5. Find the limit. a) lim X x-+(1/2) 2x-1 6. Find the derivative of the function by the limit process. f(x)=x²+x-3 b) x + 1 lim 2+1
Answers
a) The limit is lim X x-+(1/2) 2x-1 = 3/2
b) The derivative of the function f(x) = x² + x - 3 is f'(x) = 2x + 1.
a) To find the limit of x(2x-1)/2 as x approaches 1/2, we can substitute 1/2 into the expression and evaluate. However, this will result in 0/0, which is an indeterminate form. To solve this, we can use L'Hôpital's rule. L'Hôpital's rule states that the limit of f(x)/g(x) as x approaches a is equal to the limit of f'(x)/g'(x) as x approaches a. In this case, f(x) = x(2x-1) and g(x) = 2. Therefore, the limit of x(2x-1)/2 as x approaches 1/2 is equal to the limit of 2x-1/2 as x approaches 1/2. Substituting 1/2 into the expression, we get 2(1/2)-1/2 = 3/2.
b) To find the derivative of the function f(x) = x² + x - 3 using the limit process, we start by taking the definition of the derivative:
f'(x) = lim (h -> 0) [f(x + h) - f(x)] / h
Substituting the given function, we have:
f'(x) = lim (h -> 0) [(x + h)² + (x + h) - 3 - (x² + x - 3)] / h
Expanding the terms within the limit, we get:
f'(x) = lim (h -> 0) [x² + 2xh + h² + x + h - 3 - x² - x + 3] / h
Simplifying, we have:
f'(x) = lim (h -> 0) [2xh + h² + h] / h
Now, we can cancel out the 'h' term:
f'(x) = lim (h -> 0) [2x + h + 1]
Taking the limit as h approaches 0, we get:
f'(x) = 2x + 1
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Related Questions
6g + 3 = 21 ???? plz help lol
Answers
Answer:
3
Step-by-step explanation:
Answer:
g=3
Step-by-step explanation:
6g + 3 = 21
6g=18
divide by 6
g=3
Hope this helps!!
factor 5a2 – 30a 40. question 17 options: a) 5(a – 2)(a 4) b) 5(a – 2)(a – 4) c) (5a – 5)(a – 8) d) (a – 20)(a – 2)
Answers
The answer that you are looking for is b) 5(a – 2)(a – 4). In order to factor the formula, we must first locate two numbers whose sum is equal to -30 and whose product is equal to 40. Both constraints are met by the values -4 and -10, and as a result, we are able to factor the statement as 5(a – 2)(a – 4).(option b)
The following procedures can be used by us while factoring polynomials:
Find two numbers that, when added together, give you the coefficient of the middle term, and then multiply those two values by themselves to get the constant term.
Create the expression as the product of two binomials, with each binomial having one of the two numbers discovered in step 1. Write the equation as a product of two binomials.
Eliminate any factors that are frequent.
In this particular instance, the coefficient of the intermediate term is -30, while the value of the constant term is 40. When added together, the numbers -4 and -10 equal -30, and when multiplied together, they equal 40. Therefore, the expression can be factored as 5(a minus 2)(a minus 4).
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16. A radioactive isotope has a half-life of 13 hours. Find the amount of the isotope left from a 400-milligram
sample after 65 hours. If necessary, round your answer to the nearest thousandth.
a. 25 mg
c. 0.049 mg
b. 7.692 mg
d. 12.5 mg
Please help. I only see answers for 52 hours
Answers
Answer:
Without the math: 65 hours is 5 half-lives
13 hrs = 1/2
26 hrs = 1/4
39 hrs = 1/8
65 hrs = 1/32
(1/2)^5 = 1/32
400 mg / 32 = 12.5 mg that is, after 5 half-lives
Find the product of 6 • 2/15 simplify if possible.
Answers
Answer: 4/5
Step-by-step explanation:
\(6 \cdot \frac{2}{15}=(2)(3) \cdot \frac{2}{3(5)}=\frac{4}{5}\)
Consider 6x2 + 6x + 1. Which term immediately tells you that this expression is NOT a perfect square trinomial? Justify your answer.
Answers
Answer:
Step-by-step explanation:
The 6x^2 because 6 is not a perfect square.
