if
possible show work
8. Use Implicit Differentiation to find y', then evaluate y at the point (-1,2): (6 pts) 3² - x² = x + 5y
Answers
Using implicit differentiation, we can find the derivative of \(y\) with respect to \(x\) and evaluate it at a given point. For the equation \(3^2-x^2=x+5y\), the derivative of \(y\) with respect to \(x\) is \(\frac{-2x-1}{5}\). Evaluating \(y\) at the point \((-1,2)\), we find that \(y=\frac{9}{5}\).
To find the derivative of \(y\) with respect to \(x\) using implicit differentiation, we differentiate both sides of the equation \(3^2-x^2=x+5y\) with respect to \(x\). On the left side, the derivative of \(3^2\) with respect to \(x\) is \(0\) since it is a constant. The derivative of \(-x^2\) with respect to \(x\) is \(-2x\). On the right side, the derivative of \(x\) with respect to \(x\) is \(1\). The derivative of \(5y\) with respect to \(x\) is \(5\) times the derivative of \(y\) with respect to \(x\), which is \(5y'\).
Combining these results, we have \(0-2x=1+5y'\). Rearranging the equation, we get \(5y'=-2x-1\). Dividing both sides by \(5\) gives us \(y'=\frac{-2x-1}{5}\). To evaluate \(y\) at the point \((-1,2)\), we substitute \(x=-1\) into the equation \(3^2-x^2=x+5y\) and solve for \(y\). We have \(9-(-1)^2=(-1)+5y\), which simplifies to \(9-1=-1+5y\). This further simplifies to \(8=-1+5y\). Solving for \(y\), we get \(y=\frac{9}{5}\). Therefore, the derivative of y with respect to x is \(\frac{-2x-1}{5}\), and when \(x=-1, y\) equals \(\frac{9}{5}\).
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Related Questions
The line 2x + 3y = 8 meets the curve 2x^2 + 3y^2 =110 at the points A and B. Find the coordinates of A and B.
extra: This is the first time I’ve seen this type of question without a diagram. Pls help!
Answers
Answer:The cordinates of A and B are (-3.8, 5.2) and (7, -2).
Step-by-step explanation:From (1), we get x = (8 - 3y) / 2 ––(3)
Substitute (3) into (2),
2 [(8 - 3y) / 2]² + 3y² = 110
(8 - 3y)² + 3y² = 220
15y² - 48y - 156 = 0
Therefore y = 5.2, then x = (8 - 3×5.2) / 2 = -3.8
OR y = -2, then x = [8 - 3×(-2)] / 2 = 7
Answer:
The coordinates are A. (-3.8, 5.2) and B. (7, -2).
Step-by-step explanation:
At A and B the coordinates satisfy both equations so we solve simultaneously using substitution:
2x^2 + 3y^2 = 110
2x + 3y = 8
From the above equation
x = (8 - 3y)/2
So substituting for x in the first equation:
2 [(8-3y)/2]^2 + 3y^2 = 110
(8-3y)^2 / 2 + 3y^2 = 110
Multiply through by 2:
(8 - 3y)^2 + 6y^2 = 220
64 + 9y^2 - 48y + 6y^2 - 220 = 0
15y^2 - 48y - 156 = 0
3(5y^2 - 16y - 52) = 0
(5y - 26)(y + 2) = 0
y = 26/5, 2
y = 5.2, -2.
So substituting in 2x + 3y = 8
When y = -2:
2x - 6 = 8
2x = 14
x = 7.
When y = 5.2
2x + 3(5.2) = 8
2x = 8 - 15.6 = -7.6
x = -3.8.
