A. Find the derivative of the function f in the following equations below. You do not need to solve for f. 1.6x2 + 5(f(x))? 36 11. 7x2 = 5f(x)2 + 4xf(x) + 1 B. Find the equation of the tangent line at point (1,2) of the following equation. For ease of notation, let y = f() In(x + y) = n'y + In(z? + 2) – 4
Answers
The equation of the tangent line at the point (1,2) is given by the equation:
y - 2 = ((1/3 - n') / (n' - 1/(z? + 2)))(x - 1), where n' and z? are constants.
To find the derivative of the function f in the given equations, we will differentiate with respect to the variable x using the appropriate rules of differentiation.
1. For the equation 1.6x^2 + 5(f(x)):
The derivative of 1.6x^2 with respect to x is 3.2x.
To find the derivative of 5(f(x)), we need to use the chain rule. Let's denote f(x) as u.
The derivative of 5u with respect to x is 5 * du/dx.
So, the derivative of the function f in this equation is 3.2x + 5 * du/dx.
2. For the equation 7x^2 = 5f(x)^2 + 4xf(x) + 1:
To find the derivative of f(x), we can use the implicit differentiation method. Let's denote f(x) as u.
Differentiating both sides with respect to x:
14x = 10f(x) * du/dx + 4x * du/dx + 4f(x) + 1 * du/dx.
Simplifying the equation:
14x - 4x * du/dx - 4f(x) = (10f(x) + 1) * du/dx.
Dividing both sides by (10f(x) + 1):
(14x - 4x * du/dx - 4f(x)) / (10f(x) + 1) = du/dx.
So, the derivative of the function f in this equation is (14x - 4x * du/dx - 4f(x)) / (10f(x) + 1).
B. To find the equation of the tangent line at the point (1,2) of the equation In(x + y) = n'y + In(z? + 2) – 4, we need to find the slope of the tangent line at that point. Let's denote y = f(x).
Differentiating both sides of the equation implicitly with respect to x:
(1/(x + y)) * (1 + dy/dx) = n' * dy/dx + (1/(z? + 2)) * dz/dx.
Substituting the values x = 1 and y = 2 into the equation:
(1/(1 + 2)) * (1 + dy/dx) = n' * dy/dx + (1/(z? + 2)) * dz/dx.
Simplifying the equation:
1/3 * (1 + dy/dx) = n' * dy/dx + 1/(z? + 2) * dz/dx.
To find the slope of the tangent line, we need to solve for dy/dx. Rearranging the equation, we have:
dy/dx = (1/3 - n') / (n' - 1/(z? + 2)).
Therefore, the equation of the tangent line at the point (1,2) is given by the equation:
y - 2 = ((1/3 - n') / (n' - 1/(z? + 2)))(x - 1), where n' and z? are constants.
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Related Questions
i need the solution for
Answers
Step-by-step explanation:
\( - 2x + 4y = - 4 \\ 2x + 8y = 16 \\ 2x = 16 - 8y \\ x = \frac{16 - 8y}{2} \\ x = 8 - 4y \\ - 2(8 - 4y) + 4y = - 4 \\ - 16 + 5y + 4y = - 4 \\ 9y = 12 \\\)
\( y = \frac{12}{9} = 1.33 \\ x = 8 - 4y \\ x = 8 - 4 \frac{12}{9} \\ x = 8 - \frac{48}{9} \\ x = 2.67 \\ \)
(2.67, 1.33)
GIVING BRAINLIEST! (YOU MUST ANSWER CORRECTLY)
Answers
Answer:
100
Step-by-step explanation:
did you do tangent?
if so
you know that:
you needed to use a scientific calculator and use the TAN button
formula:
Tan 60=100/x
if not
you could measure but it might not have been exact and you should just use the calculator
If you are standing 75 ft away from a tree and looking up at the top at a 40° angle, what is the height of the tree?
Answers
Answer:
Step-by-step explanation:
Sometimes linear equations are written in forms other than y=mx+b . One common form looks like Ax+By=C .When you see an equation like this, you can find the slope and y-intercept by solving the equation for y, rewriting it into slope-intercept form.Rewrite 6x+2y=6 into slope-intercept form by solving for y.y=______From that we can see that:m=____b=____
Answers
Okay, here we have this:
Considering the provided equation, we are going to rewriting it into slope-intercept form. So we obtain the following:
6x+2y=6
2y=-6x+6
y=(-6x+6)/2
y=-3x+3
Finally we obtain that the equation of the line is slope-intercept form is y=-3x+3. Then replacing in y=mx+b, we have:
y=-3x+3
y=mx+b
Then, m=-3 and b=3.
Margaret and Sam each drew a triangle with a base of length 1 cm. The height of Sam's triangle is one-fourth the height of Margaret's
triangle.
How many times greater is the area of Margaret's triangle than the area of Sam's triangle?