Answer:
6x^2
Step-by-step explanation:
6 isn't a perfect square
Statistical analyses are least likely to be found in a. applied research b. basic research c. field research d. qualitative research
Answers
Statistical analyses are least likely to be found in a (D) qualitative research.
What is qualitative research?Data from first-hand observation, interviews, questionnaires (on which participants write descriptively), focus groups, participant-observation, recordings recorded in natural settings, documents, case studies, and artifacts are used in qualitative research. The information is mostly nonnumerical. Ethnography, grounded theory, discourse analysis, and interpretative phenomenological analysis are examples of qualitative approaches. Sociology, anthropology, political science, psychology, social work, and educational research have all used qualitative research methods. Qualitative researchers investigate people's perceptions of their social reality.A qualitative study is unlikely to contain statistical analyses.Therefore, statistical analyses are least likely to be found in a (D) qualitative research.
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A student is running a 3-kilometer race. He runs 1 kilometer every 2 minutes. Select the function that describes his distance from the finish line after x minutes. f of x equals negative one third x plus 2 f of x equals negative one half x plus 3 f of x equals one half x plus 3 f of x equals one third x plus 2
Answers
Answer:x - number of minutes;
f ( x ) - the distance from the finish line.
x : 0 2 4 6
f ( x ) : 3 2 1 0
f ( x ) = 3 - x/2
Answer: B ) f ( x ) = -1/2 x + 3
Step-by-step explanation:
Answer:
f(x) = (1/2)X
Step-by-step explanation:
speed = distance / time
distance = speed x time
3 = (1/2) X
X = 3/(0.5) = 6min
let distance = F(X)
f(x) = (1/2)X
5+4(2 + 4)2
6+ 12 : 3 - (6 x 2)
12 -
(4+8) : 2
(6 + 1)2 – 2(3+6)
(8 + 9) – 10+ (2 + 3)?
Answers
Answer:
−72x2+18?
Step-by-step explanation:
please help, easy question
Answers
Answer:
whats the question???
Step-by-step explanation:
Answer:
whats the question ?
Step-by-step explanation:
How to find the area of the circle
Answers
Answer:
200.96
Step-by-step explanation:
Using the formula they give you, find the area
8²*π= 64π= 64*3.14 = 200.96
the area of an circle is = 64
Step-by-step explanation:
w x l
8x8 = 64.
Please help me. WILL GIVE BRAINLIEST
Answers
Answer:
d
Step-by-step explanation:
Answer:
third option
Step-by-step explanation:
Given that x = - 2 + \(\sqrt{8}\) is a root
Complex roots always occur as conjugate pairs , thus
x = - 2 + \(\sqrt{8}\) is a root then x = - 2 - \(\sqrt{8}\) is a root
The required factor is then
(x - (- 2 - \(\sqrt{8}\) ) )
set up the integral for the volume of the solid of revolution rotating region between y = sqrt(x) and y = x around x=2
Answers
Plug these into the washer method formula and integrate over the interval [0, 1]:
V =\(\pi * \int[ (2 - x)^2 - (2 - \sqrt(x))^2 ] dx \ from\ x = 0\ to\ x = 1\)
To set up the integral for the volume of the solid of revolution formed by rotating the region between y = sqrt(x) and y = x around the line x = 2, we will use the washer method. The washer method formula for the volume is given by:
V = pi * ∫\([R^2(x) - r^2(x)] dx\)
where V is the volume, R(x) is the outer radius, r(x) is the inner radius, and the integral is taken over the interval where the two functions intersect. In this case, we need to find the interval of intersection first:
\(\sqrt(x) = x\\x = x^2\\x^2 - x = 0\\x(x - 1) = 0\)
So, x = 0 and x = 1 are the points of intersection. Now, we need to find R(x) and r(x) as the distances from the line x = 2 to the respective curves:
R(x) = 2 - x (distance from x = 2 to y = x)
r(x) = 2 - sqrt(x) (distance from x = 2 to y = sqrt(x))
Now, plug these into the washer method formula and integrate over the interval [0, 1]:
V =\(\pi * \int[ (2 - x)^2 - (2 - \sqrt(x))^2 ] dx \ from\ x = 0\ to\ x = 1\)
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There are 8 bags of yellow and green balloons. Each bag contains 7 balloons. How many total balloons are there? There are 56 total balloons. Nice! If there are 30 yellow balloons, how many green balloons are there?
