Answer:
Splitting that number into 10 equal wholes.
Step-by-step explanation:
(fractions)
Hello find the limit stated below
[tex]\\ \rm\Rrightarrow {\displaystyle{\lim_{x\to 0}}}\dfrac{sin^3x+3cosx-cot^2x}{tan^3x+7sinx+3sec^2x}-e^{3x}[/tex]
Note:-
Make sure to include proper explanation and all steps
Answer:
[tex]\displaystyle \lim_{x \to 0} \frac{\sin^3 x + 3\cos x - \cot^2 x}{\tan^3 x + 7 \sin x + 3 \sec^2 x} - e^{3x} = \boxed{- \infty}[/tex]
General Formulas and Concepts:
Calculus
Limits
Graphical LimitsRight-Side Limit:
[tex]\displaystyle \lim_{x \to c^+} f(x)[/tex]
Left-Side Limit:
[tex]\displaystyle \lim_{x \to c^-} f(x)[/tex]
Limit Rule [Variable Direct Substitution]:
[tex]\displaystyle \lim_{x \to c} x = c[/tex]
Discontinuities
Removable (Hole)JumpInfinite (Asymptote)Step-by-step explanation:
Step 1: Define
Identify given.
[tex]\displaystyle \lim_{x \to 0} \frac{\sin^3 x + 3\cos x - \cot^2 x}{\tan^3 x + 7 \sin x + 3 \sec^2 x} - e^{3x}[/tex]
Step 2: Find Limit
Let's start out by directly substituting x = 0 into our limit.
[Limit] Apply Limit Rule [Variable Direct Substitution]:We can see that the cotangent of 0 is undefined. Since we do not have an indeterminate form, we cannot use L'Hopital's Rule. Let's look at the function graphically (refer to the attachment).
Approaching the left limit, we can see that the graph heads towards negative infinity.
Approaching the right limit, we can see that the graph also heads towards negative infinity.
∴ we can say that the limit as x approaches 0 is equal to negative infinity.
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Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Limits
It's plain to see that [tex]e^{3x}\to1[/tex] as [tex]x\to0[/tex], so I'll focus on the trigonometric expression.
Multiply uniformly through the expression by [tex]\sin^2(x)\cos^3(x)[/tex] :
[tex]\dfrac{\sin^3(x) + 3\cos(x) - \cot^2(x)}{\tan^3(x) + 7\sin(x) + 3\sec^2(x)}[/tex]
[tex]= \dfrac{\cos^3(x) \left(\sin^5(x) + 3\cos(x)\sin^2(x) - \cos^2(x)\right)}{\sin^2(x) \left(\sin^3(x) + 7\cos^3(x)\sin(x) + 3\cos(x)\right)}[/tex]
Now as [tex]x\to0[/tex],
• [tex]\cos^3(x)\to1[/tex]
• [tex]\sin^5(x)+3\cos(x)\sin^2(x)-\cos^2(x)\to-1[/tex]
• [tex]\sin^3(x) + 7\cos^3(x)\sin(x) + 3\cos(x) \to 3[/tex]
but [tex]\sin^2(x)\to0[/tex], so [tex]x = 0[/tex] a non-removable discontinuity. Then from either side of [tex]x = 0[/tex], [tex]\frac1{\sin^2(x)}\to+\infty[/tex], and taking into account the sign from the second point above, the overall limit would be
[tex]\displaystyle \lim_{x\to0} \frac{\sin^3(x) + 3\cos(x) - \cot^2(x)}{\tan^3(x) + 7\sin(x) + 3\sec^2(x)} - e^{3x} = -\infty-1 = \boxed{-\infty}[/tex]
Dara and Jo share £420 in the ratio 2:5.
Calculate how much Dara and Jo receive each.
Answer:
Dara receives £120 and Jo receives £300
Step-by-step explanation:
D:J
2:5
5+2=7
£420÷7= £60
1 on the ratio= £60
Dara:
£60 × 2= £120
Jo:
£60× 5= £300
What is 3/4 divided by 7/10
Answer:
1.07
Step-by-step explanation:
A shipping crate is shaped like a rectangular
prism. It is 5 feet long by 3 feet wide by 3 feet
high. What is the volume of the crate?
The volume of the rectangular prism having the dimension 3 feet wide, 5 feet long, and 3 feet tall is 45 cubic feet.
What is a rectangular prism?A rectangular prism is a closed solid that has two parallel rectangular bases connected by a rectangle surface.
