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2 years ago

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Mari has a part time job. She earns $7 an hour. She makes at most $143.50 a week. What is the greatest number of hours that she

worked

1 answer:

Readme [11.4K]2 years ago

8 0

591.928571 is your answer

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Rewrite the expression as an algebraic expression in x. <br> cos(tan−1 x)

zhenek [66]

It's hard to type and hard to read the "inverse tangent" function, as you've seen (above).

So, use "arctan x" instead.

Then the problem becomes: "differentiate cos (arctan x)."

You must apply first the rule for differentiating the cosine function, and next apply the rule for differentiating the arctan function:

(d/dx) cos (arctan x) = - sin (arctan x) * [1/(1+x^2)]

7 0

3 years ago

Food pill: $9<br> Sales tax:6%<br> Tip:20%<br><br> Can you help me please

steposvetlana [31]

Answer: $11.45

Step-by-step explanation:

Food pill: $9

Tax: 6%

Tip: 20%

$x=(9)+(9)(0.06)+[(9)+(9)(0.06)](0.20)\\x=11.45$

3 0

3 years ago

A cylinder’s radius is reduced to 2004-06-01-04-00_files/i0480001.jpg its original size and the height is quadrupled. How has th

asambeis [7]

I can't answer this question if we don't know by what scale the cylinder's radius was reduced. Luckily, I found the same problem that says the radius was reduced to 2/5. So, we find the ratio of both volumes.

V₁ = πr₁²h₁
V₂ = πr₂²h₂

where r₂ = 2/5*r₁ and h₂ = 4h₁

V₂/V₁ = π(2/5*r₁ )²(4h₁)/πr₁²h₁= 8/5 or 1.6

<em>Thus, the volume has increased more by 60%.</em>

6 0

3 years ago

Solve the simultaneous equations<br>4x+3y=1<br>4x^2+3xy+y^2=2

Fantom [35]

Notice that the second equation,

4<em>x</em> ² + 3<em>xy</em> + <em>y</em> ² = 2

can be written as

<em>x</em> (4<em>x</em> + 3<em>y</em>) + <em>y</em> ² = 2

and the first equation says 4<em>x</em> + 3<em>y</em> = 1, so this reduces to

<em>x</em> + <em>y</em> ² = 2

Solve the first equation for <em>x</em> :

4<em>x</em> + 3<em>y</em> = 1

4<em>x</em> = 1 - 3<em>y</em>

<em>x</em> = (1 - 3<em>y</em>)/4

Substitute this into the reduced second equation to get a quadratic equation in <em>y</em>, which happens to be easily factorized and solved:

(1 - 3<em>y</em>)/4 + <em>y</em> ² = 2

1 - 3<em>y</em> + 4<em>y</em> ² = 8

4<em>y</em> ² - 3<em>y</em> - 7 = 0

(4<em>y</em> - 7) (<em>y</em> + 1) = 0

4<em>y</em> - 7 = 0 <u>or</u> <em>y</em> + 1 = 0

<em>y</em> = 7/4 <u>or</u> <em>y</em> = -1

Solve for <em>x</em> :

<em>x</em> = (1 - 3 (7/4))/4 <u>or</u> <em>x</em> = (1 - 3 (-1))/4

<em>x</em> = -17/16 <u>or</u> <em>x</em> = 1

So the two solutions are (<em>x</em>, <em>y</em>) = (-17/16, 7/4) and (<em>x</em>, <em>y</em>) = (1, -1).

8 0

2 years ago

What is the decimal multiplier to increase by 3%?

nlexa [21]

If you want to increase something by 3%, you would ADD 100% to it, so:
3% + 100% = 103%
Then you divide it by 100 to turn it into a decimal, so:
103% / 100 = 1.03
So to increase by 3%, the multiplier would be 1.03

If you wanted to decrease by 3%, you would SUBTRACT 100% from 3%, so:
100% - 3% = 97%
And then you would divide 97% by 100 to turn it into a decimal (multiplier), so:
97% / 100 = 0.97
So to decrease by 3%, the multiplier would be 0.97

7 0

2 years ago