Write the sentence as an equation.<br><br> 306 is equal to 80 subtracted from q

Suppose the sound wave has the form y=7cos(3x-pi/6) for x in the interval [pi/6 , 7pi/18]. Express x as a function of y, and sta

Vesnalui [34]

Answer:

x = ⅓ acos(y/7) + π/18, [-7, 7/2]

Step-by-step explanation:

y = 7 cos(3x − π/6)

Solving for x:

y/7 = cos(3x − π/6)

acos(y/7) = 3x − π/6

acos(y/7) + π/6 = 3x

x = ⅓ acos(y/7) + π/18

The domain of x is the same as the range of y.

When x = π/6:

y = 7 cos(3π/6 − π/6)

y = 7 cos(π/3)

y = 7/2

When x = 7π/18:

y = 7 cos(21π/18 − π/6)

y = 7 cos(π)

y = -7

So the domain of x as a function of y is [-7, 7/2].

5 0

4 years ago

The value of 7 rounded to the nearest hundredth

erma4kov [3.2K]

Answer: 9.22

Step-by-step explanation:

2^2 + 9^2 = C^2

4+81=C^2

85=C^2

(square root both sides)

C=9.219544

C=9.22

3 0

3 years ago

What is the best way to do math problems. Please give me your opinion.

Anna11 [10]

For me personally i can work nearly any equation with a calculator. definitely a good choice <span />

8 0

4 years ago

Read 2 more answers

Amir throws a stone off of a bridge into a river. The stone's height (in meters above the water) ttt seconds after Amir throws i

Harrizon [31]

Answer:

1) The vertex form of $h(t) = -5\cdot t^{2}+20\cdot t +160$ is $h -180 = -5\cdot (t-2)^{2}$ , 2) The stone reaches its maximum height 2 seconds after being thrown.

Step-by-step explanation:

1) Given that height of the stone is represented by a second-order polynomial, which depicts a parabola as graph. The best approach to determine the instant when stone reaches its highest is by vertex form, whose form is:

$h-k = C\cdot (t-r)^{2}$

Where:

$r$ , $k$ - Instant and maximum height of the stone, measured in seconds and meters.

$C$ - Vertex constant, which must be negative as there is an absolute maximum, measured in meters per square second.

Let be $h(t) = -5\cdot t^{2}+20\cdot t +160$ , which is transformed into vertex form:

i) $h = -5\cdot t^{2}+20\cdot t +160$ Given

ii) $h = -5\cdot (t^{2}-4\cdot t -32)$ Distributive property/ $(-a)\cdot b = -a\cdot b$

iii) $h = -5\cdot [(t^{2}-4\cdot t +4)+(-36)]$ Existence of additive inverse/Definitions of addition and subtraction

iv) $h = (-5)\cdot (t-2)^{2}+180$ Distributive property/ $(-a)\cdot (-b) = a\cdot b$ /Perfect square binomial

v) $h -180 = -5\cdot (t-2)^{2}$ Compatibility with addition/Existence of additive inverse/Modulative property/Definition of subtraction/Result

The vertex form of $h(t) = -5\cdot t^{2}+20\cdot t +160$ is $h -180 = -5\cdot (t-2)^{2}$ .

2) The time can be extracted from previous results, which indicates that stone reaches its maximum height 2 seconds after being thrown.

4 0

3 years ago

Gretta earns $450 per week plus a 10% commission on book sales. How many dollars of books must she sell to earn at least $650 pe

Dmitry_Shevchenko [17]

Answer:

$6050.00

Step-by-step explanation:

.10x + 45 = 650

.10x = 605

x = $6050

8 0

3 years ago

Write the sentence as an equation. 306 is equal to 80 subtracted from q