The equation of the tangent to the curve at the point corresponding to the given value of the parameter will be x + y = c.
How to calculate the tangent of the parameter curves at a point?The curves are given below.
x = t⁵ + 1 and y = t⁶ + t
Then differentiate the functions with respect to t, then we have
[tex]\rm \dfrac{dx}{dt} = 5t^4\\[/tex] ...1
and
[tex]\rm \dfrac{dy}{dt} = 6t^5 + 1[/tex] ...2
Divide equation 2 by equation 1, then we have
[tex]\rm \dfrac{\dfrac{dy}{dt} }{\dfrac{dx}{dt} } = \dfrac{dy}{dx} = \dfrac{6t^5 + 1}{5t^4}[/tex]
Then the slope of the equation at t = −1, then we have
dy/dx = [6(-1)⁵ + 1]/[5(-1)⁴]
dy/dx = (-6+1)/5
dy/dx = -5/5
dy/dx = -1
Then the equation of the tangent line will be
y = -x + c
x + y = c
Where c is a constant.
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Please please please help meeeeeeeee and I WILL mark you brainliest
A population of paramecia, P, can be modeled using the exponential
function P(t) 3(2), where t is the number of days since the
population was first observed. Which domain is most appropriate
=
to use to determine the population over the course of the first two
weeks?
The appropriate domain of the population function is 0 ≤ t ≤ 14
How to determine the domain?The function is given as:
P(t) = 3(2)^t
From the question, we understand that the maximum time is 2 weeks.
2 weeks in days is 14 days
This means that the function is valid for 14 days i.e. t = 0 to 14
Hence, the appropriate domain of the population function is 0 ≤ t ≤ 14
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Combine the radicals [tex]9\sqrt{x} -3\sqrt{x} \\[/tex]
The combination of the radicals 9√x - 3√x will be equal to 6√x.
What is a radical?The radical is the symbol that is used to represent the root in the expression n√x.
The given radicals can be combined as shown below,
9√x - 3√x
Taking √x as the common term,
= √x(9-3)
= 6√x
Hence, the combination of the radicals 9√x - 3√x will be equal to 6√x.
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What is the product of (2x – 6)(2x + 6)
[tex]~~~(2x-6)(2x+6)\\\\=(2x)^2 -6^2~~~~~~~~~~~~~~~~~~~~~;[a^2 -b^2 = (a+b)(a-b)]\\\\=4x^2 -36[/tex]
Select the correct answer.
Consider the function given below.
f(x)= |x-51 +2
Which of the following statements about the y-values of the graph of the function is true?
OA. The y-values are all less than or equal to 5.
B.
The y-values are all greater than or equal to 5.
OC.
The y-values are all less than or equal to 2.
D.
The y-values are all greater than or equal to 2.
Answer: The correct answer is D.
Step-by-step explanation: A and B are incorrect because you can plug in 5 for x to get 2, and there are multiple values that can be greater than 5. C is incorrect because you cannot reach lower than 2. Therefore, the correct answer is D.
The y values are all greater than or equal to 2.
The correct option is D.
Given,
Function : f(x) = |x − 5| + 2
Here,
A function is a law that relates a dependent and independent variable.
The function is
f(x) = |x − 5| + 2
The domain of the function is all negative and positive integers.
The range is all the possible function values, the function value will always be greater than or equal to 2.
At x = 5 , f(x) = 2
Therefore, the y values are all greater than or equal to 2. The correct option is D.
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Which is a coefficient in the expression below?
(r – 2) + s(10 – t)
Answer:
-2
Step-by-step explanation:
coefficient is the number without a letter next to it
Choose the correct option that explains what steps were followed to obtain the system of equations below.
System B
A.
To get system B, the second equation in system A was replaced by the sum of that equation and the first equation multiplied by 3. The solution to system B will be the same as the solution to system A.
B.
To get system B, the second equation in system A was replaced by the sum of that equation and the first equation multiplied by -6. The solution to system B will not be the same as the solution to system A.
C.
To get system B, the second equation in system A was replaced by the sum of that equation and the first equation multiplied by -5. The solution to system B will not be the same as the solution to system A.
D.
To get system B, the second equation in system A was replaced by the sum of that equation and the first equation multiplied by 5. The solution to system B will be the same as the solution to system A.
