All categories

4 years ago

Verify the identity cos quantity x plus pi divided by two = -sin x

Mathematics

1 answer:

In-s [12.5K]4 years ago

6 0

Answer:

Identity is verified.

Step-by-step explanation:

We have to verify the identity $cos(x+\frac{\pi }{2}) = (- sinx)$

To prove any identity we always prove one side(either left hand side or right hand side) of the equation equal to the other side.

In this identity we take the left hand side first

$cos(x+\frac{\pi}{2})$

$=cosx\times cos(\pi/2)-sinx\times sin(\pi/2))$ (as we know cos(a+b) = cosa×cosb-sina×sinb)

$= cosx\times0-sinx\times1$

$= 0-sinx$

= - sinx ( Right hand side)

Hence identity is proved.

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How to find slope y=3x+5

klemol [59]

This equation is in slope-intercept form; y = mx+b.

m is the slope and b is the y-intercept, so to find the slope you'd look at the coefficient of x.

In this equation, y = 3x+5, the coefficient of x is 3, so that means that the slope of this equation is 3.

Answer is:

3 is the slope

3 0

4 years ago

Suppose X, Y, and Z are random variables with the joint density function f(x, y, z) = Ce−(0.5x + 0.2y + 0.1z) if x ≥ 0, y ≥ 0, z

dexar [7]

Answer:

The value of the constant C is 0.01 .

Step-by-step explanation:

Given:

Suppose X, Y, and Z are random variables with the joint density function,

$f(x,y,z) = \left \{ {{Ce^{-(0.5x + 0.2y + 0.1z)}; x,y,z\geq0 } \atop {0}; Otherwise} \right.$

The value of constant C can be obtained as:

$\int_x( {\int_y( {\int_z {f(x,y,z)} \, dz }) \, dy }) \, dx = 1$

$\int\limits^\infty_0 ({\int\limits^\infty_0 ({\int\limits^\infty_0 {Ce^{-(0.5x + 0.2y + 0.1z)} } \, dz }) \, dy } )\, dx = 1$

$C\int\limits^\infty_0 {e^{-0.5x}(\int\limits^\infty_0 {e^{-0.2y }(\int\limits^\infty_0 {e^{-0.1z} } \, dz }) \, dy }) \, dx = 1$

$C\int\limits^\infty_0 {e^{-0.5x}(\int\limits^\infty_0{e^{-0.2y}([\frac{-e^{-0.1z} }{0.1} ]\limits^\infty__0 }) \, dy }) \, dx = 1$

$C\int\limits^\infty_0 {e^{-0.5x}(\int\limits^\infty_0 {e^{-0.2y}([\frac{-e^{-0.1(\infty)} }{0.1}+\frac{e^{-0.1(0)} }{0.1} ]) } \, dy }) \, dx = 1$

$C\int\limits^\infty_0 {e^{-0.5x}(\int\limits^\infty_0 {e^{-0.2y}[0+\frac{1}{0.1}] } \, dy }) \, dx =1$

$10C\int\limits^\infty_0 {e^{-0.5x}([\frac{-e^{-0.2y} }{0.2}]^\infty__0 }) \, dx = 1$

$10C\int\limits^\infty_0 {e^{-0.5x}([\frac{-e^{-0.2(\infty)} }{0.2}+\frac{e^{-0.2(0)} }{0.2}] } \, dx = 1$

$10C\int\limits^\infty_0 {e^{-0.5x}[0+\frac{1}{0.2}] } \, dx = 1$

$50C([\frac{-e^{-0.5x} }{0.5}]^\infty__0}) = 1$

$50C[\frac{-e^{-0.5(\infty)} }{0.5} + \frac{-0.5(0)}{0.5}] =1$

$50C[0+\frac{1}{0.5} ] =1$

$100C = 1$ ⇒ $C = \frac{1}{100}$

C = 0.01

3 0

3 years ago

Becky bought a magazine for $3.90, and the sales tax was 8.25%. How much sales tax did Becky pay on the magazine?

Ilya [14]

Answer:

$4.22 Is your answer.

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

(3a) You spend $72 on tapes and CDs. Each tape costs $8 and each CD costs $12.

Makovka662 [10]

Answer:

3a. 8t + 12c = 72

3b. t + c = 7

Step-by-step explanation:

number of tapes is t

number of Cds is c

so 8t + 12c = 72

and t + c = 7

so t = 7 - c

replace t = 7 - c in to the first equation

8(7 - c) + 12c = 72

56 - 8c + 12c = 72

4c = 72 - 56 = 16

c = 4

if c = 4, then t = 7 - c = 7 - 4 = 3

6 0

2 years ago

Write the equation of the line that passes through (0, 3) and is parallel to the line 3x + 5y = 6.

Pavel [41]

Please, see the offered decision:
1) common equation for lines is y=kx+b. If k₁=k₂ (for line 1 and line 2) ⇒ 'line 1' || 'line 2'.
2) for line 3x+5y=6 k= -3/5. It means (according to item 1) for unknown line k is the same (-3/5).
3) using points (0;3) it is easy to find parameter b (x=0, y=3) via y=kx+b:
3=0*(-3/5)+b ⇔ b=3.
4) finaly (k=-3/5; b=3):
$y=- \frac{3}{5}x+3 \ or \ 3x+5y=15$

3 0

3 years ago