What is the x value ?????

Verify the identity. tan x plus pi divided by two = -cot x

kogti [31]

Recall that sin(π/2) = 1, and cos(π/2) = 0,

$\bf \textit{Sum and Difference Identities}
\\\\
sin(\alpha + \beta)=sin(\alpha)cos(\beta) + cos(\alpha)sin(\beta)
\\\\
sin(\alpha - \beta)=sin(\alpha)cos(\beta)- cos(\alpha)sin(\beta)
\\\\
cos(\alpha + \beta)= cos(\alpha)cos(\beta)- sin(\alpha)sin(\beta)
\\\\
cos(\alpha - \beta)= cos(\alpha)cos(\beta) + sin(\alpha)sin(\beta)\\\\
-------------------------------\\\\
$

$\bf tan\left(x+\frac{\pi }{2} \right)=-cot(x)\\\\
-------------------------------\\\\
tan\left(x+\frac{\pi }{2} \right)\implies \cfrac{sin\left(x+\frac{\pi }{2} \right)}{cos\left(x+\frac{\pi }{2} \right)}
\\\\\\
\cfrac{sin(x)cos\left(\frac{\pi }{2} \right)+cos(x)sin\left(\frac{\pi }{2} \right)}{cos(x)cos\left(\frac{\pi }{2} \right)-sin(x)sin\left(\frac{\pi }{2} \right)}\implies \cfrac{sin(x)\cdot 0~~+~~cos(x)\cdot 1}{cos(x)\cdot 0~~-~~sin(x)\cdot 1}
\\\\\\
\cfrac{cos(x)}{-sin(x)}\implies -cot(x)$

7 0

3 years ago

Give my answer in terms of pi and state it's units

Soloha48 [4]

Answer:

113.1 square mm

Step-by-step explanation:

A=πr2=π·62≈113.09734

3 0

3 years ago

Read 2 more answers

14.) Write an equation of a line with the given slope and y-intercept.

melomori [17]

Answer:

y= x +4

Step-by-step explanation:

m = slope and b= y-intercept.

4 0

3 years ago

Last year 40 people adopted a manatee through Fia's Foundation.This year 30% more people adopted a manatee. How many more people

Nana76 [90]

Convert 30% into a decimal. Divide the percentage by 100:

$30 / 100 = 0.3$

The problem can be solved with the following equation:

$0.3(40) = difference$

Multiply 0.3 by 40.

$0.3 * 40 = 12$

12 more people adopted a manatee this year.

7 0

3 years ago

A broker has calculated the expected values of two different financial instruments X and Y. Suppose that E(x)= $100, E(y)=$90 SD

Sveta_85 [38]

Expectation is linear, meaning

E(a X + b Y) = E(a X) + E(b Y)

= a E(X) + b E(Y)

If X = 1 and Y = 0, we see that the expectation of a constant, E(a), is equal to the constant, a.

Use this property to compute the expectations:

E(X + 10) = E(X) + E(10) = $110

E(5Y) = 5 E(Y) = $450

E(X + Y) = E(X) + E(Y) = $190

Variance has a similar property:

V(a X + b Y) = V(a X) + V(b Y) + Cov(X, Y)

= a^2 V(X) + b^2 V(Y) + Cov(X, Y)

where "Cov" denotes covariance, defined by

E[(X - E(X))(Y - E(Y))] = E(X Y) - E(X) E(Y)

Without knowing the expectation of X Y, we can't determine the covariance and thus variance of the expression a X + b Y.

However, if X and Y are independent, then E(X Y) = E(X) E(Y), which makes the covariance vanish, so that

V(a X + b Y) = a^2 V(X) + b^2 V(Y)

and this is the assumption we have to make to find the standard deviations (which is the square root of the variance).

Also, variance is defined as

V(X) = E[(X - E(X))^2] = E(X^2) - E(X)^2

and it follows from this that, if X is a constant, say a, then

V(a) = E(a^2) - E(a)^2 = a^2 - a^2 = 0

Use this property, and the assumption of independence, to compute the variances, and hence the standard deviations:

V(X + 10) = V(X) ==> SD(X + 10) = SD(X) = $90

V(5Y) = 5^2 V(Y) = 25 V(Y) ==> SD(5Y) = 5 SD(Y) = $40

V(X + Y) = V(X) + V(Y) ==> SD(X + Y) = √[SD(X)^2 + SD(Y)^2] = √8164 ≈ $90.35

8 0

4 years ago