To get system B, the second equation in system A was replaced by the sum of that equation and the first equation multiplied by 5. The solution to system B will be the same as the solution to system A.
How to find the relationship between two equations?
System A equations:
-x - 2y = 7 ------ (1)
5x - 6y = -3 ------(2)
We multiply the first equation by 5, to get :
-5x - 10y = 35 -----(3)
The sum of equation (2) and equation (3) gives:
-16y = 32
y = 32/-16
y = -2
Thus, solution of system B is;
-x - 2(-2) = 7
-x + 4 = 7
x = -3
So, the solution of system B is (-3, -2), that means the solution of both systems are same.
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If f(x) = (1/9)(9*), what is f(3)? A. 729 B. 81 C.1/729 D.1/81
Answer:
B. 81Step-by-step explanation:
Note. It is assumed * is x in the function notation.
GivenFunction f(x) = (1/9)(9ˣ)Rewrite it as:f(x) = 9⁻¹ 9ˣ = 9⁻¹⁺ˣ = 9ˣ⁻¹Find f(3)Substitute the value of x into equation:
f(3) = 9³⁻¹ = 9² = 81Correct answer choice is B
Which of the following best describes the slope of the line below?
Answer:
Zero
Step-by-step explanation:
the line is not going up or down therefore there is no slope
BRAINLIEST!!!!
Use triangle XYZ to answer the questions
Use special right triangles to help find the length of segment XY. What is the exact base of triangle XYZ?
What is the exact area of triangle XYZ? Leave your answer in RADICAL terms
What is the area of triangle XYZ to the nearest tenth of a Square feet
The trigonometric function gives the ratio of different sides of a right-angle triangle. The area of the triangle is 55.4256 ft².
What are Trigonometric functions?The trigonometric function gives the ratio of different sides of a right-angle triangle.
[tex]\rm Sin \theta=\dfrac{Perpendicular}{Hypotenuse}\\\\\\Cos \theta=\dfrac{Base}{Hypotenuse}\\\\\\Tan \theta=\dfrac{Perpendicular}{Base}[/tex]
where perpendicular is the side of the triangle which is opposite to the angle, and the hypotenuse is the longest side of the triangle which is opposite to the 90° angle.
For the given triangle the length of AB and BC can be written as,
[tex]\rm Sin \theta=\dfrac{Perpendicular}{Hypotenuse}\\\\\\Sin(30^o) = \dfrac{AB}{AC}\\\\\\AB = Sin(30^o) \times 16 \\\\\\AB=8\rm\ ft[/tex]
[tex]Cos \theta=\dfrac{Base}{Hypotenuse}\\\\\\Cos(30^o) = \dfrac{BC}{AC}\\\\\\BC = Cos(30^o) \times AC\\\\\\BC = 13.8564\rm\ ft[/tex]
Now, the area of the triangle is,
Area of triangle = 0.5× 8 × 13.8564 = 55.4256 ft²
Hence, the area of the triangle is 55.4256 ft².
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Estimate the quotient of 21.49 ÷ 3.76 using compatible numbers.
The quotient of 21.49 ÷ 3.76 using compatible numbers is approximately 5.69
What are quotients?Quotients are result derived from the ratio of two rational or integers. Given the expression
21.49 ÷ 3.76
Convert to fraction
21.49 ÷ 3.76 = 2140/100 ÷ 376/100
21.49 ÷ 3.76 = 2140/376
21.49 ÷ 3.76 = 5.69
Hence the quotient of 21.49 ÷ 3.76 using compatible numbers is approximately 5.69
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Which expression is equivalent to -6.50 -5.1 + 2.3c - 1.8?
Answer:
-13.4+2.3c
Step-by-step explanation:
Add the like terms.
-6.5-5.1-1.8=-13.4
-13.4+2.3c
Hope this helps!
If not, I am sorry.
A cylindrical water tank is 12 feet high and 10 feet in diameter. the entire tank, inside and out, is to be painted. if a gallon of paint covers 200 sq ft, how many gallons will be needed?
if we paint the tank on the outside, we'll be covering SA of surface area, however we're also painting it on the inside, so the area inside assuming the material thickness is negligible, we'll be covering SA as well, so we'll be needing SA + SA = 2SA ft² of paint to do the whole thing.
so, its diameter is 10, that means its radius is 5.
