The limit of the expressions [tex]3^{2n} + 1[/tex] and [tex]4^{n + 2} - 3[/tex] for n to infinity is infinity
How to calculate the limits?The expressions are given as:
[tex]3^{2n} + 1[/tex]
[tex]4^{n + 2} - 3[/tex]
The limits of the expressions as they approach infinity are represented as:
[tex]\lim_{n \to \infty} 3^{2n} + 1[/tex] and [tex]\lim_{n \to \infty} 4^{n + 2} - 3[/tex]
Substitute [tex]\infty[/tex] for n in both expressions
[tex]\lim_{n \to \infty} 3^{2 * \infty} + 1[/tex] and [tex]\lim_{n \to \infty} 4^{\infty + 2} - 3[/tex]
Solve both expressions independently;
[tex]\lim_{n \to \infty} 3^{2n} + 1 = 3^{2 * \infty} + 1[/tex]
Evaluate the product
[tex]\lim_{n \to \infty} 3^{2n} + 1 = 3^{\infty} + 1[/tex]
Evaluate the exponent
[tex]\lim_{n \to \infty} 3^{2n} + 1 = \infty + 1[/tex]
Evaluate the sum
[tex]\lim_{n \to \infty} 3^{2n} + 1 = \infty[/tex]
Also, we have:
[tex]\lim_{n \to \infty} 4^{n + 2} - 3 = 4^{\infty + 2} - 3[/tex]
Evaluate the sum
[tex]\lim_{n \to \infty} 4^{n + 2} - 3 = 4^{\infty} - 3[/tex]
Evaluate the exponent
[tex]\lim_{n \to \infty} 4^{n + 2} - 3 =\infty - 3[/tex]
Evaluate the difference
[tex]\lim_{n \to \infty} 4^{n + 2} - 3 =\infty[/tex]
Hence, the limit of the expressions for n to infinity is infinity
Read more about limits at:
https://brainly.com/question/282767
#SPJ1
Consider the triangle shown in the picture. Express the perimeter of the triangle as an expression in terms of
x
. Simplify your answer.
Answer:
The perimeter of the triangle is 11x+1
Mrs.Mason the art teacher is mixing red and yellow paint. The ratio of red to yellow is 3:5. How much red paint should be mixed with 20 ounces of yellow?
Divide total yellow by its ratio portion.
20/5 = 4
multiply that by the portion for red:
3 x 4 = 12
answer: 12 ounces
Kindly Answer This And Don't Waste My PTS! ☁️
PROBLEM NUMBER 1: Solve 5x+2=22
PROBLEM NUMBER 2: Solve 2x+5=12
PROBLEM NUMBER 3: Solve 2x-5=7
====================================
[tex] \large \sf \underline{Problems:}[/tex]
PROBLEM NUMBER 1: Solve 5x+2=22PROBLEM NUMBER 2: Solve 2x+5=12PROBLEM NUMBER 3: Solve 2x-5=7====================================
[tex] \large \sf \underline{Answers:}[/tex]
[tex] \large \qquad \qquad \bold{ \#1. \: x \: = \: 4}[/tex]
[tex] \large \qquad \qquad \bold{ \#2. \: x \: = \: \frac{7}{2} }[/tex]
[tex] \large \qquad \qquad \bold{ \#3. \: x \: = \: 6}[/tex]
====================================
[tex] \large \sf \underline{Solutions:}[/tex]
Problem Number 1:-[tex] \large\rm{5x \: + \: 2 \: = \: 22}[/tex][tex] \large\rm{5x \: = \: 22 \: - \: 2}[/tex][tex] \large\rm{5x \: = \: 20}[/tex][tex] \large\rm{x \: = \: \frac{20}{5} }[/tex][tex] \large\rm\green{x \: = \: 4}[/tex][tex] \therefore[/tex] The answer of you're problem is x = 4.
