8/9 Divided by 6/9 = ?
A. 17/54


B. 16/27


C. 4/3


D. 24/5

The function f(x) = sin⁻¹x, x ≠ π/4 and sinx, x = π/4 is continuous on[-1, π/4) ∪ (π/4, 1]. There is a removable discontinuity at x = π/4

A function is said to be continuous if there are no breaks or jumps in the functions

Conditions for continuity of a function

Now, for the given function f(x) = sin⁻¹x, x ≠ π/4 and sinx, x = π/4

We need to determine the interval of continuity, We proceed as follows.

Since f(x) = sin⁻¹x, x ≠ π/4 , we know that the minimum value of x is - 1 and its maximum value is 1.

So, x must lie in the interval (-1, 1) for x ≠ π/4,

Now, when x = π/4 f(x) = sinx. We know that x = π/4 lies in the interval (-1, 1).

But we know that f(x) = sinx at x = π/4. So, there is a removable discontinuity at x = π/4.

So, from the left, f(x) is continuous on the interval [-1, π/4) and  from the right, f(x) is continuous on the interval (π/4, 1]

So, combining both intervals, we have f(x) is continous on the interval [-1, π/4) ∪ (π/4, 1] and since f(x) = sinx at x = π/4, there is a removable discontinuity at x = π/4

So, the function f(x) is continuous on[-1, π/4) ∪ (π/4, 1]. There is a removable discontinuity at x = π/4

Learn more about continuity of a function here:

https://brainly.com/question/28830920

#SPJ1

Answer:

The fence shall be 86.55 ft long

Step-by-step explanation:

Let's say, this garden should consist of two parts - rectangle and semicircular, so the rectangle part fence shall be 24 ft + 15 ft + 24 ft = 63 ft long. Since semicircular is aligned to the rectangle, then the diameter of the semicircular will be a opposite side length - D = 15 ft. Let's find out a semicircular length:

C = pi * D = 3.14 * 15 ft = 47.1 ft

Since this is circular length, we should divide it by 2, so semicircular length is 47.1 / 2 = 23.55 ft

So the fence shall be 63 ft + 23.55 ft = 86.55 ft long

Answer:

4700 minus 1200 = 3500

Step-by-step explanation:

round 4704 down to 4700 and 1193 up to 1200

Answer:

4704 - 1193 ≈ 3,500

Step-by-step explanation:

We are given the first step to round each number to the nearest hundred.

=====================================

4,704 can be rounded down since the rounding digit (zero) is less than or equal to 4.

4,704 ≈ 4,700

1,193 can be rounded up since the rounding digit (nine) is greater than more equal to 5.

1,193 ≈ 1,200

=====================================

We will now take the difference of these two numbers:

4700 - 1200 = 3500

=====================================

Hope this helps!

The selection that comes closest to the correct value of the compound interest is option (c), which equals Rs. 1776.

To calculate the compound interest earned by the money lender on Rs. 7,000 for 3 years, we need to use the formula:

A = \(P(1 + r/n)^(nt)\)

where A is the amount after t years, P is the principal, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the time in years.

Let's first calculate the amount after 1 year at 7% interest compounded annually:

\(A = 7000(1 + 0.07/1)^(1*1) = Rs. 7490\)

Now, we can use this amount as the principal for the second year, and calculate the amount after 1 year at 8% interest compounded annually:

\(A = 7490(1 + 0.08/1)^(1*1) = Rs. 8087.20\)

Finally, we can use this amount as the principal for the third year, and calculate the amount after 1 year at 8.5% interest compounded annually:

\(A = 8087.20(1 + 0.085/1)^(1*1) = Rs. 8773.11\)

The compound interest earned over 3 years is the difference between the final amount and the principal:

CI = 8773.11 - 7000 = Rs. 1773.11

So the answer is (c) Rs. 1776, which is the closest option to the actual value of the compound interest.