[tex]\textit{surface area of a cylinder}\\\\ SA=2\pi r(h+r)~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ h=12\\ r=5 \end{cases}\implies \begin{array}{llll} SA=2\pi (5)(12+5)\implies SA=170\pi \\\\\\ \stackrel{\textit{twice as much}}{2SA=340\pi } \end{array}[/tex]
now, hmmm we know that 1 gallon can do 200 ft², how many gallons are there in 340π ft²?
[tex]\begin{array}{ccll} gallons&ft^2\\ \cline{1-2} 1 & 200\\ x& 340\pi \end{array} \implies \cfrac{1}{x}~~=~~\cfrac{200}{340\pi } \\\\\\ 340\pi =200x\implies \cfrac{340\pi }{200}=x\implies \stackrel{gallons}{5.34}\approx x[/tex]
Mike buys a large goldfish for $22 and food for his new friend
that costs $3. He receives a birthday with $5 in the afternoon.
Then Mike had $7. How much money did he start the day off
with
Answer:
Mike started off the day with $27.
Step-by-step explanation:
Using the information given to us, we can set up an equation. Knowing that Mike ended the day with $7, and the amount of money that he spent and received can help us set up an equation. The amount of money that he started the day off with, is unknown, and recognized as x. [tex]7=x-22-3+5[/tex]
To solve this, we can simply solve the numbers that we know on the right hand side, to get this:
[tex]7=x-20[/tex]
Now, to get our final answer we must isolate x. We can do this by simply adding 20 to both sides. This cancels out the -20 on the right, and makes the 7 on the left become 27.
[tex]27=x[/tex]
Therefore, Mike started the day off with $27.
A stock is changing value by -$0.12 each minute. The stock’s value will have changed by -$1.68 after
minutes.
Answer:
14 Minutes
Step-by-step explanation:
1.68 divided by 0.12 is 14 or Multiply 0.12 by 14 and you get 1.68.
Find all the missing side lengths for the following ITS WORTH 20 points plsss help and ill like !!
Jennifer starts a new investment account that grows exponentially. Her financial advisor tells her
the initial investment of $50,000 grows at a rate of about 15% annually.
1. Determine a function, I(t), that determines Jennifer’s investment account balance after t years. For the exponential growth function, what are the “a” and “b” values? What do those values represent? (5 points for the explanation of “a” and “b” and 5 points for the function)
The exponential function is given by [tex]I(t) = 50000(1.15)^t[/tex]. The initial investment of $50,000 grows at a rate of about 15% annually.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
An exponential function is in the form:
y = abˣ
Where a is the initial value and b is the rate of increase per period.
Let I(t) represent Jennifer’s investment account balance after t years, hence:
a = 50000, b = 100% + 15% = 115% = 1.15
[tex]I(t) = 50000(1.15)^t[/tex]
The exponential function is given by [tex]I(t) = 50000(1.15)^t[/tex]. The initial investment of $50,000 grows at a rate of about 15% annually.
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Find the value of k (k,3) and (2,3) is 5
A: 5
B: 6
C: 7
D: 8
Answer:
its option c (7)
Step-by-step explanation:
trust your bro
Answer:
[tex]C)~ 7[/tex]
Step-by-step explanation:
[tex]\text{Given that,}~~ (x_1,y_1) = (k,3)~ \text{and}~ (x_2 ,y_2) = (2,3)\\\\\text{Distance,}~ \\\\~~~~~~~~d= \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2}\\\\\implies 5=\sqrt{(2-k)^2 + (3-3)^2}\\\\\implies 5=\sqrt{(2-k)^2 +0}\\\\\implies 5 = \sqrt{(2-k)^2}\\\\\implies 5=|2-k|\\\\\implies \pm 5=2-k \\\\\implies 2-k =5~~~~~~\text{or}~~~~~~~~2-k = -5\\\\\implies k = 2-5~~~~~~\text{or}~~~~~~~~k = 2+5\\\\\implies k = -3~~~~~~~~~\text{or}~~~~~~~~k = 7[/tex]
please hurry it’s timed
Which of the following is an asymptote of y=csc(x)?
x= -pi
x= -pi/3
x= pi/4
x= pi/2
Answer:
x = -π
Step-by-step explanation:
An asymptote line is a line that the graph does not intercept or pass through but rather approaches it. An asymptote line also is considered to be a line of undefined value of function because if an asymptote is x = a then f(a) is undefined.