====================================
Problem Number 2:-[tex] \large\rm{2x \: + \: 5 \: = \: 12}[/tex][tex] \large\rm{2x \: = \: 12 \: - \: 5}[/tex][tex] \large\rm{2x \: = \: 7}[/tex][tex] \large\rm\green{x \: = \: \frac{7}{2} } [/tex][tex] \therefore[/tex] The answer of you're problem is 7/2.
====================================
Problem Number 3:-[tex] \large\rm{2x \: - \: 5 \: = \: 7}[/tex][tex] \large\rm{2x \: = \: 7 \: + \: 5}[/tex][tex] \large\rm{2x \: = \: 12}[/tex][tex] \large\rm{x \: = \: \frac{12}{2} } [/tex][tex] \large\rm\green{x \: = \: 6}[/tex][tex] \therefore[/tex] The answer of you're problem is x = 6.
====================================
Hope this helps!
Please answer! Will give brainliest please and thank you
Answer:
119 square ft is the answer now give me brainliest
Alguien sabe como conversar en brainly osea, poder conversar con otras personas o no se puede? perdon si pongo matematicas XD
Answer:
Hola, supongo que estás preguntando si hay una forma de conversar con otras personas en privado en Brainly.
Actualmente, no hay forma de conversar en privado con otras personas. Muchas personas conversan en los comentarios de preguntas o respuestas, pero Brainly es un sitio web educativo y le recomendaría que use Brainly solo con fines educativos.
¡Espero que esto te ayude! Que tengas un buen día.
which of the following is(are) the solution(s) to |5x+2|=8
A. x=-2,6/5
B. x=6/5
C. x=2
D. x=2,-6/5
Option A.
Hope it helps.
Answer:
A
Step-by-step explanation:
|5x+2|=8 this mean that:
5x+2=8 and 5x+2=-8
5x+2-2+8-2 and 5x+2-2=8-2
5x=6 and 5x=-10 then divided both sides by 5
x=6/5 and x=-2
Due to the depreciation of the Rand, the import price of a particular raw material
rises from $22 562,25 per tonne to $25 507,59 per tonne. What was the
percentage increase in price (to two decimal places)?
Answer:
13.05%
Step-by-step explanation:
[tex]\begin{aligned}\sf Percentage\:increase &= \sf\dfrac{final\:value-initial\:value}{initial\:value} \times 100\\\\& = \sf \dfrac{25507.59-22562.25}{22562.25} \times 100\\\\& = \sf \dfrac{2945.34}{22562.25} \times 100\\\\& = \sf 0.1305428315 \times 100\\\\& = \sf 13.05 \% \:(2\:dp)\end{aligned}[/tex]
1: In a class of 30 students, half of the students like to watch cartoon channels on TV and one sixth like to watch informative channels. The rest like to watch movies. How many students like to watch movies?
The student body of a large university consists of 60% female students. A random sample of 8 students is selected. What is the probability that among the students in the sample at least 6 are female?
Using the binomial distribution, it is found that there is a 0.3154 = 31.54% probability that among the students in the sample at least 6 are female.
What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.In this problem:
The student body of a large university consists of 60% female students, hence p = 0.6.A random sample of 8 students is selected, hence n = 8.The probability that among the students in the sample at least 6 are female is given by:
[tex]P(X \geq 6) = P(X = 6) + P(X = 7) + P(X = 8)[/tex]
In which:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 6) = C_{8,6}.(0.6)^{6}.(0.4)^{2} = 0.2090[/tex]
[tex]P(X = 7) = C_{8,7}.(0.6)^{7}.(0.4)^{1} = 0.0896[/tex]
[tex]P(X = 8) = C_{8,8}.(0.6)^{8}.(0.4)^{0} = 0.0168[/tex]
Then:
[tex]P(X \geq 6) = P(X = 6) + P(X = 7) + P(X = 8) = 0.2090 + 0.0896 + 0.0168 = 0.3154[/tex]
0.3154 = 31.54% probability that among the students in the sample at least 6 are female.