To learn more about compound interest visit;

https://brainly.com/question/14295570

#SPJ9

9514 1404 393

Answer:

  (x +yi)²

Step-by-step explanation:

Comparing the given expression to the square of a binomial, we can determine the given expression to be a square.

  (a +b)² = a² +2ab +b²

Here, we have a=x and b=yi. Then the factorization is ...

  x² +2xyi +(yi)² = (x +yi)²

Answer:

Step-by-step explanation:

(19/3)+(7/2)

(11/2)+(13/3)

=> 6.33 + 3.5   /   5.5 + 4.33  = 1

Step-by-step explanation:

To compare the two amounts of fabric, we need to express them with a common denominator:

15/2 = 30/4

7 1/2 = 15/2

Now we can compare the two amounts:

30/4 > 15/2

This is true because 30/4 is equal to 7.5 yards, which is greater than 7.5 yards (or 15/2 yards) of silver fabric.

Therefore, Ms. Thompson needs more red fabric than silver fabric.

The solution is: Piece-wise function

f(x)=x+6 , x≤1

f(x) = x^2 + 3 , x>1, the following functions is graphed below.

Option C is correct.

Explanation:

We are given a graph of piece-wise function which break at x=1

We need to choose correct option for graph.

Function is break at x=1.

We will get two function

For x≤1 and x>1

As we can see x≤1, graph is linear and x>1 graph is parabolic.

Equation of linear graph, x≤1

Take two point of graph (0,6) and (-6,0)

Equation of line:

y-y1/y2-y1 = x-x1/x2-x1

y = x+1

f(x)=x+6 , x≤1

Equation of parabolic graph, x>1

f(x) = x^2 + 3

Piece-wise function

f(x)=x+6 , x≤1

f(x) = x^2 + 3 , x>1

Please see the attached figure.

Hence, The option C is correct.

learn more on function:

https://brainly.com/question/2412552

#SPJ1

Answer:

2

Step-by-step explanation:

Answer: y = 11 - x / -6

Step-by-step explanation:

X - 6y = 11

Since we are solving for y, we need to isolate the variable.

Move x to the other side of the equation.

- 6y = 11 - x

Now divide bith sides by -6 to cancel out -6y and get the variable y

-6y/ -6 = 11 - x/ -6

y = 11 - x / -6

Im not sure if it was solving for y, or if it was solve for x if y = 11

We can simplify cosec(t)tant(t) to sec(t). A trigonometric function is a mathematical function that relates the angles of a triangle to the ratios of its sides.

The most common trigonometric functions are sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc).

To simplify the expression cosec(t)tant(t), we need to use the trigonometric identity:

cosec(t) = 1/sin(t)

tant(t) = sin(t)/cos(t)

Substituting these expressions into the original expression, we get:

cosec(t)tant(t) = (1/sin(t))(sin(t)/cos(t))

The sin(t) term in the numerator and denominator cancel out, leaving:

cosec(t)tant(t) = 1/cos(t)

Recalling the definition of secant, sec(t) = 1/cos(t), we can express the simplified expression as:

cosec(t)tant(t) = 1/sec(t)

Therefore, we can simplify cosec(t)tant(t) to sec(t).

Learn more about trigonometric identity :

https://brainly.com/question/3785172

#SPJ1

Answer:

-12

Step-by-step explanation:

(-3)4

-3*4

-12

Elaborate ur question about - 34

Answer:

153.846153846

Step-by-step explanation:

{\__/}

( • . •) want this cookie?

/ >

{\__/}

( • - •)

< \ just kidding its for me

Answer:

Line ZL and line LZ.

Step-by-step explanation:

Since it is a line (because a line needs to have two or more points to be able to graph), it can be represented in two ways. The first being ZL, and the second being LZ.

Brainliest please.

Answer:

Step-by-step explanation

Oh

Answer: x=3\(\sqrt{2\). y=3\(\sqrt{2\)

Step-by-step explanation: This is a 45-45-90 triangle. Both of the legs, x and y, are congruent. To find the length of the legs, divide 6, the hypotenuse, by \(\sqrt{2\). 6/\(\sqrt{2\)=3\(\sqrt{2\).

