someone pls help me uh

Answer:

a. For the function:

f(x) = { sin x/3, if x ≤ π

{ x√3/2π, if x > π

I. To find lim f(x) as x approaches π from the negative side, we need to evaluate f(x) for values of x that are slightly less than π. In this case, since sin(x/3) is a continuous function, we can simply evaluate it at x = π:

lim f(x) as x approaches π- = f(π-) = sin(π/3) = √3/2

II. To find lim f(x) as x approaches π from the positive side, we need to evaluate f(x) for values of x that are slightly greater than π. In this case, we can simply evaluate the other part of the piecewise function at x = π:

lim f(x) as x approaches π+ = f(π+) = π√3/2π = √3/2

III. To find lim f(x) as x approaches π, we need to check whether the left-hand and right-hand limits are equal. In this case, since both the left- and right-hand limits exist and are equal, we have:

lim f(x) as x approaches π = √3/2

b. For the function:

f(x) = (x^2 - 36)/√(x^2 - 12x + 36)

I. To find lim f(x) as x approaches 6 from the negative side, we need to evaluate f(x) for values of x that are slightly less than 6. In this case, we can substitute x = 6 - h, where h is a positive number approaching zero, to get:

lim f(x) as x approaches 6- = lim f(6 - h) as h approaches 0

Substituting x = 6 - h into the function, we get:

f(6 - h) = [(6 - h)^2 - 36]/√[(6 - h)^2 - 12(6 - h) + 36]

= [h^2 - 12h]/√[h^2]

Simplifying the numerator and denominator separately, we get:

f(6 - h) = h(h - 12)/|h|

Since h approaches 0 from the positive side, we have:

lim f(6 - h) as h approaches 0+ = lim h(h - 12)/h as h approaches 0+ = lim (h - 12) as h approaches 0+ = -12

II. To find lim f(x) as x approaches 6 from the positive side, we need to evaluate f(x) for values of x that are slightly greater than 6. In this case, we can substitute x = 6 + h, where h is a positive number approaching zero, to get:

lim f(x) as x approaches 6+ = lim f(6 + h) as h approaches 0

Substituting x = 6 + h into the function, we get:

f(6 + h) = [(6 + h)^2 - 36]/√[(6 + h)^2 - 12(6 + h) + 36]

= [h^2 + 12h]/√[h^2]

Simplifying the numerator and denominator separately, we get:

f(6 + h) = h(h + 12)/|h|

Since h approaches 0 from the positive side, we have:

lim f(6 + h) as h approaches 0+ = lim h(h +

Step-by-step explanation:

Consider the fraction first ;

\({:\implies \quad \sf \dfrac{\dfrac{3}{(x-1)}-4}{2-\dfrac{2}{(x-1)}}}\)

\({:\implies \quad \sf \dfrac{\dfrac{3-4(x-1)}{\cancel{(x-1)}}}{\dfrac{2(x-1)-2}{\cancel{(x-1)}}}}\)

\({:\implies \quad \sf \dfrac{3-4x+7}{2(x-1-1)}}\)

\({:\implies \quad \boxed{\bf{\dfrac{-4x+7}{2(x-2)}}}}\)

Hence, Option B) is required answer

Answer:

x = 8

Step-by-step explanation:

The rate (in km/h) at which the distance from the plane to the radar station is increasing a minute later is 0 km/h (rounded to the nearest whole number).

To solve this problem, we can use the concepts of trigonometry and related rates.

Let's denote the distance from the plane to the radar station as D(t), where t represents time. We want to find the rate at which D is changing with respect to time (dD/dt) one minute later.

Given:

The plane is flying with a constant speed of 360 km/h.

The plane passes over the radar station at an altitude of 1 km.

The plane is climbing at an angle of 30°.

We can visualize the situation as a right triangle, with the ground radar station at one vertex, the plane at another vertex, and the distance between them (D) as the hypotenuse. The altitude of the plane forms a vertical side, and the horizontal distance between the plane and the radar station forms the other side.