Answers
Answer:
26 green balloons
Step-by-step explanation:
56-30 = 26 green balloons
The total number of balloons is 56. And the number of green balloons will be 26.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
There are 8 sacks of yellow and green inflatables. Each sack contains 7 inflatables. The total number of balloons will be given as,
⇒ 8 x 7
⇒ 56
If there are 30 yellow balloons. Then the number of green balloons will be calculated as,
⇒ 56 - 30
⇒ 26
The total number of balloons is 56. And the number of green balloons will be 26.
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What are the slope and y-intercept for the equation: −4x+2y=−16
Answers
Answer:
slope = 2 , y- intercept = -8
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
given
- 4x + 2y = - 16 ( add 4x to both sides )
2y = 4x - 16 ( divide both sides by 2 )
y = 2x - 8 ← in slope- intercept form
with slope m = 2 and y- intercept c = - 8
Answer:
the slope is 2 and y-intercept is (0,-8)
Step-by-step explanation:
Step 1: is to subtract 2y from both sides, -4x+2y-2y=-16-2y
Step 2: Simplify, -4= -16-2y
Step 3: Divide both sides by -4, -4x/4=-16/-4-2y/-4
4x/4=x=1
In a regression model, the __________ exists when a predictor variable has a different partial effect on the outcome of another predictor variable.
a. target effect
b. interaction effect
c. dummy effect
e. predictor effect
Answers
Answer:
b. interaction effect
Step-by-step explanation:
In a regression model, the interaction effect is present when a predictor variable changes the effect of another predictor variable on the outcome.
Explanation:In a regression model, the interaction effect exists when one predictor variable impacts the outcome of another predictor variable differently than when examined individually. It refers to the interaction between two or more predictor variables and their influencers on an outcome or response variable. For example, in a regression model, studying and having a quiet place may individually contribute to a better score on a test, but perhaps studying in a quiet place provides a significantly better effect than the sum of those two effects separately. This would be considered an interaction effect.
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I will mark you brainiest!!!
A passenger train left the station and traveled toward Las Vegas at an average speed of 55mph. A cattle train left at the same time and traveled in the opposite direction with an average speed of 65mph. Which equation best represents this situation when the trains are 960 mi apart?
A - 65x - 55(2) = 960
B - 65x - 55x = 960
C - 65x + 55(2) = 960
D - 65x + 55x = 960
E - 65(2) + 55x = 960
Answers
Answer:
The answer is b
Step-by-step explanation:
The distance traveled by the passenger train and the cattle train is equal to the total distance between them, which is 960 miles. Let x be the time (in hours) traveled by the passenger train and cattle train. Then, the equation that represents this situation is:
55x + 65x = 960
Simplifying the left-hand side of the equation, we get:
120x = 960
Dividing both sides by 120, we get:
x = 8
Therefore, the correct equation is:
B - 65x - 55x = 960
expand : (x-2y) cube
Answers
Answer:
Xcube- 8(ycube) - 6(xsquare)y+12x(ysquare)
Step-by-step explanation:
(x-2y)^3 = x^3 +(-2y)^3+3(x^2)(-2y)+3(x) (-2y)^2
=x^3 -8y^3-6x^2×y+12xy^2
is it possible to build a triangle with side lengths of 5, 5, 10
Answers
8. The area of the parallelogram whose adjacent sides formed by the vectors usi+i-k and v= 2i-j+3k is a) √32 b) 12 c) √38 d) √38 2 e) None of the above. 9. The direction in which the function f(x,y) = x² + xy + y² increases most rapidly at the point P(-1, 1) is a) < > b) < 1/2, 2/2² > <唔唔> d) < = 1/2 - 1/²2 > d) <= 1/2, 1/2 > e) None of the above. aw Let w = √² + s², r = y + x cost and s= x + y sint. Then at -rxsin + sy cost √r²+5² rxsint-s y cost √r²+5² rxsint+s y cost √r²+ s² sxsint-ry cos t d) √r²+ s² e) None of the above. 10. a) b) c) is
Answers
The direction in which the function f(x, y) = x² + xy + y² increases most rapidly at the point P(-1, 1) is e) None of the above.
To determine the direction of the greatest increase, we need to find the gradient of the function at point P. Substituting the coordinates of P into the gradient vector, we have ∇f(-1, 1) = (-2 + 1, -1 + 2) = (-1, 1). Therefore, the direction of the greatest increase at point P is in the direction of the vector (-1, 1).
