If you mean
[tex]\displaystyle \lim_{x\to0^+} \frac{(1+\sin(7x))^8}x[/tex]
then the limit doesn't exist, since 1 + sin(7x) approaches 1 while the denominator approaches 0.
However, if instead you mean
[tex]\displaystyle \lim_{x\to0^+}(1+\sin(7x))^{8/x}[/tex]
rewrite the limand as
[tex](1+\sin(7x))^{8/x} = \exp\left(\ln(1+\sin(7x))^{8/x}\right) \\\\ = \exp\left(\dfrac{8\ln(1+\sin(7x))}x\right) \\\\ =\exp\left(\dfrac{\ln(1+\sin(7x))}x\right)^8[/tex]
The exponential function is continuous at 0, so we can pass the limit through it:
[tex]\displaystyle\lim_{x\to0^+}\exp\left(\dfrac{\ln(1+\sin(7x))}x\right)^8 = \exp\left(\lim_{x\to0^+}\dfrac{\ln(1+\sin(7x))}x\right)^8[/tex]
The remaining limit takes the indeterminate form 0/0, since ln(1 + sin(7x)) approaches ln(1) = 0, and so does x in the denominator. Apply L'Hopital's rule:
[tex]\displaystyle\exp\left(\lim_{x\to0^+}\dfrac{7\cos(7x)}{1+\sin(7x)}\right)^8 = \exp\left(7\right)^8 = \left(e^7\right)^8 = \boxed{e^{56}}[/tex]
Please Help!!! Will give brainliest
Answer:
e) and f) doesn't exist.
Step-by-step explanation:
Other you can see in picture.
Find the measure of e . A. 88 B. 46 C. 44 D. 90
Answer:
The answer is A. 88.
Step-by-step explanation:
To solve for the measure of angle ( [tex]e[/tex] ), start by noticing that 92 degrees and ( [tex]e[/tex] ) sum up to 180 degrees, which makes them supplementary angles.
Two angles are said to be supplementary angles if they add up to 180 degrees. Supplementary angles form a straight angle (180 degrees) when they are put together. In other words, angle 1 and angle 2 are supplementary, if Angle 1 + Angle 2 = 180 degrees.
Since angle 92 degrees and angle ( [tex]e[/tex] ) sum up to 180 degrees, the equation will look like [tex]92[/tex]°[tex]+e=180[/tex]°. To solve the equation, start by subtracting 92 degrees from both sides, and the equation will look like [tex]e=88[/tex]°. The final answer will be that the measure of angle ( [tex]e[/tex] ) is 88 degrees.
Answer:
88
Step-by-step explanation:
Which inequality is the same 7 - 2/b ≤ 5/b
Answer:
1. B
2. A
Step-by-step explanation:
Those are the correct answers
Find three solutions for this linear function and choose the correct graph by clicking on it. F(x) = x + 3
Answer: The picture that shows 0,3 and 0,3.
They are points on the graph that show the function
Step-by-step explanation: I know because I just did this. I passed!!!
Mrs. Kaur brought identical gift for her 6 nieces and nephews. She spent a total of $94.20. what was the cost of each gift.
Answer:
$15.7 for each
Step-by-step explanation:
here, peice of 6 gifts= $94.20
now price of each gift= $94.20/6
answer is 15.7 dollars
Cam went to the beach and collected seashells. when he put them into 2 piles, 3 piles, and then 5 equal piles. he didn't have any extra. when he put them into 4 piles, he had exactly 2 extra. how many seashells could cam have collected?
Hey there! I'm happy to help!
We see that the number of seashells is divisible by 5, 3, and 2, but not 4. One thing I like to do to find this number is to multiply together all of the numbers it is divisible by. This product will be divisible by all of the numbers because you multiplied them all together! Let's do this below.
2×3×5=30
We see that our answer is 30, and it is divisible by 2, 3, and 5. 30 also isn't divisible by four. If you tried to do so, you would get 28 (4×7) with a remainder of two.
Therefore, Cam could have collected 30 shells.
Have a wonderful day! :D
what is the answer to this question ????
Answer:
yesdbdjxjsjdxjskskamd
Answer:
options B is the check answer
Find the area of this figure.
3 m
4 m
8 m
4 m
[?] square meters
Find the area of each rectangle first
and then add the two areas together.
