Answers
The limit [tex]\lim _{x\to \infty \:}\frac{1}{3^x}+3^{\frac{1}{x}}[/tex] without using L'Hopital's Rules has a value of 1
Evaluate this limit without using L'Hopital's RulesFrom the question, we have the following parameters that can be used in our computation:
[tex]\lim _{x\to \infty \:}\frac{1}{3^x}+3^{\frac{1}{x}}[/tex]
By substitution, we have
[tex]\lim _{x\to \infty \:}\frac{1}{3^x}+3^{\frac{1}{x}} = \frac{1}{3^{}\infty}+3^{\frac{1}{\infty}}[/tex]
So, we have
[tex]\lim _{x\to \infty \:}\frac{1}{3^x}+3^{\frac{1}{x}} = 0+3^0[/tex]
Evaluate the exponents
[tex]\lim _{x\to \infty \:}\frac{1}{3^x}+3^{\frac{1}{x}} = 0+1[/tex]
Evaluate the sum
[tex]\lim _{x\to \infty \:}\frac{1}{3^x}+3^{\frac{1}{x}} = 1[/tex]
Hence, the solution is 1
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Related Questions
Given (x – 7)2 = 36, select the values of x. x = 13 x = 1 x = –29 x = 42
Answers
The solution for x in the equation (x – 7)^2 = 36 are x = 13 and x = 1
Solving for x in the equationWe can solve for x by taking the square root of both sides of the equation:
(x – 7)^2 = 36
Taking the square root of both sides:
x - 7 = ±6
Adding 7 to both sides:
x = 7 ± 6
Therefore, the values of x are:
x = 7 + 6 = 13
x = 7 - 6 = 1
So the correct answers are x = 13 and x = 1. The values x = -29 and x = 42 are not solutions to the equation.
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The height y(in feet) of a ball thrown by a child isy=−114x2+2x+3
where x is the horizontal distance in feet from the point at which the ball is thrown.
(a) How high is the ball when it leaves the child's hand? (Hint: Find y
when x=0)
Your answer is y=____
(b) What is the maximum height of the ball? _____
(c) How far from the child does the ball strike the ground?_____
Answers
y = -114(0)^2 + 2(0) + 3
y = 3
So the ball is 3 feet high when it leaves the child's hand.
(b) The maximum height of the ball occurs at the vertex of the parabola. We can find the x-coordinate of the vertex using the formula:
x = -b/2a
where a = -114 and b = 2. Substituting these values, we get:
x = -2/(2*(-114)) = 0.0088
We can find the maximum height by substituting this value of x into the equation:
y = -114(0.0088)^2 + 2(0.0088) + 3
y ≈ 3.036
So the maximum height of the ball is approximately 3.036 feet.
(c) To find how far from the child the ball strikes the ground, we need to find the value of x when y = 0. We can solve the equation for x:
-114x^2 + 2x + 3 = 0
Using the quadratic formula, we get:
x = (-2 ± sqrt(2^2 - 4*(-114)*3))/(2*(-114))
x = (-2 ± sqrt(9252))/(-228)
We can ignore the negative root since the ball is moving in the positive x-direction. Simplifying the expression for the positive root, we get:
x = (-2 + sqrt(9252))/(-228) ≈ 0.232
So the ball strikes the ground approximately 0.232 feet away from the child.
Which number is irrational?
0.020202
0.8
0.333...
Answers
All the numbers are rational numbers.
We have,
Rational numbers are those numbers that are terminating and recurring non-terminating.
Irrational numbers are those numbers that are non-terminating and non-recurring.
The numbers are:
1)
0.020202
This is non terminating recurring number.
It is a rational number.
2)
0.8
This is a terminating number.
It is a rational number.
3)
0.020202
This is non terminating recurring number.
It is a rational number.
Thus,
All the numbers are rational numbers.
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what is the probability that either event will occur
Answers
The probability that either event will occur is 7/25
What is probability?A probability is a number that reflects the chance or likelihood that a particular event will occur. The certainty of an event is 1 which is equivalent to 100% in percentage.
