mph while Mary’s speed = 62.55 + 5 = 67.55 mph
Evaluate and simplify the expression when x=14 and y=1/3
2x/13-9y=?/?
Answer:
Step-by-step explanation:
It’s 14/5 lol
C(x)=15+(15x)(.07) how do i solve this question
Answer:
Step-by-step explanation
At a sale, dresses were sold for $34 each. This price was 85% of a dress's original
price. How much did a dress originally cost?
Answer:
The original price was $40
Step-by-step explanation:
let x = original price
34= 0.85x
Divide both sides by 0.85
34/0.85 = x
40 = x
Check:
0.15 × 40 = 6
40 – 6 = 34
Perform the indicated operation. Express answer as a simplified fraction (You may have
improper fractions)
Step-by-step explanation:
[tex]4 + \frac{2}{3} = \frac{3 \times 4 + 2}{3} = \frac{14}{3} = 4 \frac{2}{3} [/tex]
[tex] \frac{67}{71} \times \frac{381}{399} = \frac{67 \times 381}{71 \times 399} = \frac{25527}{28329} = \frac{8509}{9443} [/tex]
[tex] \frac{684}{795} \div \frac{24}{37} = \frac{684}{795} \times \frac{37}{24} = \frac{25308}{19080} = 1.33[/tex]