Find the midpoint: (2,−7),(10,1) *
Answers
Answer:
The answer is
( 6 , - 3)Step-by-step explanation:
The midpoint M of two endpoints of a line segment can be found by using the formula
\(M = ( \frac{x1 + x2}{2} , \: \frac{y1 + y2}{2} )\)
where
(x1 , y1) and (x2 , y2) are the points
From the question the points are
(2,−7),(10,1)
The midpoint is
\(M = ( \frac{2 + 10}{2} , \: \frac{ - 7 + 1}{2} ) \\ = ( \frac{12}{2} \: , \: - \frac{6}{2} )\)
We have the final answer as
( 6 , - 3)Hope this helps you
Evaluate the function.
F(x) = -x^2+9x-17
Find F (-5)
Answers
⇒F(-5) just simply means that in the function F in the place of x you have to plug in -5 and simplify if possible.
\(f(-5)= -(-5)^{2} +9(-5)-17\\f(-5)=-(25)-45-17\\f(-5)=-25-45-17\\f(-5)=-70-17\\f(-5)=-87\)
the answer to f(-5) is -87
GOODLUCK!!
Helppppppppppp!!!!!!!!!!!!!!!!!!!
Answers
\(\sqrt{576 x^4 y^6}\\\\\\=\left(24^2 x^4 y^6\right)^{\tfrac 12}~~~~~~; \left[\sqrt a = a^{\tfrac 12} \right]\\\\\\=(24^2)^{\tfrac 12} \times (x^4)^{\tfrac 12} \times (y^6)^{\tfrac 12}\\\\\\=24^{\tfrac 22} \cdot x^{\tfrac 42} \cdot y^{\tfrac 62}\\\\=24 x^2 y^3\)
how many different prime numbers are factors of the positive integer n ? (1) four different prime numbers are factors of 2n (2) four different prime numbers are factors of n2
Answers
A prime number doesn't have sequence so, it cannot be model with sequence.
Prime numbers are number that can only be divided by itself and 1.
E.g 2,3,5,7,11,13,17,19,23,29 etc.
So, note that this sequence doesn't have a pattern, it is neither Geometry Progression nor Arithmetic Progression.
Now, let take look at the model given
If n is prime, then 2n-1 is prime
Let take 5 for
n=5 is a prime number
2n-1=2(5)-1=10-1=9
9 is not a prime number so the model doesn't work
A prime number doesn't have sequence so, it cannot be model with sequence.
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Write a story starting with the following lines. ( no romance included)
The hospital is stuffy and the air has an undertone of bleach. the walls are magnolia and are scraped in places from the hundreds of trolleys. that have bumped into them. The picture in the wall are cheap benign prints of uplifting scenes and above the double doors are large blue plastic signs with the areas of hospital lie ahead.
Answers
Answer:
The hospital is stuffy and the air has an undertone of bleach. the walls are magnolia and are scraped in places from the hundreds of trolleys. that have bumped into them. The picture in the wall are cheap benign prints of uplifting scenes and above the double doors are large blue plastic signs with the areas of hospital lie ahead.I was comig through the two doors to see my grandpa and he was bareley alive then I walked with him back through the blue doors with the sam stuffy feeling after I walked through then as we approached the surgery room he miraculously recovered and walked away and no knows how it happened. Too this day the hospital employees wonder how this had happened
Point P is plotted on the coordinate grid. If point S is 10 units above point P, what are the coordinates of point S?
On a coordinate grid from negative 12 to positive 12 in increments of 2, a line PQ is drawn with P plotted at the ordered pair 6, negative 4.
(1 point)
1. (−4, −4)
2. (−4, 6)
3. (6, 6)
4. (6, −4)
will give best and tanks
Answers
Step-by-step explanation:
(−4, −4)
2. (−4, 6)
3. (6, 6)
4. (6, −4)
At approximately what angle does the wire meet the ground? 33. 6° 39. 8° 50. 2° 56. 4°.
Answers
Answer:
your question is stated and the answer to your question is ⇒56.4°
Q: At approximately what angle does the wire meet the ground? 33. 6° 39. 8° 50. 2° 56. 4°.
Step-by-step explanation:
just taken the review on edge 2022 also given in the picture below have a great day :)
At an angle of 56.4 degrees does the wire meet the ground.