Probability = sample space /Total outcome
P(A or B) = P(A) +P(B) -P(A and B)
The total element = 25+5+15+5 = 50
therefore total outcome = 50
P(A) = 25/50
P(B) = 15/50
P(A and B) = 5/40
Therefore P(A and B) = 25/50+15/50 - 5/50
= 35/50 = 7/25
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Find f(−3), f(0) and f(1) for the following function.
f(x)=2x
Answers
Answer:
-6, 0, 2Step-by-step explanation:
f(x)=2x
note: putting anything in the f(x) parentheses replaces x in the function with that value
so,
f(-3) = 2(-3) = -6
f(0) = 2*0 = 0
f(2) = 2(2) = 4
How do you find area?
Answers
The area of a shape is calculated by calculating the amount of space on the shape
How do you find area?By definitinon, the area of a shape is the amount of space on the shape
using the above as a guide, we have the following:
Area of rectangle = Length * WidthArea of square = Length²Area of triangle = 1/2 * base * heightArea of circle = π * radius²Area of parallelogram = base * heightThere are several formulas to calculate area
The formula to use is dependent on the shape whose area is being calculated
This means that the area of trapezoid cannot be calculated using the area of parallelogram
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The table represents the quadratic functions f(x) and g(x).
x f(x) g(x)
−8 16 4
−4 4 1
0 0 0
4 4 1
8 16 4
What transformation of f(x) will produce g(x)?
g of x equals one fourth times f of x
g of x equals f of the quantity of one fourth times x end quantity
g(x) = 4f(x)
g(x) = f(4x)
Answers
The transformation of f(x) that will produce g(x) is given as follows:
g(x) = f(x)/4.
How to obtain the function g(x)?If we observe at the table, we have that each value of g(x) is one fourth of the value of the function f(x).
Hence the transformation of f(x) that will produce g(x) is given as follows:
g(x) = f(x)/4.
The transformation means that the function g(x) is a vertical compression by a factor of 4 of the function f(x).
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The earrings that Mrs.Moore wants to buy are $55.00. She won’t buy them until they are at least 45% off. What is the most that Mrs.Moore is willing to spend?
Answers
Answer:
$30.25
Step-by-step explanation:
55% of 55$ is $30.25. she wants 45 % off of 55$. which is $24.75. 55-24.75 is 30.25
$30.25
since it's 45% off, you need to subtract 45% from 100%
100%-45%=55%
then turn the % into a decimal
55%/100=0.55
now multiply the original price by 0.55
0.55*55=30.25
WILL AWARD BRAINLIEST!!
The base of a right prism ABC is an isosceles triangle with AB = BC and m∠ACB 35°. The diagonal of lateral face ABA is 18 cm and m∠BAB = 50°. Find the volume of the prism. Round your answer to the nearest cm
Answers
Answer:
351 cm^3
Step-by-step explanation:
The base of a right prism ABC is an isosceles triangle with AB = BC and m∠ACB 35°. The diagonal of lateral face ABA is 18 cm and m∠BAB = 50°. Find the volume of the prism. Round your answer to the nearest cm
ChatGPT
Let AB = BC = x be the base of the isosceles triangle ABC. Then, the third side AC is:
AC = 2x * sin(35°)
Using the sine rule in triangle ABA, we have:
AB / sin(50°) = 18 / sin(80°)
Solving for AB, we get:
AB = 18 * sin(50°) / sin(80°)
The height of the prism is AB * cos(35°). Therefore, the volume of the prism is:
V = (1/2) * x^2 * 2x * sin(35°) * AB * cos(35°)
Substituting the values we have calculated, we get:
V = (1/2) * x^2 * 2x * sin(35°) * [18 * sin(50°) / sin(80°)] * cos(35°)
V ≈ 351 cm^3
Therefore, the volume of the prism is approximately 351 cubic centimeters.
A store has 300 televisions on order, and 90% are high definition. How many televisions on order are high
definition? You may find the bar model useful in completing this problem.
20% 30% 40%
70%
0%
0
10%
30
The store has
50% 60%
high-definition televisions on order.
80%
90%
100%
300
Answers
Answer:
90% of 300 = .90 × 300 = 270 high- definition televisions on order.
Help please!!!!
Whoever answers right gets brainliest!
Answers
Answer:
25
Step-by-step explanation:
To solve this problem you have to use this formula [tex](\frac{b}{2})^{2}[/tex] it. So in this case b is the term next to the x term. This number is 10. So all we have to do is insert it into the formula. This would give us:
[tex]=(\frac{10}{2})^{2}\\\\=(5)^{2}\\\\= 25[/tex]
The constant term is 25.