A crate is shaped like a rectangular prism. The crate is 3 feet wide, 5 feet long, and 3 feet tall.
The volume of the rectangular prism will be given as
Volume = length × width × height
Then put the values, we have
Volume = 3 × 5 x 3
Volume = 45
The volume of the rectangular prism having the dimension 3 feet wide, 5 feet long, and 3 feet tall is 45 cubic feet.
More about the rectangular prism link is given below.
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Volume
LBH5(3)(3)5(3)²5(9)45ft³Paul is going to buy a collectible vintage painting from a local art gallery. the painting is priced at $600 in the gallery. the gallery owner does accept credit cards but prefers cash. in fact, he offers to give paul a 5% discount if he can pay in cash. paul doesn't have any cash but can get a cash advance on his credit card. his credit card has an apr of 16% on credit purchases and a 32% apr on cash advances. assuming paul wants to pay the painting off over 12 months, which of the following is true? a. paul will pay a total of $696, over 12 months, if he purchases the painting with his credit card. b. paul will pay a total of $653.28, over 12 months, if he purchases the painting with his credit card. c. paul will pay a total of $782.40, over 12 months, if he purchases the painting with a cash advance for discounted purchase price. d. paul will pay a total of $708.96, over 12 months, if he purchases the painting with a cash advance for discounted purchase price.
When Paul will pay the amount over 12 months, if he purchases the painting with cash advance the discounted purchase price will be $782.40. Then the correct option is C.
What is APR?APR on a credit card is the way of saying that the interest you are charged over a year is equal to roughly of your balance.
Paul is going to buy a collectible vintage painting from a local art gallery.
The painting is priced at $600 in the gallery.
The gallery owner does accept credit cards but prefers cash.
In fact, he offers to give paul a 5% discount if he can pay in cash.
Paul doesn't have any cash but can get a cash advance on his credit card.
His credit card has an apr of 16% on credit purchases and a 32% apr on cash advances.
When Paul will pay the amount over 12 months, if he purchases the painting with cash advance the discounted purchase price will be
[tex]\rm A = 0.95 \times 600 (1+\dfrac{0.32}{12})^{12}\\\\A = 782.40[/tex]
More about the APR link is given below.
https://brainly.com/question/8846837
5.0.75% of 80 is what number?
A. 0.6
B.0060
C.60
D.6000
Answer:
Um im sure the answer is C btw
Step-by-step explanation:
correct me if im wrong
The function f(t) is given by the graph. What is the domain of f(t)?
Check the picture below.
Answer:
-4 ≤ t ≤ 4
Step-by-step explanation:
A locker requires a three-digit code to open the lock. The code must contain one letter and two numbers, and no letter or number can be repeated. You can choose from among four letters, A, B, C, and D, and two numbers, 5 and 6.
The size of the sample space is
If a code is chosen at random, the probability that it has a letter that immediately follows an odd number is
If a code is chosen at random, the probability that D is in the code but is not in the first position is
Answer:
B56 or D65 or B65 or D56
Step-by-step explanation:
a. 36, 26letters + 10 numbers
b. 1/2
c. 1/4
The size of the sample space is 8.
The probability that it has a letter that immediately follows an odd number is 1/2.
There is no probability that D is in the code but not in the first position.
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
Example:
The probability of getting a head in tossing a coin.
P(H) = 1/2
We have,
The size of the sample space is the number of ways to choose one letter and two numbers, without repetition.
We can choose the letter in 4 ways, the first number in 2 ways, and the second number in 1 way (since we can't repeat a number), giving a total of 4 x 2 x 1 = 8 possible codes.
Let's list all the possible codes: 5A6, 5B6, 5C6, 5D6, 56A, 56B, 56C, 56D
The probability that a code has a letter that immediately follows an odd number:
We need to count the number of codes that have a letter following an odd number.
From the list above, we see that the codes 5B6, 5D6, 56B, and 56D have a letter following an odd number.
Therefore, there are four favorable outcomes out of eight possible outcomes.
So the probability is 4/8 = 1/2.
The Probability that D is in the code but not in the first position:
D can be in the second or third position.
If D is in the second position, there are 3 ways to choose the first digit (since we can't use D, and we can't repeat the first digit), and 1 way to choose the third digit, giving a total of 3 * 1 = 3 codes.