Answer:
44m²
Step-by-step explanation:
Area of larger rectangle
= length × breadth
= 8m × 4m
= 32m²
Area of smaller rectangle
= length × breadth
= 4m × 3m
= 12m²
Total area of the figure
= Area of larger rectangle + Area of smaller rectangle
= 32m² + 12m²
= 44m²
Suppose you have 60 kg of a radioactive material that decays 50% of its mass every year how much material would you have left after 4 years?
Answer:
Step-by-step explanation:
60 kg × 0.5⁴ = 3.75 kg
It doesn’t match any of the answers
The area of a rectangle is 44m^2, and the length of the rectangle is 3m less than twice the width. Find the dimensions of the rectangle.
Answer:
the length=8
the rectangle=5.5
Step-by-step explanation:
+)convention:
the lengt=a
the width = b => the area of the rectangle = a.b=44m^2 (1)
+) "the length of the rectangle is 3m less than twice the width"
=> 2b-a = 3 (m)
=> a=2b-3
substitute a for (1), we get
the area of the rectangle = a.b = (2b-3).b=44 m^2
=> 2b^2-3b-44=0
=> b=-4 (wrong)
=> b= 5.5 =the width
the lengt = the area of the rectangle/the width=44/5.5=8 m
If 5cm and 3cm are added to the length and width of a square, the perimeter of the resulting rectangle is between twice and three times the perimeter of the original square. Find the possible lengths of the sides of the original square.
Answer:
The answer is between 2 and 4. 2 and 4 can be included if you are including the twice or three times. If it doesn't include those then it would only be anything inbetween.
Step-by-step explanation:
So to start off I would always give placeholder for all the sides. Lets label it x.
2(x+5) + 2(x+3) < 3(4x)
In the equation above, we created a simple equation with 2 representing 2 sides each and the 3 and 5 plugged in. That all is going to be less than 3 times the original perimeter which is 4x for the 4 sides.
2x + 10 + 2x + 6 < 12x
4x + 16 < 12x
16 < 8x
2 < x
We learn that the original x is greater than 2. We don't say it is equal to since it says between. Which doesn't usually include the number stated.
Now we repeat, just instead of 3 its 2 and instead of less than its greater than.
2x + 10 + 2x + 6 > 8x
4x + 16 > 8x
16 > 4x
4 > x
So your answer is between 2 and 4.
The possible lengths of the sides of the original square (x) any value between 4 cm and 8 cm, inclusive.
Let's denote the side length of the original square as "x" centimeters. The perimeter of the square is 4x.
When 5 cm and 3 cm are added to the length and width of the square, a rectangle with dimensions (x + 5) cm and (x + 3) cm. The perimeter of the rectangle is 2 × (x + 5) + 2 × (x + 3) = 2x + 10 + 2x + 6 = 4x + 16.
According to the given information, the perimeter of the rectangle is between twice and three times the perimeter of the original square:
2 × perimeter of square ≤ perimeter of rectangle ≤ 3 × perimeter of square
Substitute the values:
2 × 4x ≤ 4x + 16 ≤ 3 × 4x
Simplify:
8x ≤ 4x + 16 ≤ 12x
Subtract 4x from all parts:
4x ≤ 16 ≤ 8x
Now, divide all parts by 4:
x ≤ 4 ≤ 2x
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write the decimal values of the digits given in bold : 0.437
please tell step by step explaination
Answer:
na na na na na I don't know
How to find the area of the shape on the right
Answer:
19 units²
Step-by-step explanation:
First, divide the shape into two triangles, find the area of those triangles, and then add the areas together.
Big Triangle:
1/2bh
1/2 6(5)
1/2 30
15
Little Triangle
1/2bh
1/2 2(4)
1/2 8
4
Total Area:
15 + 4 = 19 units squared
The temperature dropped a total of 84 degrees in a 3 hour period in Canada. Suppose the temperature dropped
the same amount each hour. What is the hourly drop in temperature?
Answer:
84dgree÷3hours=26 degrees/ hour
Please Help! Evaluate the function at each specified value of the independent variable and simplify. (If an answer is undefined, enter UNDEFINED.)