More can be learned about the binomial distribution at https://brainly.com/question/24863377
#SPJ1
5. Find the largest difference between a 3-digit number and a 2-digit number.
Answer:
989
Step-by-step explanation:
The largest difference could be possible between Largest 3 digit number and smaller two digit number
I.e,
999-10=989
complete the steps to solve the equation
Answer:
attached below
Step-by-step explanation:
minus 2 from each side in order to isolate T with the coefficient. To get rid of the coefficient multiply to get 1 which is 5 in this case. Then the answer will be 75
1.2 The following pattern is given: -100,-97; -91;
1.2.1 What is the fifth term for the pattern?
1.2.2 Determine the general rule for the pattern (the nth term)
Brainly 505 Server Error
A teacher bought 12 packets of crayons. Seven of the packets had 9 crayons and the other 5 packets had 10 crayons. How many crayons did the teacher buy in all
Answer:
The teacher bought 113 crayons.
4x10^2+3x10^3=
Please see the attached photo
Answer:
3.4
Step-by-step explanation:
Converting all terms to multiples of 10³ :
4 × 10² + 3 × 10³0.4 x 10³ + 3 x 10³(0.4 + 3) × 10³3.4 × 10³Please help me GENIUS Rank
Directions: Complete the following frequency distribution table, then compute the mean, median, and mode of the distribution. Show your complete solutions. (25 points)
Class interval] frequency (f)] fxm
99-101 ] 17 ].
102-104 ] 25 ]
105-107 ] 13 ]
108-110 ]. 16 ]
111-113 ]. 29 ]
total ]N= ]. Efxm=
less than cumutalti frequency (<cf)
[. ]
[. ]
[. ]
[. ]
[. ]
[. ]
The equation whose roots are multiplied by 3 of those of 2x^2 + 3x – 1=0 is
Answer:
I have got the answer
Step-by-step explanation:
Let the roots of 2x² + 3x - 1 = 0 be a and
To find:
The quadratic equation whose roots are 3a
Solution:
See picture attahed
The rest of explanation is given in your previously asked question see there I have also answered it
PLEASE MARK ME BRAINLIEST IF MY ANSWER IS CORRECT PLEASE
The graph of y=-3x+ 2 is:
go on desmos and see what the graph looks like
Solve 4x+3>3x+7
This one is so confusing
Answer:
x>4
Step-by-step explanation:
Answer:
x > 4
Step-by-step explanation:
1. 4x+3>3x+7
2. x>4
Choose the graph that represents the equation y = 2|x – 2|.
Answer:
Graph D. is the correct graph.
-6 -5(6x-4)
Explain please
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
let's evaluate ~
[tex]\qquad \sf \dashrightarrow \: - 6 - 5(6x - 4)[/tex]
[tex]\qquad \sf \dashrightarrow \: - 6 - [(5 \cdot6x) - (5 \cdot4)][/tex]
[tex]\qquad \sf \dashrightarrow \: - 6 - (30x - 20)[/tex]
[tex]\qquad \sf \dashrightarrow \: - 6 -30x + 20[/tex]
[tex]\qquad \sf \dashrightarrow \: - 30x + 14[/tex]
I hope you understood the whole procedure ~
can you please help me please:(…
Answer:
The function is linear
Step-by-step explanation:
"I disagree with Maryam because if we substitute the values and graph the function, it will turn out to be linear."
