Answer:
x ≈ 8.99
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you of the relationship between trig functions and sides in a right triangle. Here, the geometry of the problem can be modeled by a right triangle. We are given one side and want to find the difference in lengths of the other side for two different angles.
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<h3>setup</h3>
The tower height is the side opposite the angle of elevation. The distance from the tower to the end of the shadow is the side adjacent to the angle of elevation, so the relevant trig relation is ...
Tan = Opposite/Adjacent
tan(angle of elevation) = (tower height)/(length of shadow)
Solving for the length of shadow, we have ...
length of shadow = (tower height)/tan(angle of elevation)
The difference in shadow lengths is 2x for the two different angles, so we have ...
2x = 24.57/tan(30°) -24.57/tan(45°)
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<h3>solution</h3>
Dividing by 2 and factoring out the tower height, we have ...
x = 12.285(1/tan(30°) -1/tan(45°)) = 12.285(√3 -1)
x ≈ 8.993244
The value of x is about 8.99.
Answer:
Options A and C are the only polynomials.
Step-by-step explanation:
We know that,
A polynomial is an expression having more than one algebraic terms.
<em>It is of the form,
,</em>
<em>where the coefficients
for i = 1,2,3,4,... are real numbers and the degree 'n' are natural numbers.</em>
So, from the options, we see that,
Options B, D and E are not of the above form and so are not polynomials.
Thus, options A and C are the only polynomials.
Division yields

Now for partial fractions: you're looking for constants <em>a</em>, <em>b</em>, and <em>c</em> such that


which gives <em>a</em> + <em>b</em> = 2, <em>c</em> = 0, and 2<em>a</em> = -7, so that <em>a</em> = -7/2 and <em>b</em> = 11/2. Then

Now, in the integral we get

The first two terms are trivial to integrate. For the third, substitute <em>y</em> = <em>x</em> ² + 2 and d<em>y</em> = 2<em>x</em> d<em>x</em> to get

The answer would be 2y(3x²+ y²).
Let x = hours worked as a clerk ($12 per hour).Let y = hours worked as a cashier ($8.25 per hour).She worked 55 hours, thereforex + y = 55 (1)She earned $585, therefore12x + 8.25y = 585 (2)From (1), obtainy = 55 - x (3)Substitute (3) into (2).12x + 8.25(55 - x) = 58512x + 453.75 - 8.25x = 5853.75x = 131.25x = 35y = 55 - x = 55 - 35 = 20
Answer: c) Office clerk: 35 hours; cashier: 20 hours.