g(t) = 5t^2 − 8t + 3
Answer:
Given:
g(t) = 5t² − 8t + 3Find the following
g(2)
g(2) = 5(2²) - 8(2) + 3 = 20 - 16 + 3 = 7g(t - 2)
g(t - 2) = 5(t - 2)² - 8(t - 2) + 3 = 5t² - 20t + 20 - 8t + 16 + 3 = 5t² - 28t + 39g(t) - g(2)
g(t) - g(2) = 5t² − 8t + 3 - 7 = 5t² − 8t - 4g(t)=5t^2-8t+3
[tex]\\ \sf\longmapsto g(2)=5(2)^2-8(2)+3[/tex]
[tex]\\ \sf\longmapsto g(2)=5(4)-16+3[/tex]
[tex]\\ \sf\longmapsto g(2)=20-13[/tex]
[tex]\\ \sf\longmapsto g(2)=7\checkmark[/tex]
And
[tex]\\ \sf\longmapsto g(t-2)=5(t-2)^2-8(t-2)+3[/tex]
[tex]\\ \sf\longmapsto g(t-2)=5(t^2-4t+4)-8t+16+3[/tex]
[tex]\\ \sf\longmapsto g(t-2)=5t^2-20t+20-8t+19[/tex]
[tex]\\ \sf\longmapsto g(t-2)=5t^2-28t+39\checkmark[/tex]
And
[tex]\\ \sf\longmapsto g(t)-g(2)[/tex]
[tex]\\ \sf\longmapsto 5t^2-8t+3-7[/tex]
[tex]\\ \sf\longmapsto 5t^2-8t-4[/tex]
Which expression is equivalent to (5^3)−2?
A 1
-
5^3
B -1/ 5•5•5•5•5•5
C 5^3
D 1/5•5•5•5•5•5
Answer:
D 1/5•5•5•5•5•5
Step-by-step explanation:
(5^3)^−2
We know a^b^c = a^(b*c)
5^(3*-2)
5^(-6)
We know a^-b = 1/a^b
1/5^6
1/(5*5*5*5*5*5)
A blueprint has a scale of 1cm : 4 feet. On the blueprint, a room is drawn with dimensions 5cm x 2cm.
Find the area of the room (the units of the answer are square feet).
It is a great idea to use a sheet of graph paper to work this problem.
square feet
Answer:
On the blue print, the room will measure 20 by 8 feet
Step-by-step explanation:
Simplify the expression. 3(7) – 3(3)
Answer:
[tex]12[/tex]
Step-by-step explanation:
[tex]3\times 7-3\times 3[/tex]
This term's numerical factors have been multiplied:-
[tex]=12[/tex]
OAmalOHopeO
A city currently has a population of 8200 people, and is expected to grow by 4%
every year. To the nearest whole person, what is the population expected to be 10
years from now?
The population expected to be 10 years from now is 12,138.
Given that,
The population is 8,200 people.It should be predicted to grow by 4%.Based on the above information,
The population expected to be 10 years from now is
[tex]= Number\ of\ people \times (1+ growth\ rate)^{number\ of\ years}\\\\= 8,200 \times (1 + 0.04)^{10}\\\\[/tex]
= 12,138
Therefore we can conclude that The population expected to be 10 years from now is 12,138.
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Find an equation for the line that passes through the points -4, -1 and 2, 3
Answer:
x1=-4,y1=-1,x2=2,y2=3
Now,
slope (m)=3/2
By formula,
(y-y1)=m (X-x1)
y-(-1)=3/2(x+4)
y+1=3/2(x+4)
2y+2=3x+12
3x-2y+10=0,which is required equation.
Find the distance between the points (3,4) and (6,0).
I
Answer:
first you use distance formula then urr answer will come out....first u try ok.......
A mother whale is at 35meters below the surface and her calf is at the surface. How far does the calf have to swim to get to its mother
What comes next in this sequence? - [ 1, 45, 104, 1034 ] - Please state the pattern and why you chose that answer.
A. 34556
B. 4567
C. 401
D. 54
Answer:
The answer is A. 34556
Step-by-step explanation:
The 5th term of the sequence would be a{5} = 10334.
What is a mathematical function, equation and expression?Sequence : A sequence is defined as an arrangement of numbers in a particular order.
Function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function
Expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators
Equation : A mathematical equation is used to equate two expressions.
Given is the sequence -
1, 45, 104, 1034
We can write the next term as -
a{n} = 10a{n - 1} - 6
So, we can write -
a{5} = 10 x 1034 - 6
a{5} = 10340 - 6
a{5} = 10334
Therefore, the 5th term of the sequence would be a{5} = 10334.
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56-x=728+2x what's the answer?