The question gives a function y = csc(x) which is in another form, y = 1/sin(x).
We have to find the value of x that turns the function in undefined and that x-value will be your asymptote.
From a unit circle, we know that sin(-π) = -sin(π) = 0. Since sin(-π) = 0 —> y = csc(-π) = 1/sin(-π) = 1/0
Now we find out that at x = -π, csc(x) is not defined and hence, an asymptote is x = -π
Cylinder A has a radius of 10 inches and a height of 5 inches. Cylinder B has a volume of 750n. What is the percentage change in volume between cylinders A and B? Cylinder B is 50% smaller than cylinder A. Cylinder B is 75% smaller than cylinder A Cylinder B is 50% bigger than cylinder A Cylinder B is 200% bigger than cylinder A
Answer: Cylinder B is 50% bigger than cylinder A
Cylinder A volume:
= πr²h
= π(10)²(5)
= 500π
Cylinder B volume:
= 750π
Cylinder B bigger than Cylinder A by:
= (750π - 500π)/500π × 100 = 50%
[tex]\hrulefill[/tex]
Hence, cylinder B is bigger than cylinder A by 50%
Answer:
Cylinder B is 50% bigger than Cylinder A
Step-by-step explanation:
[tex]\textsf{Volume of a cylinder}=\sf \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}[/tex]
Cylinder A
Given:
r = 10 inh = 5 inSubstituting the given values into the formula:
[tex]\implies \sf Volume_A=\pi (10)^2(5)=500\pi \:in^3[/tex]
Cylinder B
Given:
volume = 750 in³[tex]\implies \sf Volume_B=750\pi \:in^3[/tex]
Percentage Change
[tex]\begin{aligned}\sf percentage\:change & =\sf \dfrac{final\:value-initial\:value}{initial\:value} \times 100\\\\& = \sf \dfrac{Volume_B-Volume_A}{Volume_A} \times 100\\\\& = \sf \dfrac{750\pi-500\pi}{500\pi} \times 100\\\\& = \sf \dfrac{1}{2} \times 100\\\\& = \sf 50\%\end{aligned}[/tex]
Therefore, Cylinder B is 50% bigger than Cylinder A
A triangle has a base of 53 and a height of 21. What is the hypotenuse?
Answer:
Approximately 57
Step-by-step explanation:
The Pythagorean theorem says that a^2+b^2=c^2, where a and b are the base and height, while c is the hypotenuse. 53^2+21^2=2809+441=3250. The square root of 3250 is 57.008771255, which rounded to the nearest tenth is 57. Hope this helped!
Answer:
57.008771255 or 57
Step-by-step explanation:
53^2+21^2=57.008771255^2
kelly recorded the amount of money she earned y for hours worked x in the table shown
Answer:
10
Step-by-step explanation:
4 overtime hours - regular pay + $40
Total $ earned - $160
Total hours - 12 hours (8 reg + 4 overtime)
$160 - $40 = $120
$120/12 = $10
Her regular pay is $10 per hour.
Pineapples were packed in three large crates. for each crate, the weight of every pineapple in the crate was recorded. here are three box plots that summarize the weights in each crate. select all of the statements that are true, according to the box plots. (select all that apply. ) the weights of the pineapples in crate 1 were the most variable. the heaviest pineapple was in crate 1. the lightest pineapple was in crate 1. crate 3 had the greatest median weight and the greatest iqr. more than half the pineapples in crate 1 and crate 3 were heavier than the heaviest pineapple in crate 2
A box plot is used to study the distribution and level of a set of scores. The box plot consists of whiskers which measure the minimum and maximum numbers. The difference between these numbers is the range which measures variability.
On the box, the first line to the left represents the lower (first) quartile. The next line on the box represents the median. The third line on the box represents the upper (third) quartile. The difference between the first quartile and the third quartile is the interquartile range.
