The chain rule of differentiation and then the power rule of differentiation.
2 sinh 7x cosh 7x.
Given the function:
y = sinh² 7x.
The derivative of y with respect to x is given by;
dy/dx = 2 sinh 7x . (7) cosh 7x
= 14 sinh 7x cosh 7x
To find the derivative of
y = sinh² 7x,
we will first use the chain rule of differentiation and then the power rule of differentiation.
The chain rule states that if
y = f(g(x)),
then
dy/dx = f'(g(x)) . g'(x).
Let u = 7x, hence,
y = sinh² u.
Then
dy/dx = dy/du .
du/dx= 2 sinh u .
7 cosh u= 2 sinh
7x cosh 7x.
Therefore, the correct option is;
2 sinh 7x cosh 7x.
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The area of a circle is 121 π ft². What is the circumference, in feet? Express your answer in terms of π.
Answer:
22π feet
Step-by-step explanation:
Area of circle = π r ²
121π = πr ²
121 = r ²
r = 11.
diameter D = 2r = 22.
Circumference = π X D
= 22π feet
If you invest $25.00 at 6% interest compounded monthly,
how much will you have after 1 year?
Point B has coordinates (4,1). The x-coordinate of point A is -4. The distance between point A and point B is 10 units. What are the possible coordinates of point A?
Given:
Point B has coordinates (4,1).
The x-coordinate of point A is -4.
The distance between point A and point B is 10 units.
To find:
The possible coordinates of point A.
Solution:
Let the y-coordinate of point A be y. Then the two points are A(-4,y) and B(4,1).
Distance formula:
\(D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)
The distance between point A and point B is 10 units.
\(\sqrt{(4-(-4))^2+(1-y)^2}=10\)
Taking square on both sides, we get
\((8)^2+(1-y)^2=100\)
\((1-y)^2=100-64\)
\((1-y)^2=36\)
Taking square root on both sides, we get
\((1-y)=\pm \sqrt{36}\)
\(-y=\pm 6-1\)
\(y=1\mp 6\)
\(y=1-6\) and \(y=1+6\)
\(y=-5\) and \(y=7\)
Therefore, the possible coordinates of point A are either (-4,-5) or (-4,7).
Write a proof for the statement.
If a quadrilateral is a square, then the quadrilateral is a rectangle.
Find the value of x. 130 Х
Answer:
60
Step-by-step explanation:
edge
if oil leaks from a tank at a rate of r(t) gallons per minute at time t, what does 120 0 r(t) dt represent?
the total amount of oil that leaks out over the entire time interval [0, 120].
integral ∫₀¹₂₀ r(t) dt represents the total amount of oil that leaks from the tank in 120 minutes.
To see why, consider the definition of an integral. If we divide the interval [0, 120] into small subintervals of width Δt, then the amount of oil that leaks out during each subinterval is approximately r(t)Δt. Summing up all these small amounts over the entire interval gives:
Σᵢ r(tᵢ) Δt
where tᵢ is the midpoint of the i-th subinterval. As we take the limit as the subinterval width goes to zero, this sum becomes the integral:
∫₀¹₂₀ r(t) dt
which represents the total amount of oil that leaks out over the entire time interval [0, 120].
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What information should you check for when a figure is congruent?
Two shapes are congruent if they have the same shape and size. We can also say if two shapes are congruent, then the mirror image of one shape is the same as the other.
Geometric figures that are congruent share the same size and shape. In other words, figures are congruent if they can be transformed into one another through a series of transformations, rotations, and/or reflections. When the sides and angles of two triangles match, the triangles are said to be congruent.
Triangles that have comparable sides and equal angles are said to be congruent. Indicating congruence is the sign “≅”.
identical in size and shape.
Congruent refers to objects that are exactly the same size and shape. Even if we flip, turn, or revolve the shapes, the shape and size must remain the same.
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Find the amount of time.
I=$10, P=$100, r=2%
What is the slope of the graph shown below
Answer:
B=-5
Step-by-step explanation:
Slope=rise/run
The line passes in
P1(-1,3)
and
P2(0,-2)
So slope=(3-(-2))/(-1-0)=5/-1=-5
A shirt costs $25. A sweater costs
3
as much as the shirt.
