A line passes through the pointa (-8,8) and (12,7)

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

Right-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

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.

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]

Answer:

See below ~

Step-by-step explanation:

(a) Mean of the data

(b) New mean after each data point increased by 10

(c) New mean after each data point doubled [from (b)]

Answer:

a) 1.8

b) 11.8

c) 23.6

mean: sum of numbers/total numbers

⇒ mean: (2.4+1.6+3.2+0.3+1.6)/5 ⇒ 9/5 ⇒  1.8

If 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

if the new data doubled, the mean will be double

11.8 * 2 = 23.6

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)

Check the picture below.

Answer:

-4 ≤ t ≤ 4

Step-by-step explanation:

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)

Answer:

.2 maybe but I don't know how to do this

Answer:

1) h=(64-43)

-----------

7

Make sure to add brackets

2)Answer is $3 per hour

Step-by-step explanation:

For 2)

----------

7

-----

7

Hope it helps

BYE

Answer:

3

Step-by-step explanation:

cus it's two 80s and 2 5 so 5 minus 2 is 3

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.

Day: Hats

You can notice the number of hats she will sell follow a pattern as there are only sequential odd numbers.

By following the sequence let's add the hats she will sell everyday:

Learn more about sums in: https://brainly.com/question/13013054

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

!!PLEASE PLEASE PLEASE MARK ME THE BRAINLIEST!!

Answer:

49%

Step-by-step explanation:

465 + 485 = 950

465/950 = .489

.489 * 100 = 48.9, round up for 49 to get 49%, since it's only focused on people who tested positive, you would only have to compare the people in that column

Answer: b

Step-by-step explanation:

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

Answer: 3

Step-by-step explanation: 12/1 × 1/4

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:

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

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

Answer:

1.07

Step-by-step explanation:

Answer:

$142,857.14

Step-by-step explanation:

As per the question,

Solving for Y

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.

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 :)

Answer:

100.53cm2 if I'm not mistaken. or 32π cm2

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.

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.

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.

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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.

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

Answer:

82 degrees

Step-by-step explanation:

180-98 = 82

They are supplementary and make 180 in total so x is 82

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

The volume of the rectangular prism having the dimension 3 feet wide, 5 feet long, and 3 feet tall is 45 cubic feet.

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.

brainly.com/question/21308574

Volume

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=×