We can use the trigonometric relationship of sine to relate the altitude, angle, and hypotenuse:

sin(30°) = 1/D.

To find dD/dt, we can differentiate both sides of this equation with respect to time:

cos(30°) * d(30°)/dt = -1/D^2 * dD/dt.

Since the plane is flying with a constant speed, the rate of change of the angle (d(30°)/dt) is zero. Thus, the equation simplifies to:

cos(30°) * 0 = -1/D^2 * dD/dt.

We can substitute the known values:

cos(30°) = √3/2,

D = 1 km.

Therefore, we have:

√3/2 * 0 = -1/(1^2) * dD/dt.

Simplifying further:

0 = -1 * dD/dt.

This implies that the rate at which the distance from the plane to the radar station is changing is zero. In other words, the distance remains constant.

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Answer:

x=70

Step-by-step explanation:

when added together, verticle angles equal 180 degrees.

2x-10+x+20=180

3x-10+20=180

3x-30=180

3x=210

x=70

Answer: choice (B)

Step-by-step explanation:

(-4,4)

(0,5)

slope=  \(\frac{5-4}{0-(-4)}= \frac{1}{4}\)

Answer:

  c = (7/2)√3

  a = (3/2)√2

Step-by-step explanation:

You want the length of the adjacent side in the special right triangles shown.

The unknown side in each triangle is the side adjacent to the angle. The known side is the hypotenuse. This tells us we can make use of the relation ...

  Cos = Adjacent/Hypotenuse

  Adjacent = Hypotenuse × Cos

The ratios of side lengths in these triangles are ...

  30°-60°-90° triangle: 1 : √3 : 2   ⇒   cos(30°) = (√3)/2

  45°-45°-90° triangle: 1 : 1 : √2   ⇒   cos(45°) = 1/√2 = (√2)/2

  c = 7 · cos(30°)

  c = (7/2)√3

  a = 3 · cos(45°)

  a = (3/2)√2

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Answer:

The balancing point is 23

Step-by-step explanation:

Given

The above graph

Required

Determine the balancing point

This simply means that we calculate the mean.

From the above graph, we have:

\(\begin{array}{cc}x & {f} & {21} & {3} & {22} & {5} & {28} & {1} & {29} & {1}\ \end{array}\)

So, the mean is:

\(\bar x = \frac{\sum fx}{\sum f}\)

\(\bar x = \frac{21*3+22*5+28*1+29*1}{3+5+1+1}\)

\(\bar x = \frac{230}{10}\)

\(\bar x = 23\)

Hence, the balancing point is 23

Answer:

Radius = 9mi

Step-by-step explanation:

Radius = 9mi

R = D/2

R = 18/2

R= 9mi

The value of the side labelled x is equal to 3.8 to the nearest tenth using the trigonometric ratio of sine.

The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.

The basic trigonometric ratios includes;

sine, cosine and tangent.

Considering the sine of angle 41°

sin 41° = 2.5/x {opposite/hypotenuse}

x = 2.5/sin 41° {cross multiplication}

x = 3.8106

Therefore, the value of the side labelled x is equal to 3.8 to the nearest tenth using the trigonometric ratio of sine.

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The initial value problem's solution becomes closer to 0, the problem's limit, as time gets closer to infinity.

1. Determine both sides of the equation's Laplace transform: d2y + 4dy + 13y = u5(t) Y(s) = s2Y(s) + 4sY(s) + 13Y(s) = U5 (s)

2. Rewrite the equation to Y(s) = U5(s) / (s2 + 4s + 13) to find the value of Y(s).

3. Consider the reverse Finding y(t) using the Laplace transform on both sides

y(t) = (1/12)e(-t) + (1/24)sin(3t) + (1/8)cos (3t)

4. As t approaches infinity, determine the limit:

Laplace transformations are used to resolve the initial value issue d2y + 4dy + 13y = u5(t), where y(0) = 0 and y′(0) = 1. Y(s) = s2Y(s) + 4sY(s) + 13Y(s) = U5 is the result of first doing the Laplace transform of both sides of the equation (s). To find Y(s), we rewrite the equation as Y(s) = U5(s) / (s2 + 4s + 13). Then, to get y(t), we use the inverse Laplace transform of both sides: y(t) = (1/24)e(-2t) + (1/12)e(-t) + (1/24)sin(3t) + (1/8)cos (3t). Finally, when t approaches infinity, we compute the limit: limt[infinity]y(t) = 0. As a result, as time gets closer to infinity, the initial value problem's solution gets closer to 0.