What is the cost, in dollars, of the sweater?
Answer:
28 dollars
Step-by-step explanation:
A shirt cost 25
a sweater Is 3 ”more”
so shirt= 25+ x Sweater: 28
Write an equation of the form y=a sin bx or y= a cos bx to describe the graph below
The sinusoidal equation of the trigonometric function is equal to y = 3 · sin (π · x / 4).
How to derive the sinusoidal equation behind a graph
In this problem we find the representation of a trigonometric function on Cartesian plane. This equation can be described by the following sinusoidal equation:
y = b + A · sin (2π · x / T)
Where:
b - MidpointA - AmplitudeT - Periodx - Independent variable.y - Dependent variable.If we know that b = 0, A = 3 and T = 8, then the sinusoidal equation is:
y = 3 · sin (π · x / 4)
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What is the least amount of cardboard in square centimetres needed to make this popcorn container 24 cm 12 cm 20 cm
Step-by-step explanation:
20 sc i don't no why but mybe it will be correct
Men and women aren’t equal evaluate this statement. Give some religous scriptures
Answer:
Indeed, men and women are not the same. They have structural differences in their genetic makeup that make them different and compatible with each other. In addition, they have differences in character, behavior, strength and even emotional sensitivity.
Even the scriptures themselves speak of differences between the two: according to the book of Genesis, the woman was created from the rib of Adam, the first man on earth. With this, the woman, theoretically, has one more rib than the man.
What is an equation for the line that passes through points (8,-3) and (9,10)
Answer:
y = 13x -107
Step-by-step explanation:
(10 - -3) / (9-8) =13
10= 13* 9 + b
b = 10 - 117 = -107
Please help question is in the picture
PLZ HELPPPPPPPPPPPPPPPPPPPPPPPP
Answer:
I think the awnser is probably b
Answer:
m=3.5h
Step-by-step explanation:
Just by looking at this, you know that it won't be either of the adding equations because it only works for the bottom input and output. So, we'll just look at the multiplying ones.
We know that multiplying should get us a bigger number (unless it's a fraction), so the equation h=3.5m won't work very well with this because h would be getting smaller not bigger.
That leaves us with m=3.5h.
To check this, I'll multiply 3.5 by 4 to see if it equals what m is on the table. Sure enough, it's 14. This also works with 2.5 and 8.75.
When can a correlation coefficient based on an observational study be used to support a claim of cause and effect? Never When the correlation coefficient is close to -1 or +1. When the correlation coefficient is equal to -1 or +1. When the scatterplot of the data has little vertical variation.
Never. Correlation does not imply causation. A correlation coefficient based on an observational study can only be used to suggest a relationship between two variables, but it cannot be used to support a claim of cause and effect.
Correlation is a measure of the relationship between two variables. It is used to measure how two variables move together. A correlation coefficient based on an observational study can only be used to suggest a relationship between two variables, but it cannot be used to support a claim of cause and effect. This is because correlation does not imply causation. A correlation coefficient close to -1 or +1 is an indication of a strong linear relationship between the two variables, but this does not necessarily imply a cause-and-effect relationship. Additionally, even if the scatterplot of the data has little vertical variation, this does not guarantee a cause-and-effect relationship. In summary, correlation coefficients based on observational studies can never be used to support a claim of cause and effect.
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Given the domain {-3, 0, 6}, what is the range for the relation 2x + y = 3?
Therefore, the range of the relation 2x + y = 3 for the given domain {-3, 0, 6} is {9, 3, -9}.
To determine the range of the relation 2x + y = 3 for the given domain {-3, 0, 6}, we need to find the corresponding range values when we substitute each value from the domain into the equation.
Substituting -3 into the equation, we have 2(-3) + y = 3, which simplifies to -6 + y = 3. Solving for y, we get y = 9.
Substituting 0 into the equation, we have 2(0) + y = 3, which simplifies to y = 3.
Substituting 6 into the equation, we have 2(6) + y = 3, which simplifies to 12 + y = 3. Solving for y, we get y = -9.
