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3 years ago

Evaluate lim x --> 1 [(x^1000)-1]/[x-1]

1 answer:

6 0

Do L'hospital's rule.

 $\lim_{x \to 1} \frac{x^{1000}-1}{x-1}= \lim_{x \to 1} \frac{(x^{1000}-1)'}{(x-1)'}= \lim_{x \to 1} \frac{1000x^{999}}{1}=
\\
\\ \frac{1000\times1^{999}}{1}=\frac{1000}{1}=1000$

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“Find the slope of the line through each pair of points.” (17, -13) , (17, 8)

iren2701 [21]

Slope = (y2 - y1)/(x2 - x1)

Slope = (8 -(-13))/(17-17)= 21/0 - slope is undefined. This is a vertical line x = 17.

8 0

3 years ago

Question 1 (1 point)

Firdavs [7]

Answer:

B. false

Step-by-step explanation:

Square units

I hope that is useful for you :)

6 0

3 years ago

Sarah would like to make a 6 lb nut mixture that is 60% peanuts and 40% almonds. She has several pounds of a mixture that is 80%

ivolga24 [154]

Answer:

a. The system of equations that models the situation is....

$0.80x+0.50y=3.60\\\\ 0.20x+0.50y=2.40$

b. The solution to the system: x = 2 and y = 4

The amount of 80/20 mixture is 2 pounds and the amount of 50/50 mixture is 4 pounds.

Step-by-step explanation:

Suppose, the amount of 80/20 mixture is $x$ pounds and the amount of 50/50 mixture is $y$ pounds.

So, the amount of peanuts in 80/20 mixture $= 0.80x$ pound and the amount of almonds in 80/20 mixture $=0.20x$ pound.

And the amount of peanuts in 50/50 mixture $=0.50y$ pound and the amount of almonds in 50/50 mixture $=0.50y$ pound.

Now, Sarah would like to make a 6 pounds nut mixture that is 60% peanuts and 40% almonds.

So, the amount of peanuts in that mixture $=(6\times 0.60)=3.60$ pounds

and the amount of almonds in that mixture $=(6 \times 0.40)= 2.40$ pounds.

So, the system of equations will be.........

$0.80x+0.50y=3.60 ...................(1)\\\\ 0.20x+0.50y=2.40...................(2)$

Subtracting equation (2) from equation (1), we will get.....

$(0.80x+0.50y)-(0.20x+0.50y)=3.60-2.40\\ \\ 0.60x=1.20\\ \\ x= \frac{1.20}{0.60}=2$

Now, plugging this $x=2$ into equation (1), we will get......

$0.80(2)+0.50y=3.60\\ \\ 1.60+0.50y=3.60\\ \\ 0.50y=3.60-1.60=2\\ \\ y=\frac{2}{0.50}=4$

So, the amount of 80/20 mixture is 2 pounds and the amount of 50/50 mixture is 4 pounds.

7 0

3 years ago

Mr. Charles gave both of his sons, Joe and Bill, $5,000. Joe deposited the money in an account that offered simple interest of 1

Maksim231197 [3]

Answer:

Bill by $85

Step-by-step explanation:

Bill : Compound interest is calculated by multiplying the initial principal amount by one plus the annual interest rate raised to the number of compound periods minus one. The total initial amount of the money given is then subtracted from the resulting value.

Compounded annually for 6 years at 9 % interest Bill would have $8385.50.

Joe : Simple interest at 11% a year The formula we'll use for this is the simple interest formula.

P is the principal amount, $5000.00.

r is the interest rate, 11% per year, or in decimal form, 11/100=0.11.

t is the time involved, 6year(s) time periods.

So, t is 6year time periods.

To find the simple interest, we multiply 5000 × 11 × 6 = 3300

Usually now, the interest is added onto the principal to figure some new amount after 6 year(s),

or 5000.00 + 3300.00 = 8300.00

As you can see Bill has more by $85.

^Check yourself

5 0

2 years ago

Can someone help me with 19,20,and 21 will mark brainiest for the first answer and it has to be correct

Archy [21]

Do you need help with all of these?

3 0

3 years ago