Could I get Brainilest, please? I'm trying to get to the expert level
Anna baked 4 batches of cookies with c cookies in each batch she then ate 8 cookies there were 72 cookies left after Anna ate her cookies
Answers
The expression for the number of cookies Anna has left is [tex]3c - 8[/tex].
What does an expression means?An expression refers to statement that have minimum of two numbers or variables or both and an operator connecting them.
The total number of cookies Anna baked is:
= 3 batches * c cookies/batch
= 3c cookies
After eating 8 cookies, Anna has left:
= 3c cookies - 8 cookies
So, the expression for the number of cookies Anna has left is [tex]3c - 8[/tex].
Full question "Anna baked 3 batches of cookies with c cookies in each batch she then ate 8 cookies. How many cookies does anna have left write your answer as an expression.
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The formula v= √√2gh gives the velocity v, in feet per second, of an object after it falls h feet accelerated by gravity g, in feet
per second squared. If g is approximately 32 feet per second squared, find how far an object has fallen if its velocity is 96 feet
per second.
Answers
We can rearrange the formula to solve for h:
v = √√2gh
Squaring both sides: v^2 = 2gh
Dividing both sides by 2g: h = v^2 / 2g
Substituting v = 96 ft/s and g = 32 ft/s^2, we get:
h = (96 ft/s)^2 / (2 × 32 ft/s^2)
h = 288 ft
Therefore, the object has fallen 288 feet.
A radioactive substance decays at a continuous rate of 14.4 % per day. After 15 days, what amount of the substance will be left if you started with 140 mg? (a) First write the rate of decay in decimal form. r = (b) Now calculate the remaining amount of the substance. Round your answer to two decimal places.
Answers
Answer:(a) The rate of decay is 14.4% per day, which can be written as a decimal by dividing by 100: r = 0.144.
(b) The formula for continuous decay is given by:
A = A₀ * e^(-rt)
where A is the remaining amount of the substance after time t, A₀ is the initial amount, r is the rate of decay, and e is the mathematical constant approximately equal to 2.71828.
Plugging in the given values, we get:
A = 140 * e^(-0.144*15)
A = 140 * e^(-2.16)
A ≈ 47.23
Therefore, after 15 days, approximately 47.23 mg of the radioactive substance will be left, rounded to two decimal places.
Step-by-step explanation:
Solve the following quadratic equation by completing the square. Simplify the solutions and rationalize denominators, if necessary.
3x^2−30x=−2
Answers
The solutions to this quadratic equation are x = √(73/3) + 5 or x = -√(73/3) + 5.
What is a quadratic equation?In Mathematics and Geometry, the standard form of a quadratic equation is represented by the following equation;
ax² + bx + c = 0
Next, we would solve the given quadratic equation by using the completing the square method;
3x² - 30x = -2
By dividing all through by 3, we have:
x² - 10x = -2/3
In order to complete the square, we would have to add (half the coefficient of the x-term)² to both sides of the quadratic equation as follows:
x² - 10x + (-10/2)² = -2/3 + (-10/2)²
x² - 10x + 25 = -2/3 + 25
x² - 10x + 25 = 73/3
By simplifying, we have;
(x - 5)² = 73/3
x = √(73/3) + 5 or x = -√(73/3) + 5
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Solve the equation for the indicated variable
X= (simplify your answer)
Answers
B = (715x) / (h^2)
Step 1: Get rid of the denominator by multiplying both sides by h^2
(B)(h^2) = 715x
Step 2: Isolate x by dividing both sides by 715
(Bh^2) / 715 = x
Answer: x = Bh^2 / 715
Hope this helps!
Seven days a year, Tiger Stadium becomes the fifth largest city in the state of Louisiana. Over 92,000 fans pack the stadium to watch the Tigers play. After the game, if the fans leave at a rate of 10% per minute, how long will it take before the stadium is half empty?
1. Find the data using at least 10 numbers in the x column.
2. Create a scatter plot. Label the graph and show increments.
3. Write an exponential equation.
4. Interpret the meaning of the "a" and "b" in your function y=ab^x including the units.
5. Find out how long it will take before the stadium is half empty and all the way empty.
Answers
y = 92000(0.9)^x
where y is the number of fans remaining in the stadium after x minutes.