Answer:
56-x=728+2x
1.) rearrange
[tex]56x = 728 + 2x \\ \ - x + 56 = 728 + 2x[/tex]
[tex] - x + 56 = 728 + 2 x \\ \\ - x + 56 = 2x + 728[/tex]
2.)subtract 56 on both side
[tex] - x + 56 = 2x + 728 \\ \ - x + 56 - 56 = 2x + 728 - 56[/tex]
3.) simplify
[tex] - x = 2x + 672[/tex]
4.)Subtract 2 on both sides
[tex] - x = 2x + 672 \\ \\ - x - 2x = 2x + 672 - 2x[/tex]
5.) simplify
[tex] - x - 2x = 2x + 672 - 2x \\ \\ - 3x = 2x + 672 - 2x \\ \\ - 3x = 672[/tex]
6.)divide both sides on the same equation
[tex] - 3x = 672 \\ \\ \frac{ - 3x}{ - 3} = \frac{672}{ - 3} [/tex]
7.) simplify
[tex]x = - 224[/tex]
8.) answer
[tex]x = - 224[/tex]
if u need any help, just let me know
Plz help me with this
9514 1404 393
Answer:
see attached
Step-by-step explanation:
a) A table and graph are attached.
__
b) The relationship is NOT PROPORTIONAL. The line does not go through the origin (0, 0).
पाठशाला
Date
Page
amount of Rs sooo at the
annual Rate or 127.
is as
8ooo, and
find the interest
and time 2
what is the x intercept of y + 4 =− 4(x − 1)
Answer:
0
Step-by-step explanation:
since the "b" in y=mx+b ends up being 0, that means that the y intercept is 0, which also means that the x intercept is 0.
Pls Someone Help me Question:make the greatest and smallest 4 digit number by using any one digit twice
= 8,2,7
Answer:
Greatest digit: 8872.
Smallest digit:2278.
9514 1404 393
Answer:
greatest: 8872smallest: 2278Step-by-step explanation:
Greatest
The greatest possible number is created by putting the greatest allowable digit in the space available that has the highest possible place value. Here, the greatest digit is 8, and the highest place value of a 4-digit number is the thousands place: 8000. Once you have filled that place, you can use the digit 8 one more time in the hundreds place: 8800.
Now, the greatest digit available is the digit 7, and the left-most place you can put it is the tens place: 8870. Finally, the only digit and place available are the digit 2 and the ones place.
Your greatest 4-digit number is 8872.
Smallest
To form the smallest number, you use a similar process, filling places in the number from left to right with the smallest allowable digit. The smallest digit, 2, is allowed twice, so the smallest number that can be formed is 2278.
write the equation of the line that passes through points (-7,8) and (4,-5)
Answer:
y=-3/11x+67/11
Step-by-step explanation:
y-8=-5-8/4--7(x--7)
y-8=-3/11(x+7)
11y-88=-3x-21
11y=-3x-21+88
11y=-3x+67
y=-3/11x+67/11
Answer:
y = -13/11x - 3/11
Step-by-step explanation:
First, find the slope of the line using the slope formula.
[tex]m=\frac{y_2-y_1}{x_2-x_1}\\m=\frac{-5-8}{4-(-7)}\\m=-\frac{13}{11}[/tex]
Then, use the point-slope formula and substitute the values for the variables.
[tex]y-y_1=m(x-x_1)\\y-8=-\frac{13}{11}(x-(-7))\\y-8=-\frac{13}{11}x-\frac{91}{11}\\y=-\frac{13}{11}x-\frac{3}{11}[/tex]
(c) 5 points possible (graded) The problem you encountered in part (b) is called separation . It occurs when the can be perfectly recovered by a linear classifier, i.e., when there is a such that In order to avoid this behavior, one option is to use a prior on . Let us investigate what happens if we assume that is drawn from a distribution, i.e., What is the joint log likelihood of this Bayesian model
We have that these are the key points given below
The Bayesian Theorem is a theorem that centers or basis its claim on the facts that the probability of an event occurring is based on Prior Knowledge that of situation or Prior factors of the Event.
Likelihood function is a function that take into account all statistical model and determine there best application given the statistical data given.
Bayesian Theorem
The Bayesian Theorem is a theorem that centers or basis its claim on the facts that the probability of an event occurring is based on Prior Knowledge that of situation or Prior factors of the Event
i'll explain further with an example
Given that when two unfair dice are thrown a 100 times the probability of getting the higher figure in the range of 6-8 , Therefore the Bayesian Theorem simply assumes that this range of 6-8 to be the highest for all 100 throws of two dice.
The Bayesian model is given as
[tex]B=Prior * Likelihood=Posterior * Marginal[/tex]
Bayesian model is a statistical model.
This leads us to the definition of the Likelihood function
Likelihood function is a function that take into account all statistical model and determine there best application given the statistical data given.
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