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Salsk061 [2.6K]
3 years ago
13

Question 1(Multiple Choice Worth 2 points) Find the derivative of f(x) = 7 divided by x at x = 1.

Mathematics
2 answers:
nydimaria [60]3 years ago
5 0

Answer:

Step-by-step explanation:

Vaselesa [24]3 years ago
5 0

Question 1:

For this case we must find the derivative of the following function:

f (x) = \frac {7} {x} evaluated at x = 1

We have by definition:

\frac {d} {dx} [x ^ n] = nx ^ {n-1}

So:

\frac {df (x)} {dx} = - 1 * 7 * x ^ {- 1-1} = - 7x ^ {- 2} = - \frac {7} {x ^ 2}

We evaluate in x = 1

- \frac {7} {x ^ 2} = - \frac {7} {1 ^ 2} = - 7

ANswer:

Option A

Question 2:

For this we must find the derivative of the following function:

f (x) = 4x + 7\ evaluated\ at\ x = 5

We have by definition:

\frac {d} {dx} [x ^ n] = nx ^ {n-1}

The derivative of a constant is 0

So:

\frac {df (x)} {dx} = 1 * 4 * x ^ {1-1} + 0 = 4 * x ^ 0 = 4

Thus, the value of the derivative is 4.

Answer:

Option A

Question 3:

For this we must find the derivative of the following function:

f (x) = 12x ^ 2 + 8x\ evaluated\ at\ x = 9

We have by definition:

\frac {d} {dx} [x ^ n] = nx ^ {n-1}

So:

\frac {df (x)} {dx} = 2 * 12 * x ^ {2-1} + 1 * 8 * x ^ {1-1} = 24x + 8 * x ^ 0 = 24x + 8

We evaluate for x = 9we have:

24 (9) + 8 = 224

Answer:

Option D

Question 4:

For this we must find the derivative of the following function:

f (x) = - \frac {11} {x}\ evaluated\ at\ x = 9

We have by definition:

\frac {d} {dx} [x ^ n] = nx ^ {n-1}

So:

\frac {df (x)} {dx} = - (- 1 * 11 * x ^ {- 1-1}) = 11x ^ {- 2} = \frac {11} {x ^ 2}

We evaluate for x = 9 and we have:

\frac {11} {9 ^ 2} = \frac {11} {81}

ANswer:

Option D

Question 5:

For this case we have by definition, that the derivative of the position is the velocity. That is to say:

\frac {d (s (t))} {dt} = v (t)

Where:

s: It's the position

v: It's the velocity

t: It's time

We have the position is:

s (t) = 1-10t

We derive:

\frac {d (s (t))} {dt} = 0- (1 * 10 * t ^ {1-1}) = - 10 * t ^ 0 = -10

So, the instantaneous velocity is -10

Answer:

-10

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One container is filled with mixture that is 25% acid. A second container is filled with a mixture that is 55% acid. The second
algol13

Answer:

Therefore the third container contains   \frac{735}{17}\% = 43.23 %  acid.

Step-by-step explanation:

Given that, One container is filled with the mixture that 25% acid. 55% acid is contain by second container.

Let the volume of first container be x cubic unit.

Since the volume of second container is 55% larger than the first.

Then the volume of the second container is

= (V\times \frac{100+55}{100})   cubic unit.

=\frac{155}{100}V  cubic unit.

The amount of acid in first container is

=V\times \frac{25}{100}  cubic unit.

=\frac{25}{100}V  cubic unit.

The amount of acid in second container is

=(\frac{155}{100}V \times \frac{55}{100}) cubic unit.

=\frac{8525}{10000}V cubic unit.

Total amount of acid =(\frac{25}{100}V+\frac{8525}{10000}V) cubic unit.

                                   =(\frac{2500+8525}{10000}V) cubic unit.

                                   =(\frac{11025}{10000}V)cubic unit.

Total volume of mixture =(V+\frac{155}{100}V) cubic unit.

                                       =\frac{100+155}{100}V cubic unit.

                                       =\frac{255}{100}V  cubic unit.

The amount of acid in the mixture is

=\frac{\textrm{The volume of acid}}{\textrm{The amount of mixture}}\times 100 \%

=\frac {\frac{11025}{10000}V}{\frac{255}{100}V}\times 100\%

=\frac{735}{17}\%

Therefore the third container contains  \frac{735}{17}\%  acid.

5 0
3 years ago
6^2 + x - x^2 for x=3 <br> help me pls
Stels [109]

Answer:

30

Step-by-step explanation:

Just insert the value of x into the equation.

x = 3 right?

6^2 + 3 - 3^2 because x = 3

36 + 3 - 9 = 39 -9 = 30

:D

4 0
3 years ago
Don't know how to solve this please help. Show work, thank you
anyanavicka [17]
Hello!

We know that the sum of the three angles of a triangle is equal to 180 degrees. This can be represented using the following formula:

A1 + A2 + A3 = 180

With this knowledge, we can successfully find the missing measurements.

We’ll begin with the large right triangle. Because it is a right triangle, we know that one of its angles is equal to 90 degrees. We are also given that its second angle has a measure of 65 degrees. Insert this information into the formula above and combine like terms:

(90) + (65) + A3 = 180
155 + A3 = 180

Now subtract 155 from both sides of the equation:

A3 = 25

We have now proven that the third angle has a measure of 25 degrees. Looking at the provided image, you’ll notice that this 25 degree angle is adjacent to the 80 degree angle. We can add these neighboring angles to find one of the missing angles of the medium triangle:

25 + 80 = 105

We have now proven that this larger angle has a measure of 105 degrees. Looking again at the provided image, you’ll notice that this triangle also contains a 50 degree angle. Using the “three-angles” formula, we can find the remaining angle of the medium triangle. Insert any known values and combine like terms:

(105) + (50) + A3 = 180
155 + A3 = 180

Now subtract 155 from both sides of the equation:

A3 = 25

We have now proven the third angle of the medium triangle to have a measure of 25 degrees. Consequently, we now have now proven two of the three angles of the smallest triangle. Again using the “three-angles” formula, we can find the measure of the missing angle (x). Insert any known values (using the variable “x” to represent the missing angle) and combine like terms:

(25) + (25) + (x) = 180
50 + x = 180

Now subtract 50 from both sides:

x = 130

we have now proven that the missing angle (x) has a measure of 130 degrees.

I hope this helps!
second angle which has a value of 65 degrees. 
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3 years ago
After five weeks of dating, Terri concludes she knows next to nothing about her boyfriend, James, even though she has shared a w
seropon [69]

Answer:

d) Reciprocal

Step-by-step explanation:

Terri has revealed James a wealth of personal information about herself, but it seems that James has told Terri none personal information about himself in return. So, the revelation of secrets and personal information has not been reciprocal in their relationship. Reciprocal is something that expresses <u>mutual action or equal benefits</u> in an agreement or in a relationship.

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3 years ago
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Mike weighs 24 more pounds than Mark. Together, they weigh 250 pounds. How many do they each weigh?
djverab [1.8K]
To get your answer, follow my method :

First you take away 24 from 250=226
Then you half 226=113 which is Mark's weight
As Mike weights 24 pounds more that Mark, you have to add 24 back=137
So your answer is :
Mark weights 113 pounds and Mike weights 137 pounds.
6 0
3 years ago
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