A. 2
B. 4
C. 6
D. 8
E. 16
Answers
2x-y ;x=5,y=1 evaluating algebraic expressions
Answers
Answer:
9
Step-by-step explanation:
2(5)-(1)
10-1
9
X + 12 >7
HELP YOU NOW PLEASE
Answers
Answer:
x>−5
Step-by-step explanation:
Simplify the rational expression. 3x^3+4x+5/x+3
Answers
Answer:
hey its 8
Step-by-step explanation:
Hold on, our servers are swamped. Wait for your answer to fully load.
Algebra Find the value of x.
Answers
Answer:
8 :)
Step-by-step explanation:
Side 1: 15
Side 2: 14
Side 3: 7 + x
Side 1 and 3 are the same length so we subtract :D
15 - 7 = 8
Have an amazing day!!
Please rate and mark brainliest!!
Translate the sentence into an inequality.
Twice the difference of a number 4 and is greater than 28.
Use the variable w for the unknown number.
Answers
Answer:
(4w) > 28
Step-by-step explanation:
Please mark helpful
Steve Fossett completed the first solo balloon circumnavigation of the world after 13.5 days. Assuming the balloon travelled along a circle of diameter 12 750 km, roughly what was the average speed of the balloon in km/h?
A) 12
B) 40
C) 75
D) 120
E) 300
Answers
Answer:
B) 40
Step-by-step explanation:
Average speed = distance/time
Distance = 12750 km
Time = 13.5 days = 13.5*24 hours = 324 hours
Speed = 12750 km /324 h = 39.4 km/h ≈ 40 km/h
Correct option is B) 40
y=5+2x when x=4, what does
/
y equal
Answers
Answer:
y = 13
Step-by-step explanation:
Y = 5 + 2x but when x = 4 you replace any X variables with 4
So the equation now is 5 + 2(4) = 5 + 8 = 13
y = 13
hope with helped :)
What would it be reflected to?
Answers
what direction are you being asked to reflect them
Step-by-step explanation:
i can give an easy answer and explanation then
Can someone please help me I will mark brainliest please.
Answers
Answer:
GE = 8 inches
Step-by-step explanation:
The diagonals of a parallelogram bisect each other, then
GE = 2 × GH = 2 × 4 = 8 inches
2. Are the two expressions
equivalent when x= 5?
9(4x + 2)
36x + 18
Circle one:
Yes
No
Work Space
Answers
Answer:
Hi, I'm new can I get marked as brainlieser? It would be highly appreciated.
Hope my answer helps :)
lets get into answering your question.
Step-by-step explanation:
first sub x into the equation (x=5) [it is already given]
9 ( 4*5 + 2) 36*5 + 18
= 9 (20+2) 180+18
= 9(22) + 198
198+198
= 369
369 makes a circle So YES
it is a circle.
Which inference is incorrect?
Answers
The analysis of the logical statement from among the options indicates that the inference that is not true is the option;
If not p, not q. q therefore not not qWhat is a logical statement?A logical statement is one which draws a conclusion based on an hypothesis.
The logical statement which is incorrect can be found by examining the specified statements as follows;
If p then q,
The converse statement , found by switching the positions of the hypothesis and the conclusion is therefore;
q therefore p
The inference is correct
The statement, if not p, not q . q therefore not not p
According to the law of contraposition, a conditional statement is true when the contrapositive statement is also true.
The statement if not p, not q. which is the contrapositive of the statement if q then p
The inference, q, therefore not not q is incorrect
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can someone please help me? also please explain or you’ll get reported ;)
Answers
Answer:
PX = 2√11
Step-by-step explanation:
here's your solution
==> ZX = 12 m
==> ZP = 10 m
==> by using Pythagoras theorem
==> PX^2 = ZX^2 - ZP^2
==> PX^2 = 12^2 - 10^2
==> PX^2 = 144 - 100
==> PX^2 = 44
==> PX = √44
==> PX = 2√11
hope it helps
The temperature changing every day by - 7/18 degrees FahrenheitWhat will be the change in the temperature after 3 days?
Answers
Six less than the product of five and a number is ten.
Group of answer choices
6−5x+10
5x−6=10
6−5x=10
5−6x=10
Answers
Answer:
• Let the number be x
\({ \boxed{ \boxed{ \boxed{ \mathfrak{ \: answer \: }} \: \dashrightarrow \: } \: { \rm{5x - 6 = 10 \: }}}}\)
Answer:
let , we do
\(5x - 6 = 10\)
please help me write quadratic equation given the roots and the leading coefficient
Answers
Answer:
Example Question: f(x) = 2x^2 + 2x - 1
If the leading coefficient is positive, the graph will be opening up (U) if the leading coefficient is negative, the graph will be opening down (n)
Roots are the x-intercepts that help find the axis of symmetry (add the two roots together and divide the result by 2 to get the axis of symmetry)
To find the vertex, simply imput the axis of symmetry into the given equation.
And that’s about it.
Step-by-step explanation:
I don’t know what you’re asking for??
Are all rational numbers integers?
Are all whole numbers zahlen numbers?
Answers
Answer:
yes all rational numbers are integers
yes all whole numbers are zahlen numbers
Consider the quadratic equation below.