To find the direction of the greatest increase of a function at a specific point, we calculate the gradient vector (∇f) of the function and evaluate it at the given point. The gradient vector represents the direction of the steepest increase.
By determining the coordinates of the gradient vector at the given point, we can identify the direction of the greatest increase. In this case, the vector (-1, 1) represents the direction of the greatest increase at point P(-1, 1).
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Imagine some DEQ: y'=f(x,y), which is not given in this exercise.
Use Euler integration to determine the next values of x and y, given the current values: x=2, y=8 and y'=9. The step size is delta_X= 5. 2 answers
Refer to the LT table. f(t)=6. Determine tNum,a,b and n. 4 answers
Answers
Using Euler integration, the next values of x and y can be determined as follows:
x_next = x_current + delta_X
y_next = y_current + delta_X * y'
What are the updated values of x and y using Euler integration?Euler integration is a numerical method used to approximate solutions to differential equations. It is based on the concept of dividing the interval into small steps and using the derivative at each step to calculate the next value. In this case, we are given the current values of x=2, y=8, and y'=9, with a step size of delta_X=5.
To determine the next values of x and y, we use the following formulas:
x_next = x_current + delta_X
y_next = y_current + delta_X * y'
Substituting the given values into the formulas, we have:
x_next = 2 + 5 = 7
y_next = 8 + 5 * 9 = 53
Therefore, the updated values of x and y using Euler integration are x=7 and y=53.
It's important to note that Euler integration provides an approximate solution and the accuracy depends on the chosen step size. Smaller step sizes generally lead to more accurate results. Other numerical methods, such as Runge-Kutta methods, may provide more accurate approximations.
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Are the ratios 3:2 and 17:12 equivalent?
yes
no
Answers
Answer:
no
Step-by-step explanation:
3:2 is equal to 18:12 not 17
The graphs below have the same shape. What is the equation of the blue
graph?
Answers
Answer:
for this graph the answer is D
Consider the linear function below
Answers
4. From the top of a tower 14m high, the angle of depression of a student is 32° Make a scale drawing and find the distance of the student from the foot of the tower to the nearest 1/2
Answers
The distance of the student from the foot of the tower is 25.63m the nearest 1/2 is 25.5m.
Given that From the top of a tower 14m high
The angle of depression of a student is 32°
we can use trigonometry to find the distance from the foot of the tower to the student:
tan(32°) = opposite/adjacent = 14/distance
Rearranging this equation gives:
distance = 14/tan(32°)
= 25.63m
Therefore, the distance of the student from the foot of the tower is approximately 25.63m nearest 1/2, this is 25.5m.
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A pharmacist mixed 800 mg of a liquid drug (sg = 0.8) in enough liquid to prepare 2 liters of a final product. what is the ratio strength of the final product?
Answers
The ratio strength of the final product is 1:0.4.
What is ratio strength?One technique to indicate concentration is through ratio strength, which uses a ratio to characterize drug concentration. In this context, concentration is defined as the quantity of a solute that makes up one unit in the whole volume of a solution or combination. You should be an expert in ratio strength calculations as a pharmacy student. Ratio strength uses a ratio to describe the medication concentration. So, what it implies is, you have one unit of solute contained in the complete amount of preparation and so generally your ratio strength is expressed as one is to something. In the case of a weight-in-weight, volume-in-volume, or weight-in-volume situation, you would interpret a ratio of 1:2,000 differently.
Drug strength = 800mg
whole volume =2ltrs
The ratio of the solution in 1 ltr is = 400 mg
The ratio strength of the solutions is = 1:0.4
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We often describe winter coats as warm. Or, we say that a thick sweater "keeps out the cold. " Are these descriptions correct? Why or why not? (Remember that heat is the movement of energy. So, heat moves, not cold. )
Answers
Yes, these descriptions are correct. A winter coat is considered warm because it provides insulation that helps to retain body heat.
Likewise, a thick sweater is designed to keep out the cold by providing a layer of insulation between the body and the colder environment. However, it is important to remember that heat is the movement of energy, not cold. When we say that something "keeps out the cold," we are actually referring to the prevention of heat loss.