If D is in the third position, there are 3 ways to choose the first digit and 2 ways to choose the second digit (since we can't repeat any digit), giving a total of 3 x 2 = 6 codes.
So there are 3 + 6 = 9 favorable outcomes out of 8 possible outcomes (since there are 8 possible codes in total).
Therefore, the probability is 9/8, which is greater than 1.
This is not possible, so the answer is that there is no probability that D is in the code but not in the first position.
Thus,
The size of the sample space is 8.
The probability that it has a letter that immediately follows an odd number is 1/2.
There is no probability that D is in the code but not in the first position.
Learn more about probability here:
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3. Which value is not needed to construct a box plot?
A. upper quartile B. minimum value
C. median
D. mean
I’m game shows 30% is taken from your prize earnings. How much would a game show give you in order to equal 1 hundred thousand, after taxes?
I already have the equation worked out-
100,000= Y- (30%xY)
You gotta find Y
Answer:
$142,857.14
Step-by-step explanation:
As per the question,
Y = prize money$100,000 is the money you get30% is deducted from YSolving for Y
Convert 30% to decimal formDivide 30% by 100%30%/100% = 0.3Now, solve the equation.100,000 = Y - 0.3Y100,000 = 0.7Y100,000 = 7Y/10Y = 1,000,000/7Y = $142,857.14Any whole number that can be represented in base 10 can also be represented in base 2, although it may take ____ digits.
Answer:
More
Step-by-step explanation:
Any whole number that can be represented in base 10 can also be represented in base 2, although it may take more digits.
how do you say if a number is greater than 0 it equals one but if it's less than 0 it the actual number
Answer:
If n > 0, then n= 1
If n < 0, then n=n
If you could word this a bit differently, I might be able to help more, but this is what I'm getting from it. The way you worded it is a bit confusing.
If the diameter of the small can is 4 cm and its height 6 cm, find its total surface area, in cm².
Answer:
100.53cm2 if I'm not mistaken. or 32π cm2
Suppose that scores on an exam are normally distributed with mean 80 and standard deviation 5, and that scores are not rounded. What is the probability that a student scores higher than 85 on the exam
Answer:
3
Step-by-step explanation:
cus it's two 80s and 2 5 so 5 minus 2 is 3
please help! what is the arc RU? thank you so much!
Answer: 92° or 1.6057 radians
Step-by-step explanation:
the 4 angles created by the intersecting lines SU and RT have to equal 360°
<v = 88° because of vertical angles so
88° • 2 = 176°
360° - 176° = 184°
184°/ 2 = 92°
92°+92°+88°+88° = 360°
then, that makes 92° the central angle of arc RU and the central angle degrees is always equal to the arc it subtends
hope this helps :)
on her first day of work, mia sold one straw hat. on day two, she sold three straw hats. on day three, she sold five straw hats, on each succeeding day, she sold two more straw hats than she had sold on the previous day. how many straw hats in total had mia sold after working 40 days?
If Mia sold 2 more hats on each suceeding day, after working 40 days it is expected Mia had sold a total of 1523 hats.
How many hats will Mia sell everyday?Day: Hats
1 = 12=33 = 54=75= 96=117= 138= 159=1710=1911= 2112=2313= 25among othersYou can notice the number of hats she will sell follow a pattern as there are only sequential odd numbers.
How many hats will Mia sell in total?By following the sequence let's add the hats she will sell everyday:
1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23 + 25 + 27 + 29 + 31 + 33 + 35 + 37 + 39 + 41 + 43 + 45 + 47 + 49 + 51 + 53 + 55 + 57 + 59 + 61 + 63 + 65 + 67 + 69 + 71 + 73 + 75 + 79 = 1523Learn more about sums in: https://brainly.com/question/13013054
Rearrange 4x+2y to make Y the subject.
i will give 70 -0ints
Answer:
See below ~
Step-by-step explanation:
(a) Mean of the data
2.4 + 1.6 + 3.2 + 0.3 + 1.5 / 59/51.8(b) New mean after each data point increased by 10
12.4 + 11.6 + 13.2 + 10.3 + 11.5 / 559/511.8(c) New mean after each data point doubled [from (b)]
24.8 + 23.2 + 26.4 + 20.6 + 23 / 5118/523.6Answer:
a) 1.8
b) 11.8
c) 23.6
mean: sum of numbers/total numbers
Part A⇒ mean: (2.4+1.6+3.2+0.3+1.6)/5 ⇒ 9/5 ⇒ 1.8
Part BIf all the data's are increased by 10
{12.4, 11.6, 13.2, 10.3, 11.5}
Then mean ⇒ (12.4+11.6+13.2+10.3+11.5)/5 ⇒ 11.8
Part Cif the new data doubled, the mean will be double
11.8 * 2 = 23.6
Last week, the price of bananas at a grocery store was $0. 80 per pound.
