List all number sets that apply to each number.

How do you find the x intercepts of 3x^(5/3) - 4x^(7/3)

kaheart [24]

Set the whole expression = to 0 and solve for x.

3x^(5/3) - 4x^(7/3) = 0. Factor out x^(5/3): x^(5/3) [3 - 4x^(2/3)] = 0

Then either x^(5/3) = 0, or 3 - 4x^(2/3) = 0.

In the latter case, 4x^(2/3) = 3.

To solve this: mult. both sides by x^(-2/3). Then we have

4x^(2/3)x^(-2/3) = 3x^(-2/3), or 4 = 3x^(-2/3). It'd be easier to work with this if we rewrote it as

4 3
--- = --------------------
1 x^(+2/3)

Then

4
--- = x^(-2/3). Then, x^(2/3) = (3/4), and x = (3/4)^(3/2). According to my 3 calculator, that comes out to x = 0.65 (approx.)

Check this result! subst. 0.65 for x in the given equation. Is the equation then true?

My method here was a bit roundabout, and longer than it should have been. Can you think of a more elegant (and shorter) solution?

7 0

3 years ago

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The tens digit is three less than the units digit. If the digits are reversed, the sum of the reversed number and the original n

muminat

Answer:

Original number is 47

Step-by-step explanation:

Given: The tens digit is three less than the units digit. If the digits are reversed, the sum of the reversed number and the original number is 121.

To find: the original number

Solution:

Let x denotes digit at ones place.

As the tens digit is three less than the units digit,

Digit at tens place = $x-3$

Original number = $10(x-3)+x=11x-30$

When digits are reversed,

Reversed number = $10x+(x-3)=11x-3$

As the sum of the reversed number and the original number is 121,

$11x-30+11x-3=121\\22x-33=121\\22x=154\\x=\frac{154}{22}\\=7$

So,

original number = $11x-30=11(7)-30=77-30=47$

8 0

2 years ago

15. According to the US Census Bureau the population in Orange County, CA is growing at a rate of approximately 3.5% every 3 yea

poizon [28]

I’m sorry I don’t know but I need the points:(

5 0

2 years ago

Anna is paid $15.00 per hour. She works a long 12 hour shift, the last 4 hours being paid a double time pay rate.

balu736 [363]

Answer: $\Large\boxed{Wage=\$240}$

Step-by-step explanation:

Given information

Paid = $15.00 / hour

Paid (Last 4 hours) = Doubled the usual pay rate

Total hour = 12 hours

Given expression

Wage = Pay rate × hours except for the last 4 hours + Double Pay rate × 4 hours

Substitute values into the expression

Wage = (15) × (12 - 4) + (15 × 2) × (4)

Simplify values in the parenthesis

Wage = 15 × 8 + 30 × 4

Simplify by multiplication

Wage = 120 + 120

Simplify by addition

$\Large\boxed{Wage=\$240}$

Hope this helps!! :)

Please let me know if you have any questions

7 0

10 months ago

1) What was an advantage the British forces had during the war?

krek1111 [17]

(I’m assuming this is the Revolutionary War)
1. They had a fully formed government and powerful empire
2. They were fighting in an area that was 3,000 miles away from their home country
3. They knew the layout of the land
4. Their currency was far worse than that of the British, and they didn’t have access to gold which was a universal currency

6 0

3 years ago

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