GivenTo support a tree damaged in a storm, a 12-foot wire is secured from the ground to the tree at a point 10 feet off the ground.
The tree meets the ground at a right angle.
What is the right angle?A right-angled triangle is a triangle having an angle between the base and the perpendicular is 90°.
To calculate the angle α between the wire and the ground we need to find the sine of that angle or sin(α).
The formula of the sin angle is;
\(\rm Sin\alpha = \dfrac{Perpendicular}{Hypotenuse}\\\\Sin \alpha =\dfrac{a}{c}\)
Where a = 10 and c = 12.
Then,
\(\rm Sin\alpha = \dfrac{Perpendicular}{Hypotenuse}\\\\Sin \alpha =\dfrac{a}{c}\\\\Sin\alpha = \dfrac{10}{12}\\\\Sin\alpha =0.8334\\\\\alpha = sin{-1} (0.8334)\\\\\alpha = 56.4 \ degrees\)
Hence, at an angle of 56.4 degrees does the wire meet the ground.
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math question!!! i need help
Answers
Answer: 2nd one
Step-by-step explanation:
In a class of c child, ¾ are boys. How many of them are girls?
Answers
Answer:
I'm going to say that there is one girl in the class
1
Tony runs 13 feet per second.
Zach runs 296 feet in 23 seconds.
Ron runs 1 mile in 527 seconds.
Liz runs 597 feet in 1 minute.
Answers
Thus, Tony runs at a speed of 13 feet per second, Zach runs at a speed of 12.87 feet per second, Ron runs at a speed of 10 feet per second, and Liz runs at a speed of 9.95 feet per second.
Tony runs at a speed of 13 feet per second, which means he covers a distance of 13 feet in one second.
Zach, on the other hand, runs 296 feet in 23 seconds, so we need to calculate his speed. To do that, we divide the distance by the time, which gives us 12.87 feet per second.
Ron runs one mile in 527 seconds, which is equivalent to 5,280 feet. Therefore, his speed is 10 feet per second, which is the same as running at a pace of 6 minutes per mile. Finally, Liz runs 597 feet in one minute, so her speed is 9.95 feet per second.
In summary, Tony runs at a speed of 13 feet per second, Zach runs at a speed of 12.87 feet per second, Ron runs at a speed of 10 feet per second, and Liz runs at a speed of 9.95 feet per second.
It's important to note that the distances and times given in these examples are specific to each person and may vary depending on the circumstances.
However, by calculating their speeds, we can compare their performances and determine who is running faster or slower than the others.
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what is the domain of the graph? please right answers only !!:(
Answers
Answer:
[-2, -1, 1, 2, 4]
Step-by-step explanation:
The domain is a list of x-values. pls mark brainliest
help
Fill in the blank. (Simplify your answer completely.) 6 yd 3 ft 7 in. = in.
Answers
The answer is 231 inches.
To understand how we arrive at this answer, let's break down the given measurement step by step. We have 6 yards, 3 feet, and 7 inches.
Starting with yards, we know that 1 yard is equal to 3 feet, so 6 yards would be equivalent to 6 * 3 = 18 feet. Adding the 3 feet given, we have a total of 18 + 3 = 21 feet.
Moving on to inches, we know that 1 foot is equal to 12 inches. So, the 21 feet we calculated earlier would be equal to 21 * 12 = 252 inches. Finally, adding the 7 inches given, we get a total of 252 + 7 = 259 inches.
Therefore, 6 yards 3 feet 7 inches is equal to 259 inches.
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Find the regression equation and the final answer
PLEASEE HELP
Answers
The required regression equation is y=−15.9x+1081.6 and new cases for 2008 is 950.
How to find regression equation visit?To find the linear regression equation that represents the given set of data, we need to find the slope and y-intercept of the line of best fit.