Using this formula, we can plug in x values from 0 to 30 (or more) to generate a table of values:
| x | y |
|------|---------|
| 0 | 92000 |
| 1 | 82800 |
| 2 | 74520 |
| 3 | 67068 |
| 4 | 60361 |
| 5 | 54325 |
| 6 | 48892 |
| 7 | 43903 |
| 8 | 39313 |
| 9 | 35082 |
| 10 | 31174 |
2. Here is a scatter plot based on the above data:
The x-axis represents the time in minutes, and the y-axis represents the number of fans remaining in the stadium.
3. The exponential equation that best fits the data is:
y = 92000(0.9)^x
where y is the number of fans remaining in the stadium after x minutes.
4. In the equation y = ab^x, a represents the initial value or starting point, and b represents the rate of change or growth factor. In this case, a = 92000 represents the initial number of fans in the stadium, and b = 0.9 represents the rate at which the number of fans decreases per minute. The units of a are fans, and the units of b are fans per minute.
5. To find out how long it will take before the stadium is half empty, we need to solve the equation y = 0.5a for x:
0.5a = 92000(0.9)^x
0.5(92000) = 92000(0.9)^x
0.5 = 0.9^x
Taking the logarithm of both sides, we get:
log(0.5) = x log(0.9)
x = log(0.5) / log(0.9)
x ≈ 7.72 minutes
Therefore, it will take approximately 7.72 minutes for the stadium to be half empty.
To find out how long it will take for the stadium to be completely empty, we need to solve the equation y = 0 for x:
0 = 92000(0.9)^x
Taking the logarithm of both sides, we get:
log(0) = x log(0.9)
This equation has no real solution, which means that the stadium will never be completely empty (in theory). However, in practice, the number of fans will eventually become small enough that it can be considered empty for all practical purposes.
Select all equations that have infinitely many solutions
Answers
2nd and 4th is correct. Hope you got it!
It’s due tomorrow I really need help
Answers
Answer:
B.
Step-by-step explanation:
As the steps imply,
Step 1 is to first convert the 3.5% (0.035) and then multiply it by 16 to find out by how many grams the amount should decrease (0.035 * 16 = 0.56). Step 2 is to subtract this amount from 16 to find the amount remaining after one hour (16 - 0.56 = 15.44). Step 3 is to convert 4.25% to a decimal (0.0425) and multiply it by the amount remaining at the end of one hour to find out by how many grams this amount should decrease after two hours (0.0425 * 15.44 = 0.6562)Step 4 finally is to subtract this amount from 15.44 to find the amount remaining after two hours (15.44 - 0.6562 = 14.7838)solve for x, neg x over 4 = 12 A 48 or B -3 or C 3 or D -48?
Answers
The solution for x is -48, the answer is D) -48.
What is Algebraic expression ?
An algebraic expression is a mathematical phrase that contains variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. It represents a value that can change based on the values assigned to the variables.
Starting with:
x:4 = 12
Multiplying both sides by -1 gives:
(-x÷4) = -12
Simplifying the left side:
x÷4 = -12
Multiplying both sides by 4 gives:
x = -48
Therefore, the solution for x is -48, the answer is D) -48.
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At the time of her grandson's birth, a grandmother deposits $14,000 in an account that pays 4.5% compounded
monthly. What will be the value of the account at the child's twenty-first birthday, assuming that no other deposits
or withdrawals are made during this period?
i Click the icon to view some finance formulas.
The value of the account will be $
(Round to the nearest dollar as needed.)
4
Answers
Answer:
The value of the account will be $5,628
Step-by-step explanation:
Step-by-step explanation:
we know that
The compound interest formula is equal to
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
substitute in the formula above
therefore
The value of the account will be $5,628
Please help me who knows how to do this
Answers
Step 1: X^2+3x-4x-12
Step 2: (X^2+3x)+(-4x-12)
Step 3: X(x+3)-4(x+3)
Answer: (x-4)(x+3)
‼️‼️‼️‼️WILL MARK BRAINLIEST‼️‼️‼️‼️
Answers
Answer:
S = 2π(14^2) + 2π(14)(154)
= 2π(196) + 2π(2,156)
= 4,704π = 14,778.1 ft^2
Using 3.14 for π:
S = 4,704(3.14) = 14,770.6 ft^2
Rebecca invests 600 into an account with a 2.7% interest rate that is compounded quarterly. How much money will she have in this account if she keeps it for 10 years
Answers
The accrued value of the account in 10 years is $641.75
Determining the accrued value of the account in 10 yearsFrom the question, we have the following parameters that can be used in our computation:
Rebecca invests 600 in an account2.7% interest compounded quarterlyUsing the above as a guide, we have the following:
Amount = P * (1 + 0.25r)ᵗ
Where
P = Principal = 600
r = Rate = 2.7% = 0.27
t = time = 10
Substitute the known values in the above equation, so, we have the following representation
Amount = 600 * (1 + 0.25 * 0.27)¹⁰
Evaluate
Amount = 641.75
Hence, the amount is 641.75
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3d *5d*2=?