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Answer:

5 and 3 is vertical. 4 and 6 are vertical. 2 and 1 are supplementary angles.

Answer:

how about no

Step-by-step explanation:

did anyone ask

Answer: C

Step-by-step explanation:

The answer is C

Answer:

.3

Step-by-step explanation:

.33 is .03 greater than .3

The number which represents the smallest value between 0.3 and 0.33 is the number 0.3.

Given are two decimal numbers.

0.3 and 0.33

It is required to find the number which is the smallest between these two.

The number 0.3 can be written as 0.30.

And the other number is 0.33.

In order to find the smallest number, check the digits from left to right.

The first digit after the decimal point of both numbers is 3.

The second digit after the decimal point is 0 for 0.30 and 3 for 0.33.

Here 0 is smaller than 3.

So, 0.30 is smaller than 0.33.

Hence, the smallest value is 0.3.

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Answer:

Explanation:

√8², 3² and √17² satisfy a²+b²=c²

√8²+3² = √17²

8+9=17

Answer:

  X ≈ 117.9°

Step-by-step explanation:

The law of cosines formula is given. Solving it for C, we find ...

 C = arccos((a^2 +b^2 -c^2)/(2ab))

where a and b are the sides adjacent to the angle of interest.

Here, we have ...

  X = arccos((50^2 +55^2 -90^2)/(2·50·55)) = arccos(-2575/5500)

  X ≈ 117.9°

Answer:

A would be correct

Step-by-step explanation:

the answer is A.

The proceeds (discounted value) on the third-party discount note are $4,116.90.

The discounted value of a note is a value that is less than the maturity value.

The maturity value is the face value of the note plus the accumulated interest.

Face value of the note receivable = $4,000

Annual interest rate = 12%

Note issuance date = March 16

Note due date = November 14

The total number of days = 243 days

Discount date = June 11

Discount rate = 11%

March 16 to June 11 = 87 days

Interest on the note = $320 ($4,000 x 243/365 x 0.12)

Maturity value = $4,320 ($4,000 + $320)

Discount period = 156 days (243 - 87)

Discount on the note = $203.10 ($4,320 x 156/365 x 11%)

Discounted value = $4,116.90 ($4,320 - $203.10)

Thus, the man, who holds a note of $4,000 at 12% interest but sells it at a discount rate of 11%, will receive $4,116.90.

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Add the number he gave away to the number he has left.

28 + 4 = 32

He started with 32 books

Answer:

Initial fee charged = $5

Fee charged for a mile = $1.25

No. of miles traveled = x

Total fee charged = 5 + 1.25x

Slope = 1.25

y-intercept = 5

Answer:

the answer is 27v- 2288/5

Answer:

14.66 or 14.7

Step-by-step explanation:

if we solve the equation we get 14.6666 but since it goes on and on we round and put it on 14.7

Answer:

Step-by-step explanation:

11 ÷ 3/4 = \(11 * \frac{4}{3}\)

             \(=\frac{44}{3}\\\\=14\frac{2}{3}\)

| t | 0 | 1 | 2 | 3 | 4 | 5 |

| d | 0 | 60 | 120 | 180 | 240 | 300|

\(\rule{300pt}{3pt}\)

\(\rule{300pt}{3pt}\)

Take any two points from the table and find the slope.

Points:

(1,60) & (3,180)

\( \large \tt \: m = \frac{ y_{2} - y_{1}}{ x_{2} - x_{1}} \)

\( \sf \: m = \frac{180 - 60}{3 - 1} \)

\( \sf \: m = \frac{120}{2} \)

\( \sf \: m = \cancel \frac{120}{2} = 60\)

Therefore, Slope is 60..