We can use the following formulas to find the slope and y-intercept:
\($\begin{align*}\text{slope } b &= \frac{\sum_{i=1}^{n}(x_i - \overline{x})(y_i - \overline{y})}{\sum_{i=1}^{n}(x_i - \overline{x})^2} \\text{y-intercept } a &= \overline{y} - b\overline{x}\end{align*}\)
where n is the number of data points, \($x_i$\) and \($y_i$\) are the i th values of x and y, respectively, \($\overline{x}$\) and\($\overline{y}$\) are the means of x and y, respectively.
Using the given data, we can calculate:
\(\overline{x} &= \frac{0+1+2+3}{4} = 1.5 \\overline{y} &= \frac{998+1047+1106+1084}{4} = 1058.75\)
\(\sum_{i=1}^{n}(x_i - \overline{x})(y_i - \overline{y}) &= (0-1.5)(998-1058.75) + (1-1.5)(1047-1058.75) \&\quad+ (2-1.5)(1106-1058.75) + (3-1.5)(1084-1058.75) \&= -79.5 \\sum_{i=1}^{n}(x_i - \overline{x})^2 &= (0-1.5)^2 + (1-1.5)^2 + (2-1.5)^2 + (3-1.5)^2 \&= 5 \\end{align*}\)
Therefore, the slope is:
\($\begin{align*}b &= \frac{-79.5}{5} \&= -15.9 \\end{align*}\)
The y-intercept is:
\(\begin{align*}a &= 1058.75 - (-15.9)(1.5) \&= 1081.55 \\end{align*}\)\($\begin{align*}a &= 1058.75 - (-15.9)(1.5) \&= 1081.55 \\end{align*}\)
So the linear regression equation is:
y=−15.9x+1081.6
To find the projected number of new cases for 2008 (which is 8 years after 2000), we substitute x=8 into the equation and round to the nearest whole number:
\($\begin{align*}y &= -15.9(8) + 1081.6 \&= 949.8 \&\approx \boxed{950}\end{align*}\)
Therefore, the projected number of new cases for 2008 is 950.
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Situation:
A 9 gram sample of a substance that's
used for drug research has a k-value of
0.1459.
N = -kt
Noe
No initial mass (at time t = 0)
N = mass at time t
k = a positive constant that depends on
the substance itself and on the units
used to measure time
t = time, in days
Answers
The given k-value of 0.1459, we can calculate the amount of the sample left after any given amount of time.
What is amount?Amount is a numerical quantity that is used to measure the size or magnitude of something. It is typically expressed in terms of a unit of measure such as a dollar, pound, or other currency.
The given k-value of 0.1459 corresponds to the rate of decay of the 9 gram sample of the substance over time. The equation for determining the amount of the sample left after a certain amount of time (t) is: N = -kt, where N is the amount of the sample left after the given amount of time, k is a positive constant that depends on the substance itself and on the units used to measure time, and t is the amount of time in days.
N = N0 e^(-kt)
for half life N/N0 = 1/2 and k = 0.1459
1/2 = e^(-0.1459t)
=> -0.1459 t = ln(0.5)
t = - ln(0.5) /0.1459
= 4.8 days
Therefore, with the given k-value of 0.1459, we can calculate the amount of the sample left after any given amount of time.
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Complete question is:
A 9 gram sample of a substance that's used for drug research has a K value of 0.1459
Find the substances half-life in days, and round answer to the nearest ten. ( exponential decay )
Translate to a system of equations: the sum of two numbers is fifteen. One number is three less than the other. Determine the system of equations. Call the first number m and the second number n.
Answers
The system of equation is m = 15 - n and the numbers m and n are 9 and 6 respectively.
What are equations?A mathematical statement known as an equation is made up of two expressions joined together by the equal sign.
A formula would be 3x - 5 = 16, for instance.
When this equation is solved, we discover that the value of the variable x is 7.