4x²5= 3x + 4
Determine the correct set-up for solving the equation using the quadratic formula.
O A.
OB.
O C.
H=
AH=
O D.
H=
H =
-(3) ± √(3)²-4(-4)(1)
2(1)
−(−3) ± √(-3)² − 4(4)(9)
2(4)
-(3)± √(3)¹-4(-4)(-9)
2(-4)
-(-3) ± √(-3)²-4(4)(-9)
2(4)
Answers
Answer:
Option A:
H = 4, A = 5, B = -3, C = -4
-(B) ± √(B²-4AC)
2A
= -(-3) ± √((-3)²-4(4)(-5))
2(5)
= 3 ± √49
10
= 3 ± 7
10
Hence, x = (3 + 7)/10 or x = (3 - 7)/10, i.e. x = 1 or x = -0.4
Which culture will have the greatest population after 10 hours?
Answers
Answer:
b
Step-by-step explanation:
prove this question based on the knowledge of angle in a Circle.
Answers
Explanation
For alternate angles between parallel lines:
\(\angle SOP=\angle RQP=x\)Let's name this measure x
The measure of the arc SP is x and the measure of the arc PR is twice x, we have:
Then the measure of the arc RS is also x. We have:
\(arc(SP)=arc(SR)=x\)Since the arcs have the same measure, we can state that:
\(\bar{SP}=\bar{SR}\)
If B=-3x-7x^{2}B=−3x−7x 2 and C=-x^{2}-8-x,C=−x 2 −8−x, find an expression that equals 3B-3C3B−3C in standard form.
Answers
The standard form of 3B-3C is -24x²-9x+24.
What is an algebraic expression?An algebraic expression is consists of variables, numbers with various mathematical operations,
The given expressions are,
B = -3x-7x² and C=x²-8
The value of 3B-3C,
3B-3C= 3(-3x-7x²)-3(x²-8)
= -9x-21x²-3x²+24
= -24x²-9x+24
The standard form of 3B-3C is -24x²-9x+24.
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Chris signed-up for an experiment. The experimenter indicated that Chris would be placed into a group with nineteen other students based on a random number Chris received from the experimenter. The experimenter was most likely conducting ________________________-.
Answers
The experimenter was most likely conducting a randomized controlled trial, also known as a randomized experiment.
In this type of experiment, participants are randomly assigned to different groups, such as an experimental group or a control group, to ensure that any observed effects can be attributed to the intervention being tested rather than other factors.
In this case, the experimenter is using a random number to assign Chris to a group with nineteen other students, which suggests that there may be multiple groups involved in the experiment. This type of design is often used in scientific research to test the effectiveness of a new treatment, intervention, or program.
Randomized controlled trials are considered the gold standard in research design because they provide strong evidence for causal relationships between variables. By randomly assigning participants to different groups, researchers can control for confounding variables and ensure that any observed differences between groups are due to the intervention being tested.
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What is the answer to this question in this photo
Answers
Answer: -5x+6
Step-by-step explanation:
Find slope through slope formula (y₂-y₁)/(x₂-x₁)
By doing this you find that the slope is -5Then the y-intercept is found through the intersection of the y-axis.
If the sample space S is an infinite set, does thisnecessarily imply that any random variable X defined from S willhave an infinite set of possible values? If yes, say why. If no,give an example.
Answers
No, it does not necessarily imply that any random variable X defined from S will have an infinite set of possible values.
For instance, consider a random variable X that takes values from the set of natural numbers S = {1, 2, 3, ...}. We can define X as follows: X(n) = n for any n ∈ S.
Although S is an infinite set, X can only take values in S, which is also an infinite set, but not a larger one. Therefore, X has a countable (finite or infinite) set of possible values.
In general, the set of possible values of a random variable depends on how the variable is defined and not just on the size of the sample space.
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If m/CDE is a straight angle, DE bisects m/GDH, mZGDE = (8x-1), m/EDH = (6x +
m/CDF = 43°, find each measure.
x =
m/GDH=
mZFDH=
m/FDE =
Answers
Answer:
From the way the problem is worded:
CDE is a straight angle made up of three angles: CDF of measure 43, FDG of unknown measure and GDE of measure 8x + 1.
EDH is outside CDE and is of measure 6x + 15.
Since DE bisects GDH to form GDE and EDH, those latter two angles are equal and thus 8x + 1 = 6x + 15 and x = 7 and substituting 7 for x, both angles are equal to 57 degrees.
Since CDF is 43 and GDE is 57 and CDE is 180 in total, then FDG = 180 - 43 - 57 = 80 degrees.
ILL GIVE BRAINLIEST
A house on the market was valued at $445,000. After several years, the value decreased by 19%. By how much did the house's value decrease in dollars? What is the current value of the house?
Answers
Answer:
360,450
Step-by-step explanation:
First find 19 percent of 455,000
19*445000= 8455000
8455000/100= 84550
Then subtract:
445,000-84,550= 360,450
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