A carnival costs $10.50 to enter plus an additional $3.50 per ticket rides and food.

Lim x→π/2 1-sinx/cot^2x any genious help please

Simora [160]

Rewrite the limand as

(1 - sin(x)) / cot²(x) = (1 - sin(x)) / (cos²(x) / sin²(x))

… = ((1 - sin(x)) sin²(x)) / cos²(x)

Recall the Pythagorean identity,

sin²(x) + cos²(x) = 1

Then

(1 - sin(x)) / cot²(x) = ((1 - sin(x)) sin²(x)) / (1 - sin²(x))

Factorize the denominator; it's a difference of squares, so

1 - sin²(x) = (1 - sin(x)) (1 + sin(x))

Cancel the common factor of 1 - sin(x) in the numerator and denominator:

(1 - sin(x)) / cot²(x) = sin²(x) / (1 + sin(x))

Now the limand is continuous at x = π/2, so

$\displaystyle\lim_{x\to\frac\pi2}\frac{1-\sin(x)}{\cot^2(x)}=\lim_{x\to\frac\pi2}\frac{\sin^2(x)}{1+\sin(x)}=\frac{\sin^2\left(\frac\pi2\right)}{1+\sin\left(\frac\pi2\right)}=\boxed{\frac12}$

4 0

3 years ago

Triangle QRS has vertices Q(-4,2),R(3,0), and S(4,3).

Dafna1 [17]

The coordinates of the vertices of $\triangle Q'R'S'$ are $Q'(x,y) = (0, -4)$ , $R'(x,y) = (7,-6)$ and $S'(x,y) = (8, -3)$ , respectively.

Vectorially speaking, a point is translated to another location on Cartesian plane by means of this expression:

$A'(x,y) = A(x,y) + T(x,y)$ (1)

Where:

$A(x,y)$ - Original point.
$A'(x,y)$ - Translated point.
$T(x,y)$ - Translation vector.

If we know that $Q(x,y) = (-4,2)$ , $R(x,y) = (3,0)$ , $S(x,y) = (4, 3)$ and $R'(x,y) = (7, -6)$ $T(x,y) = (4, -6)$ , then the coordinates of the vertices of the triangle $Q'R'S'$ are:

$Q'(x,y) = Q(x,y) + T(x,y)$

$Q'(x,y) = (-4,2) + (4,-6)$

$Q'(x,y) = (0, -4)$

$R'(x,y) = R(x,y) + T(x,y)$

$R'(x,y) = (3,0) +(4,-6)$

$R'(x,y) = (7,-6)$

$S'(x,y) = S(x,y) + T(x,y)$

$S'(x,y) = (4, 3) + (4, -6)$

$S'(x,y) = (8, -3)$

The coordinates of the vertices of $\triangle Q'R'S'$ are $Q'(x,y) = (0, -4)$ , $R'(x,y) = (7,-6)$ and $S'(x,y) = (8, -3)$ , respectively.

We kindly invite to see this question on translations: brainly.com/question/17485121

5 0

3 years ago

Which two numbers are irrational? How do you know? a. 8-√56 b. 8-√25 c. 2-√73

Aleks [24]

A and C are irrational.

We know that B is rational because it's just asking 8 - 5, which is 3.

There is, however, no perfect square root of 73 or 56, and so the answer will be irrational.

8 0

4 years ago

Read 2 more answers

Order these numbers from least to greatest.

Radda [10]

6.1. 6.1091 6.809 6.89.

5 0

3 years ago

Read 2 more answers

You are choosing between two plans at a discount warehouse. Plan A offers an annual membership fee of $ 90and you pay 30 %of the

Ad libitum [116K]

Answer:

Step-by-step explanation:

We have 2 linear equations, and in both, the amount of merchandise you would have to purchase is "x", the unknown. We are asked to find that value of x.

The first equation is

C(x) = .30x + 90, which says that the cost of this plan is a fixed $90, and you pay 30% of the manufacturer's cost, x.

The second equation is

C(x) = .80x + 40, which says that the cost of this plan is a fixed $40, and you pay 80% of the manufacturer's cost, x.

If we want to know when the cost of these 2 are equal to each other, we set the equations equal to each other and solve for x:

.3x + 90 = .8x + 40 so

-.5x = -50 so

x = $100

The cost for each plan will be the same at this value of x, but we will plug in 100 for x in each just to make sure we did it right:

C(100) = .3(100) + 90

C(100) = 30 + 90

C(100) = 120 and

C(100) = .8(100) + 40

C(100) = 80 + 40

C(100) = 120

6 0

3 years ago