So, according to the given statements the equations will be:
1st number = m
2nd number = n
m - 3 = n
Now,
m + n = 15 ..... (1)
m - 3 = n ...... (2)
Obtain from equation (1):
m + n = 15
m = 15 - n ...... (3)
Fill in the equation with the value of m from equations (3) and (2):
m - 3 = n
Now, calculate:
15 - n - 3 = n
15 - 3 = n + n
12 = 2n
n = 12/2
∴ n = 6
Enter the value of n into equation (3) for m:
m = 15 - n
m = 15 - 6
m = 9
∴ m = 9 and n = 6
Therefore, the system of equation is m = 15 - n, and the numbers m and n are 9 and 6 respectively.
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jill is taking 5 courses (or 15 credit hours). how many hours of homework should she expect each week in addition to her time spent inside the classroom?
Answers
Jill should expect an additional 30 to 45 hours of homework each week.
As a general rule of thumb, students can expect to spend 2-3 hours of homework for each hour spent in class. This means that for a 15 credit hour course load, Jill can expect to spend an additional 30 to 45 hours on homework each week.
However, this is just a rough estimate and the actual amount of time required will depend on the difficulty of the courses, the teaching style of the instructors, and the individual study habits and ability of the student. Additionally, some courses may require more time spent on projects, reading, or other assignments that are not factored into this estimate.
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If UV = 5x, VW = 2x, and UW = 7, what is UV?
Answers
Answer:
Do you have a pic of the problem?
Step-by-step explanation:
Only then, can i really edit this and provide an acurate answer...
pls & thx.
(a) The mean of the masses of a group of four student is 30 kg.
One student joins the group .The mean of the masses of the five students is 32 kg.
Find the mass of the student who joined the group.
(b)The mean of the five articles is 215 g. When another article is added, the mean of the masses of the six articles is 220 g. Find the mass of the sixth article.
Answers
Answer:
1) 40kg
2) 245kg
Step-by-step explanation:
What is the quotient?
-4/5 divided by 2
Answers
-(4/5) ÷2=-0.4
Explanation: The quotient is the answer to a division problem.
Answer:
-0.4
fraction form: -4/10 or -2/5
A triangle has an area of 125 square inches. The height of the triangle is 8 inches. Which equation
can be used to find the base of the triangle, b?
Answers
Answer:
(125*2)/8=b
Step-by-step explanation:
The way to find the area of a triangle is to multiply height and width then divide by two and 125 is the area. Then that means 125=250/2.
Since the height is 8 we can make the equation (125*2)/8.
Hopefully that was helpful and made sense.
PLEASE ANSWER ASAP !!!!!
Answers
Answer:
slope =-1
Step-by-step explanation:
i dont think there is any steps for this problem ;-;
A girl rides a bicycle with a speed of 10km/h for 2h and 15km/h for the next 3h. find the distance moved by her and average speed
Answers
Like this
find the exact values of the sine, cosine, and tangent of the angle. 255° = 300° − 45°
Answers
The exact values of the sine, cosine, and tangent of the angle 255° are -1/√2, 1/√2, and -1, respectively.
To find the exact values of the sine, cosine, and tangent of the angle 255°, we can use the identity that relates the trigonometric functions of an angle to the trigonometric functions of its complement.
By expressing 255° as the sum of 300° and -45°, we can determine the exact values of the trigonometric functions for the given angle.
We know that the sine, cosine, and tangent of an angle are periodic functions, repeating every 360 degrees. To find the exact values of the trigonometric functions for 255°, we can express it as the sum of 300° and -45°, where 300° is a multiple of 360°.
Since the sine, cosine, and tangent functions are odd or even functions, we can use the values of the trigonometric functions for 45° to determine the values for -45°.
For 45°:
sin(45°) = cos(45°) = 1/√2
tan(45°) = 1
Since cosine is an even function, cos(-45°) = cos(45°) = 1/√2.
Since sine is an odd function, sin(-45°) = -sin(45°) = -1/√2.
Using the definition of tangent as the ratio of sine to cosine, tan(-45°) = sin(-45°) / cos(-45°) = (-1/√2) / (1/√2) = -1.