Please what is 3d times 5d times 2
Answers
Answer:
[tex]30d^2[/tex]
Step-by-step explanation:
50 Points! Solve the equation or inequality. Please show as much work as possible. Photo attached. Thank you!
Answers
The equation 5ʷ ⁺ ³ = 17 when solved for w is approximately w = 0.41
Solving the equations or inequalities for wFrom the question, we have the following parameters that can be used in our computation:
5ʷ ⁺ ³ = 17
Take the logarithm of both sides of the equation
So, we have
w + 3 = ln(17)/ln(3)
Evaluate the quotient on the left side of the equation
This gives
w + 3 = 2.59
So, we have
-3 + w + 3 = 2.59 - 3
Evaluate
w = 0.41
Hence, the equation when solved for w is approximately w = 0.41
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Solve for w.
w − 5
4
= 2
Answers
The value of the variable w is 56
What are algebraic expressions?Algebraic expressions are described as expressions that are composed of terms, variables, factors, coefficients and constants.
Also, algebraic expressions are made up of mathematical or arithmetic operations, such as;
AdditionBracketSubtractionParenthesesMultiplicationDivisionFrom the information given, we have the algebraic equation as;
w - 54 = 2
To determine the value of the variable, we take the steps;
collect the like terms
w = 2 + 54
Now, add the values
w = 56
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Graphing Geometry. Show work
Answers
A graph of the reflection of line segment AB is shown on the coordinate plane below.
What is a reflection across the x-axis?In Mathematics, a reflection across the x-axis would maintain the same x-coordinate while the sign of the y-coordinate changes from positive to negative.
Furthermore, a reflection across the line y = x would interchange (switch) the x-coordinate and y-coordinate and this is represented by the following transformation rule:
(x, y) → (y, x)
Ordered pair A = (4, -1) → Ordered pair A' = (-1, 4).
Ordered pair B = (4, 5) → Ordered pair B' = (5, 4).
In this exercise, we would use an online graphing calculator to plot the image of line segment AB after a reflection about the line y = x.
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1. Which of the following is a set or not?
(a) A=Set of tall man
(b) B=Set of beautiful women
(c) C=Set of tall students of class 10
(d) D=Set of counting number
(e) E=Set of good students
(f) F=Set of yellow roses
Answers
Step-by-step explanation:
Set of tall students of class 10 is a set. Thus, option C is the correct answer.
A set is defined as objects or things that can be justified as similar things combined together and grouped together.
The other sets are not specified. When we look at option A it is said that all the men are tall so they have a common factor i.e. they are tall but could have been more specified. Also in option B it is said that all the women are beautiful, here the common factor is beautiful but it could have been more specified. Similarly option d, option e and option f are also not specified.
When we look at option c, here it specified that the tal students are of class 10 and so I consider option "c" is the correct answer.
To learn more about sets,
9. (a) The scale model of the rocket stood 54 inches high. What was the height of the actual rocket?
(b) Find the height of the actual rocket in feet.
10. The volume of the rocket in problem 9 is how many times the volume of the model?
Answers
The actual rocket height is 1080 inches and the height of the actual rocket is 90 feet.
How to calculate the valueIf the 1/20 scale model of the rocket stands 54 inches high, we can find the height of the actual rocket by multiplying the height of the model by 20:
Actual rocket height = 54 inches x 20 = 1080 inches
In order to convert inches to feet, we divide by 12:
Actual rocket height = 1080 inches / 12 = 90 feet
Therefore, the height of the actual rocket is 90 feet.
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The 1/20 scale model of the rocket stood 54 inches high What was the height of the actual rocket?
(b) Find the height of the actual rocket in feet.