Answer:

B

Step-by-step explanation:

Answer:

-30 ,-2

5, -3

hope it will.help u

Answer:

x + y + z = 28,000

0.035x + 0.0425y + 0.0475z = 1160

z = 0.75x

Step-by-step explanation:

Let x = amount invested at 3.5%.

Let y = amount invested at 4.25%.

Let z = amount invested at 4.75%.

The total amount is $28,000.

Equation 1:

x + y + z = 28,000

The total interest is $1,160.

Equation 2:

0.035x + 0.0425y + 0.0475z = 1160

"The amount of money in the 4.75% account was 75% of the

amount of money in the 3.5% account."

Equation 3:

z = 0.75x

The system of equations is:

x + y + z = 28,000

0.035x + 0.0425y + 0.0475z = 1160

z = 0.75x

Answers to the system of equations:

The total amount in each account is:

x = $8,000

y = $14,000

z = $6,000

Answer:

$24

Step-by-step explanation:

The coupon is 20% off so he will pay 80% of the item so,

30*.8=24

or

30*.2=6 <--- $6 is how much the coupon will take off

30-6=24

Answer:

He'll pay $24.00

Answer:

3:8

Step-by-step explanation:

brainlest???

Answer:

3:8

8:3

11:8

8:11

11:3

3:11

Step-by-step explanation:

i put all the possible answers

stay blessed and positive

Answer:

7

Step-by-step explanation:

g(x)=4x-5

g(3)= 4(3)-5

=12-5

=7

Answer:

g(3)=4x-3

Step-by-step explanation:

put 3 into x

know g(3)=4x-3=4×3-1=12-1=11

11 will be the answer

Hello User,

Answer: n = 488

Answer:

1:2

Step-by-step explanation:

it asks for it in the order of squares to circles, and wants it in simplest form. 4 and 2 are both divisible by two, so its now 2 and 1. so now, you have to put the square number first, and the circle second. So, it is 1:2

=========================================================

Explanation:

The graph of any constant function is a horizontal flat line. The output is the same regardless of whatever input you select. Recall that a one-to-one function must pass the horizontal line test. Horizontal lines themselves fail this test. So this is sufficient to show we don't have a one-to-one function here.

Put another way: Let f(x) be a constant function. Let's say its output is 5. So f(x) = 5 no matter what you pick for x. We can then show that f(a) = f(b) = 5 where a,b are different values. This criteria is enough to show that f(x) is not one-to-one. A one-to-one function must have f(a) = f(b) lead directly to a = b. We cannot have a,b as different values.

----------------------------

The term "onto" in math, specifically when it concerns functions, refers to the idea of the entire range being accessible. If the range is the set of all real numbers, then we consider the function be onto. There's a bit more nuance, but this is the general idea.

With constant functions, we can only reach one output value (in that example above, it was the output 5). We fall very short of the goal of reaching all real numbers in the range. Therefore, this constant function and any constant function can never be onto.

Answer:

d. \(\csc x +\cot x\)

Step-by-step explanation:

\(\frac{\sin x}{1-\cos x}=\frac{\sin x(1+\cos x)}{1-\cos^2 x}=\frac{\sin x(1+\cos x)}{\sin^2 x}=\frac{1+\cos x}{\sin x}=\csc x+\cot x\)

If we divide 300 into parts using the ratio 2:3:5, we get:

2 parts = 2/10 of the total ratio = 2/10 x 300 = 60

3 parts = 3/10 of the total ratio = 3/10 x 300 = 90

5 parts = 5/10 of the total ratio = 5/10 x 300 = 150

Therefore, 300 divided in the ratio 2:3:5 would result in three parts of 60, 90, and 150.

I hope I helped!

~~~Harsha~~~

Answer:

No.

Any number multiplied by a 0 is 0.

0 is not equal to 1.

Answer:

yes i think

Step-by-step explanation:

Answer: 1.8

Step-by-step explanation: Divide 9/5