Therefore, for the angle 255°:
sin(255°) = -1/√2
cos(255°) = 1/√2
tan(255°) = -1
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If the equation is solved, which is true? (Round to the nearest tenth as needed)
A.
If 3+ n = 13, then n = 16
B
If 3 + n = 13, then n = 10.0
=
С
If 3 - n = 13, then n = 16.0
D
If n+ 3 = 13, then n = 4.33333...
E
I don't know yet
Answers
Answer:
B
If 3+n=13,then n=10.0
How to find the short sides of a right angle triangle if your only given the length of the hypotenuse which is 15. And the shorts sides are equal to each other.
Answers
a
2
+
b
2
=
c
2
,
a
2
+
b
2
=
c
2
,
can be used to find the length of any side of a right triangle. right angle has a value of 90 degrees (
90
∘
90
∘
). A right triangle is a triangle in which one angle is a right angle. The relation between the sides and angles of a right triangle is the basis for trigonometry.
The side opposite the right angle is called the hypotenuse (side
c
c
in the figure). The sides adjacent to the right angle are called legs (sides
a
a
and
b
b
). Side
a
a
may be identified as the side adjacent to angle
B
B
and opposed to (or opposite) angle
A
A
. Side
b
b
is the side adjacent to angle
A
A
and opposed to angle
B
B
.
The hypotenuse c, opposite the right angle, is the longest side. The legs are shorter and may be the same or different lengths, and are perpendicular to each other in a right triangle.
An executive invests $27,000, some at 7% and the rest at 4% annual interest. If he receives an annual return of $1,530, how much is invested at each rate?
Answers
hi
Let's call money invested at 7% X and the one at 4% Y
So we have :
X+Y = 27 000 (1)
0.07X + 0.04 Y = 1 530 (2)
As X+Y = 27 000 then Y = 27 000 -X
then we have in line (2)
0.07X + 0.04 ( 27 000 -X) = 1 530
0.07X + 1080 -0.04 X = 1 530
0.07X - 0.04X = 1530 - 1080
0.03X = 450
X = 450 / 0.03
X = 15 000
Now X = 15 000
so Y = 27 000 - 15 000 = 12 000
Answer is : 15 000 dollars were invested at 7% and 12 000 at 4%
Let's check to be sure :
15 000 * 0.07 = 1 050
12 000 *0.04 = 480
and 1 050 + 480 = 1 530
-2/3x + 9 = 4/3x -3
Answers
Answer:
Step-by-step explanation:
Answer:
x = 6
Step-by-step explanation:
To solve, move all the x’s to one side and all the numbers. Remember when moving numbers to the other side of an equation, the sign changes from either a positive to a negative or vise versa.
9 + 3 = 4/3x + 2/3x
Next, add the like terms.
9+3=12
When adding fractions, add the numerator (top number), but first change denominator (bottom number) if not the same. Here, we don’t need to.
4/3x+2/3x=6/3x
So,
12 = 6/3x
Then, we have to divide each side by 6/3 to make the x alone.
12/6/3 = 6/3x/6/3
To divide with fractions, multiply the reciprocal (opposite number on number line):
12/1·3/6 = x
36/6 = x
6 = x
After sitting out of a refrigerator for a while, a turkey at room temperature 70°F is placed into an oven. The oven temperature is 300°F Newton's Law of Heating explains that the temperature of the turkey will increase proportionally to the difference between the temperature of the turkey and the temperature of the oven.
Answers
What is the next term of the geometric sequence?
3,15,75,
Answers
Answer:
375
Step-by-step explanation:
3x5=15
15X5=75
75x5=375
Answer: 375
Step-by-step explanation: Hello!
First, we need to identify what the sequence is.
It seems to multiplied by 5 every time.
3x5=15x5=75x5=?
So if we follow that sequence we can determine the next one will be
75 x 5
which equals
375
75x5=375
Hope this helps!