you have $5600. The best interest rate you can find is 3%
compounded quarterly, for how long should you deposit the money in order
have $9600? how many years
Answer:
18 years
Step-by-step explanation:
The formula for computing accrued amount A for a principal of P at an interest rate of r(in decimal) compounded n times in a year for t years is given by
[tex]A = P(1 + \frac{r}{n})^{nt}[/tex]
Note that r is percentage converted to decimal. So 3% = 3/100 = 0.03
We can rearrange the above equation to:
[tex]\frac{A}{P} = (1 + \frac{r}{n})^{nt}[/tex]
Taking logs on both sides
[tex]log(\frac{A}{P}) = log(1 + \frac{r}{n})^{nt}[/tex]
This gives
[tex]log(\frac{A}{P}) =nt \times log(1 + \frac{r}{n})\\So,\\nt = \frac{log(\frac{A}{P})}{ log(1 + \frac{r}{n})}[/tex]
In this particular problem, n = 4, , A= 9600, P = 5600, r =0.03, so r/n = 0.03/4 = 0.0075
1 + r/n = 1+0.0075 = 1.0075
4t = log(9600/5600)/log(1.0075) = log(1.714) / log(1.0075) = 0.234 /0.00325 = 72
t = 72/4 = 18 years
In a linear function, the domain will always be _____ and the range will always be _____
Answer:
1. x values
2. y values
hope it helps you:)
Given the arithmetic sequence an= -5 + 3(n - 1), what is the domain for n?
Answer:
Domain for n is All integers where n ≥ 1.
Step-by-step explanation:
In arithmetic sequence,
where a is first term.
d is common difference.
n is number of terms.
Now, in given sequence recursive formula for nth term in
the number of term is n and it belongs to natural number.
Hence, domain for n is All integers where n ≥ 1.
Have a wonderful day/night/afternoon and stay safe my friends
15ml of Tylenol 3 to given every 4-6 hours. Your research indicates that there are 12mg of codeine per 5ml of liquid and that the safe dosage is between 0.5 and 1mg/kg/every 4-6 hours. Is this prescription safe for your child? Explain. If not, what would a safe dose be?
Answer:
If the safe dose is .5 to 1 mg/kg/dose, the safe limit depends on the side of the child. Using the more conservative limit of .5mg/kg, you have 36mg(kg/.5mg)=72kg, which is roughly 160lbs, Even with the upper limit of 1mg/kg, you still have 36mg(kg/1mg) = 36kg, or 80lbs, which is a larger child. I would say this dose isn't "safe", but you really need the weight of the child to calculate what is a safe dose.
Step-by-step explanation:
can someone please help me with this math problem please fast
Which of the following images shows only parallel lines highlighted in red? Figure A has four line segments connected to form a square, with the circle in the upper left corner colored red. Figure B has four line segments connected to form a square, the line segment on the right and the bottom line segment connect at the vertex and are colored red. Figure C has four line segments connected to form a square, with the bottom line segment colored red. Figure D has four line segments connected to form a square, with the top line segment and the bottom line segment colored red. Group of answer choices Figure A Figure B
I need help please!
Donkey Kong is rolling cylindrical barrels
of different sizes at Mario.
The RADIUS of the barrel is 6.
What is the circumference of the barrel?
If your answer is correct Mario will clear the barrel.
6
Answer:
see below
Step-by-step explanation:
cicumference= 2*pi*r
=2*(22/7)*6
=(2*22*6)/7
=264/7
=37.71
What is the volume of the shape this net makes?
Answer:
1388.13
Step-by-step explanation:
So, the formula for a cylinder is V=pi x R^2 x H
We plug in what we know.
V=3.14x4^2x27.63
V=3.14x16x27.63
V=50.24x27.63
V=1388.13
Did I do it right? If the measure of ∠DAB=51∘, ∠CAB=x, and ∠DAC=x+1, find the measure of ∠CAB
If the measure of angles ∠DAB = 51° and the value of x is 25. Then the measure of angle ∠CAB will be 25°.
What is an angle?The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.
If the measure of angles ∠DAB = 51°, ∠CAB = x, and ∠DAC = x + 1.
Then the measure of angle ∠CAB will be
We know
∠CAB + ∠CAD = ∠DAB
x + x + 1 = 51
2x = 50
x = 25
Then the measure of the angle ∠CAB will be
∠CAB = x
∠CAB = 25
∠CAB = 25°
More about the angled link is given below.
https://brainly.com/question/15767203
#SPJ1