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-) A coach is buying snacks for 22 players at a soccer match. She pays a total of $77 to
buy each player a bottle of water and an energy bar. The price of one energy bar is $2.
Let w equal the price of a bottle of water. Write an equation that
represents the situation.
Answer:
22( w + 2 ) =77 and the amount of the water bottle would be 1.50
Step-by-step explanation:
Evaluate
|-9|=
Please helpp
Answer:
9
Step-by-step explanation:
How to solve your question
Your question is
|
−
9
|
|-9|
∣−9∣
Solve
1
Find the absolute value
|
−
9
|
9
Solution
9
4-17-(-6)-3 what is the answer??
Answer:
-13
Step-by-step explanation:
Why a sample is always smaller than a population?
Answer:
A sample is a subset of the population.
A method of assigning probabilities based upon personal judgment is referred to as the:
a. subjective method b. classical method c, Crelative frequency method
d, . non-probabilistic method.
A method of assigning probabilities based upon personal judgment is referred to as the subjective method. The correct answer is a.
The subjective method of assigning probabilities is based on personal judgment or subjective beliefs about the likelihood of events occurring. It involves incorporating individual knowledge, experience, and intuition to estimate the probabilities of different outcomes.
Unlike the classical method, which assigns probabilities based on equally likely outcomes, or the relative frequency method, which uses observed frequencies to determine probabilities, the subjective method relies on individual opinions and subjective assessments of probabilities.
In the subjective method, probabilities are not determined through mathematical calculations or empirical data. Instead, they are based on an individual's expertise, opinions, and subjective reasoning.
This method is commonly used in situations where objective data or historical information is limited or unavailable, such as in decision-making under uncertainty or when dealing with complex and uncertain scenarios.
The correct answer is a.
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Painter A can paint the house in 50 hours. Painter B can paint the same house in 35 hours. If they work together, about how many hours should it take them to paint the house?
It will take 20.6 hours to paint the house if both painter A and painter B worked together.
What is Proportion?Proportions are defined as the concept where two or more ratios are set to be equal to each other.
Suppose we have two ratio p : q and r : s.
If both these ratios are proportional, then we can write it as p: q : : r : s.
This is same as p : q = r : s or p/q = r/s
Let F represent the house fully painted.
Painting done by painter A in 50 hours = F
Painting done by painter A in 1 hour = F/50
Painting done by painter B in 35 hours = F
Painting done by painter B in 1 hour = F/35
If they both paint together,
Painting done by painter A and painter B in 1 hour = F/50 + F/35
= 85/1750 F
= 17/350 F
Time taken to paint 17/350 F = 1 hour
Time taken to paint F = 1 / (17/350)
= 20.588
≈ 20.6 hours
Hence time taken to paint the house by both working together is 20.6 hours.
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Please I need help with this
Answer:
2
Step-by-step explanation:
Can someone please help me with this, it’s urgent!!
Answer:
0.25
Step-by-step explanation:
1) the probability for Spinner-1 is:
1/3;
2) the probability for the Spinner-2 is:
3/4;
3) the required probability for the Spinner-1 and the Spinner-2 is (should be used the rule logical 'AND'):
1/3 * 3/4 = 1/4=0.25
Work out x^2- 2x
when x =4
Answer:
8
Step-by-step explanation:
\(x^2-2x \\x=4\\(4)^2-2(4)\\16-8\\8\)
Find the Least Common Denominator of
12 and 3
10
5
35
70
O 17
Answer:
the least common denominator is 12
Solve using elimination method.
4x-2y=10
2x+3y=1
Answer:
x=2, y=-1
Step-by-step explanation:
Remember: Multiply each equation by a suitable number so that the two equations have the same leading coefficient. Then, go from there.
At 6 a.m., the temperature was –8°C. By noon, the temperature had risen 6°C. The temperature at 6 p.m. was –10°C. Which integer represents the temperature change between noon and 6 p.m.?
–24
–12
–8
–4
Answer:
-8
Step-by-step explanation:
so -8 + 6 = -2. and then for that to drop to -10, it would have to change -8 degrees
Answer:
Step-by-step explanation:
-8 is the answer