Using the unit circle to find sin 240 and cos 240, without using a calculator. The calculated results should match our approximations of -1/2 for sin 240 and -√3/2 for cos 240.

To find sin 240 and cos 240 without a calculator, we can use the unit circle, which is a circle with radius 1 centered at the origin in a two-dimensional coordinate system. The unit circle provides a convenient way to define the sine and cosine of an angle in terms of their coordinates on the circle.

The sine of an angle is the y-coordinate of the point on the unit circle corresponding to that angle, and the cosine of an angle is the x-coordinate of the point on the unit circle corresponding to that angle.

For an angle of 240 degrees, we can find the corresponding point on the unit circle by constructing a line from the origin to the point on the circle.

we can see that the y-coordinate of the point is negative, so sin 240 = -sin (240 - 180) = -sin 60 = -1/2.

The x-coordinate of the point is also negative, so cos 240 = -cos (240 - 180) = -cos 60 = -√3/2.

We can use a calculator to check our answers by entering sin(240) and cos(240) with parentheses around the 240, as requested by the calculator. The calculated results should match our approximations of -1/2 for sin 240 and -√3/2 for cos 240.

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\( \{ \: \alpha \: , \: \beta , \: a, \: b \}\)

\( \sf \longrightarrow \: No. \: of \: \: subsets = {2}^{n} \)

where, n denotes to number of elements in set .

Since, given set contains 4 elements .

Thus , 2⁴ {2 raise to power 4} .

\( \sf \longrightarrow \: No. \: of \: \: subsets = {2}^{4} \)

\( \sf \longrightarrow \: No. \: of \: \: subsets = 2 \times 2 \times 2 \times 2\)

\( \sf \longrightarrow \: No. \: of \: \: subsets = 4 \times 4\)

\( \sf \longrightarrow \: No. \: of \: \: subsets = 16\)

Therefore, Required subsets are 16.

They are , Namely;

\( \sf \longrightarrow \: subsets \: = \phi \: \{ \alpha \} \{ \beta \} \{ a\} \{ b\} \: \{ \alpha \beta \} \{ \alpha a\} \{ \alpha b\} \{ \beta a\} \{ \beta b\} \: .....\)

_____________________________

If n is the number of elements in the set then,

No. of subsets possible for this subset is 2^n that's the (2 raise to the power n).

Let's take another example, {1,2}

Here, n = 2

subsets =2^2 =4

Subsets = ϕ, {1}, {2},{1,2}

Note :- every set is a subset of itself i.e. {1,2} and ϕ is a subset of every set

Two possible deductibles can be the social care or the medical care

Answer:

mean=4.8

standard deviation=4.2

Step-by-step explanation:

The mean is 4.8, and the standard deviation is 4.2 if the 21% of households use a clothesline to dry their laundry. Capuchin would like to survey households that use a clothesline

It is defined as the measure of data disbursement, It gives an idea about how much is the data spread out.

Let's suppose the x is the number of household to get the first that uses a clothesline

And p is the probability of household uses' clothesline

X ~ Geo (p = 0.21)

Mean = 1/p

Mean = 4.76 ≈ 4.8

Variance = q/p²

q = 1-p

Variance = 17.9138

Standard deviation = √Variance

Standard deviation = 4.23 ≈ 4.2

Thus, the mean is 4.8, and the standard deviation is 4.2 if the 21% of households use a clothesline to dry their laundry. Capuchin would like to survey households that use a clothesline

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Answer:

1/6

Step-by-step explanation:

it is like a cube just with slightly different numbers on each side. but the probabilty structure is still the same.

we have 6 different possible outcomes, all with the same basic probabilty (as every field on the spinner is seemingly of the same size as the others).

and we desire one of these possible outcomes (6).

so the probabilty to get 6 is still 1/6 (1 desired over 6 possible outcomes).