This week, pears at the same grocery store are on sale at 25% discount.
What is the total price of 5. 5 pounds of bananas this week at the grocery
store?*
How do you solve this
Answer:
.2 maybe but I don't know how to do this
Please help. I'll mark you brainliest if right. I really need help
Δ ABC and ΔDEF are similar triangles. If m∠A =104∘and m∠E = 36∘, what is ∠C?
1. 36
2. 40
3. 76
4. 104
Answer:
2
x=40
Step-by-step explanation:
A triangle has 180 degrees and considering that triangle ABC is similar to DEF that means they have the same angle (A=D,B=E,C=F)
180=104 +36+x
180=140+x
180-140=x
40=×
please help mee i beg
Step-by-step explanation:
8.5 × -3 = a
-25.5 = a
b - 7 = -11
b = -4
c -(-3) = 15
c = 12
d - 4 = 32
d = 36
if you still have any doubts feel free to ask
What is the length of the missing leg? If necessary, round to the nearest tenth
Answer: 48 yards
Step-by-step explanation:
Answer: 48 yd
Step-by-step explanation:
when trying to find one leg of a triangle given the other two, a^2 +b^2 = c^2 is applicable. A representing the first leg, B representing the second, and C representing the hypotenouse (a and b are interchangeable). So,
formula: a^2 + b^2 = c^2
insert given: 20^2 + b^2 = 52^2
exponents: 400 + b^2 = 2704
subtract: b^2 = 2704 - 400
simplify: b^2 = 2304
square root of both sides: b = [tex]\sqrt{2304}[/tex]
answer: b = 48
Which lines best approximate the directrices of the ellipse? Round to the nearest tenth.
x = −4.6 and x = 4.6
x = −3.5 and x = 3.5
y = −4.6 and y = 4.6
y = −3.5 and y = 3.5
Answer is C
Edge 2022
C aka y = -4.6 and y = 4.6
Step-by-step explanation:
i just took the unit review test on edg. :)
Answer:
The Answer is c have a good day...
Step-by-step explanation:
Evalueate the measure x in the figure.
Answer:
82 degrees
Step-by-step explanation:
180-98 = 82
They are supplementary and make 180 in total so x is 82
whats this? mulitply 12.1/4
Answer: 3
Step-by-step explanation: 12/1 × 1/4
Identify the rule that correctly describes each sequence. 12, 8, 4, 0, –4, … each term is 4 more than the previous term. each term is 4 less than the previous term. each term is 1/2 the previous term. each term is 2/3 the previous term.
Answer:
Each term is 4 less than the previous term
Step-by-step explanation:
Term Difference
12 --
8 -4
4 -4
0 -4
-4 -4
Answer:
First one is B and the second one is D
Step-by-step explanation:
Just did it on Edge2023
Will give brainliest!!!
Answer:
5,-5,-2 are the solutions
Step-by-step explanation:
f(x)=0 thus, either:
1) x+5 = 0 and thus x= -5
or
2) x+2=0
thus x= -2
or
3) x - 5 = 0
thus x = 5
notice that the other bracket can be written as:
(x+2)(x-5)
the capacity of cylindrical water tank is 539 litres. if its height is 1.4 metres then find the radius of the base.
Answer:
350m
Step-by-step explanation:
• Capacity= volume/1000
• but we know that the volume of the cylinder is
[tex]\pi {r}^{2}h[/tex]
so substitute it I'm the volume space
• The substitute for
[tex]\pi \: as \: \frac{22}{7} \: and \: h \: as \: 1.4 \: and \: also \: capacity \: as \: 539[/tex]
• 539 = ((22/7)× r²× 1.4)/1000
• when you simplify you get r as 350m
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Explain to The Answer to Please
Answer:
X cord: 1
Y cord: -2
Step-by-step explanation:
X cord is left to right and is one point right.
Y Cord is up and down and is 2 down. the - implies negative because the point is down.
(If you need help with this or other problems Here is a good website to help, https://www.splashlearn.com/math-vocabulary/geometry/coordinate-plane)