Heat always moves from areas of higher temperature to areas of lower temperature, so when we are in a cold environment, our bodies will naturally lose heat to the surroundings. Insulating materials like winter coats and thick sweaters help to slow down this heat loss process by trapping pockets of warm air close to the body. The more insulation provided by the clothing, the less heat is lost to the environment, and the warmer we feel. Therefore, these descriptions are correct in that they accurately describe the function of winter coats and thick sweaters in helping to retain body heat and keep out the cold.
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The colliers want to put new flooring in a 6 1/2 foot by 7 1/3 foot bathroom. the tiles they want come in 12-inch squares. what is the area of the bathroom floor? if the tiles cost $3. 25 per square foot, how much will they spend on the flooring?
Answers
The cost of the flooring will be $7.65, with 2.35 tiles covering a bathroom floor space of 27.66 square inches.
what is area ?The area of a two-dimensional figure is the whole area it takes up. Square units, which are typically expressed as square inches, square feet, or square kilometers, are the accepted units of area. An area is just a surface that is free of objects. Using a shape's length and width, one can compute the area of the object. Measured in terms of feet (ft), yards (yd), inches (in), etc., length is a one-dimensional quantity. The size of a shape, however, is a two-dimensional measurement.
given
area of bathroom floor = 6 1/2 * 7 1/3
= 27 . 666 foot 2
area of tiles = side 2
area of tiles = 12 * 12
= 141 inch 2
so 1 foot = 12 inch
so 27.66 * 12 = 331.2
no. of tiles = 332.2 / 141
= 2 . 35
cost of per tile = $ 3.25
so 2.35 * 3.25
= $ 7.65
The cost of the flooring will be $7.65, with 2.35 tiles covering a bathroom floor space of 27.66 square inches.
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a line passes through the point (-10,9) and has a slope of -1/2 write an equation in slope-intercept form for this line.
PLEASE do this fast. I will mark the correct answer brainliest. Also, please only answer with the right answer not stuff unrelated or not answering the question. Please hurry. Thank you so so so much.
Answers
Answer:
\(y=-\frac{1}{2} x+4\)
Step-by-step explanation:
The equation of a straight line in slope intercept form is given by:
y = mx + c;
where y, x are variables, m is the slope of the line and c is the y intercept (that is value of y when x is 0).
The equation of a line passing through point (\(x_1,y_1\)) with a slope of -1/2 is given by:
\(y-y_1=m(x-x_1)\)
Given that the line passes through the point (-10,9) and has a slope of -1/2. Hence the equation of the line is:
\(y-9=-\frac{1}{2}(x-(-10)) \\\\y-9=-\frac{1}{2} (x+10)\\\\y=-\frac{1}{2} x-5+9\\\\y=-\frac{1}{2} x+4\)
What is the ordered pair for letter R in the image to the left? A (5, 1) B.) (1,5) C. (5,0) D. (0,5)
Answers
Answer:
Your answer would be D. (0,5)
Step-by-step explanation:
Evaluate + for x = 6, y = -4, and z = -2.
-27
Answers
The value of the expression \(+ = x^3 - y - 2z^3$ for $x = 6$, $y = -4$, and $z = -2$\) is \(236\).
To find the value of the expression \(+ = x^3 - y - 2z^3$ for $x = 6$, $y = -4$, and $z = -2$\), we substitute the given values into the expression and simplify step by step:
Step 1: Substitute the values of \(x, $y$, and \ $z$\) into the expression:
\(\[+ = (6)^3 - (-4) - 2(-2)^3\]\)
Step 2: Evaluate the exponents:
\(\[+ = 216 - (-4) - 2(-8)\]\)
Step 3: Simplify the negations:
\(\[+ = 216 + 4 + 16\]\)
Step 4: Combine like terms:
\(\[+ = 236\]\)
The concept used in evaluating the expression is substitution. In mathematics, substitution involves replacing variables in an expression with specific values. By substituting the given values for x, y, and z into the expression, we can calculate the result. This allows us to simplify the expression and obtain a numerical value. Substitution is a fundamental concept used in algebraic calculations to solve equations, evaluate functions, and perform various mathematical operations. It enables us to work with specific values and obtain meaningful results in mathematical computations.
Therefore, the answer to \(+ = x^3 - y - 2z^3$ for $x = 6$, $y = -4$, and $z = -2$\) is \(236\).
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