For the first box plot:
Maximum number = 6Minimum number = 1.5Range = 6 - 1.5 = 4.5Median = 4First quartile = 3Third quartile = 4.5IQR = 4.5 - 3 = 1.5For the second box plot:
Maximum number = 3.5Minimum number = 1 Range = 3.5 - 1 = 2.5Median = 2First quartile = 1Third quartile = 2.5IQR = 2.5 - 1 = 1.5For the third box plot:
Maximum number = 5Minimum number =2.5Range = 5 - 2.5 = 2.5Median = 4First quartile = 3.5Third quartile = 4.5IQR = 4.5 - 3.5 = 1Please find attached the box plots. To learn more about box plots, please check: https://brainly.com/question/27215146
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Find the value of x in the triangle shown below.
x=
58°
6
6
20%
5.8
Answer:
x = 61°
Step-by-step explanation:
since the triangle has 2 congruent sides then it is isosceles with the 2 base angle being congruent, both x°
the sum of the 3 angles in the triangle = 180° , then
x + x + 58° = 180°
2x + 58° = 180° ( subtract 58° from both sides )
2x = 122° ( divide both sides by 2 )
x = 61°
4. What is the measurement of 2 and 11?
Answer:
look at the photo
...................................
complete the equation of the line.
Answer:
see the attachment photo!
to get the equation of any straight line, we simply need two points off of it, let's use the provided points in the picture above.
[tex](\stackrel{x_1}{0}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{1}-\stackrel{y1}{(-3)}}}{\underset{run} {\underset{x_2}{1}-\underset{x_1}{0}}} \implies \cfrac{1 +3}{1 +0}\implies 4 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-3)}=\stackrel{m}{4}(x-\stackrel{x_1}{0}) \\\\\\ y+3=4x\implies y=4x-3[/tex]
Which two details support the key idea that pollution is threatening marine life?
Marine Debris
Source: The National Oceanic and Atmospheric Association
Marine debris is a persistent pollution problem that reaches throughout the entire ocean and Great Lakes. Our ocean and waterways are polluted with a wide variety of marine debris, ranging from tiny microplastics, smaller than 5 mm, to derelict fishing gear and abandoned vessels. Worldwide, hundreds of marine species have been negatively impacted by marine debris, which can harm or kill an animal when it is ingested or they become entangled, and can threaten the habitats they depend on. Marine debris can also interfere with navigation safety and potentially pose a threat to human health.
All marine debris comes from people with a majority of it originating on land and entering the ocean and Great Lakes through littering, poor waste management practices, storm water discharge, and extreme natural events such as tsunamis and hurricanes. Some debris, such as derelict fishing gear, can also come from ocean-based sources. This lost or abandoned gear is a major problem because it can continue to capture and kill wildlife, damage sensitive habitats, and even compete with and damage active fishing gear.
Answer:
Worldwide, hundreds of marine species have been negatively impacted by marine debris, which can harm or kill an animal when ingested or they become entangled, and can threaten the habitats they depend on.
This lost or abandoned gear is a major problem because it can continue to capture and kill wildlife, damage sensitive habitats, and even compete with and damage active fishing gear.
Step-by-step explanation:
The key idea is that pollution is threatening marine life impact of marine life and the source of marine debris.
Marine debris is risky to a wide variety of marine animals. Animals can ingest debris, which can cause health problems or death, or they may get caught in debris, which can be equally harmful. In addition, marine debris harms the environments in which many species rely on being alive.
The greater part of marine garbage is caused by human activity on land. Marine debris is produced by poor waste management methods, dumping waste, stormwater discharge, and natural disasters such as tsunamis and hurricanes. Furthermore, ocean-based sources, such as wasted fishing gear, contribute to the problem.
The key idea is that pollution is threatening marine life impact of marine life and the source of marine debris.
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Parallel to y=12x−4, through (4, 5)
Write the slope intercept form of each equation of the line. Use a fraction for slope
Answer: y = 12x - 43
Step-by-step explanation: i hope that helps
Necesito las respuestas
Answer:
I need it in English please so I can helps
Any Help Will Be Appreciated!
Answer:
-148
Step-by-step explanation:
Hello!
We can evaluate by plugging in -3 for x, and -7 for y in the expression [tex]3x^3 - 2x^2 + 7y[/tex]
Evaluate[tex]3x^3 - 2x^2 + 7y \text{ for x=-3, and y=-7}[/tex][tex]3(-3)^3 - 2(-3)^2 + 7(-7)[/tex][tex]3(-27) - 2(9) - 49[/tex][tex]-81 - 18 - 49[/tex][tex]-148[/tex]The evaluated value is -148.
Answer:
-148
Step-by-step explanation: