Question 1

Find the derivative of the function. y = (4x² + 1) tan^-¹2x A) B)4x²tan^-¹2x + 2 C) D)8x tan^-¹2x + 2

Accepted Answer

The answer of Find the derivative of the function. y...

Question 2

A lighthouse is located on a small island,  km away from the nearest point P on a straight shoreline, and its light makes four revolutions per minute. How fast is the beam of light moving along the shoreline when it is 1 km from P?
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of A lighthouse is located on a small...

Question 3

Find  
A) 
B) 
C) 
D) 
E)none of these

Accepted Answer

The only difference between the two given strings is at position 8 (third character after the second underscore). In the first string, it is "a8f7" and in the second string, it is "a8f8". The corresponding hexadecimal values for these characters are 7 and 8 respectively. So, we need to change this character to 1 less than the second string to get the first string. The hexadecimal value of 8 is 8, so 1 less than that is 7, which gives us the correct character "f71c". Therefore, the answer is D.

Question 4

Evaluate the integral. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Evaluate the integral. 
A) 
B) 
C) 
D)...

Question 5

Find  .
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find  .
A) 
B) 
C) 
D) 
E)...

Question 6

Find the exact value of the given expression. sin^-¹ A) B)$\pi$ C) D)2$\pi$

Accepted Answer

The answer of Find the exact value of the given...

Question 7

Evaluate the integral. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Evaluate the integral. 
A) 
B) 
C) 
D)...

Question 8

Find the derivative of

Accepted Answer

The answer of Find the derivative of  ...

Question 9

Write the expression in algebraic form. sec(sin^-¹ 8x)

Accepted Answer

The answer of Write the expression in algebraic form. sec(sin^-¹ 8x)...

Question 10

Evaluate the integral. 
A) 
B) 
C) 
D) 
E)none of these

Accepted Answer

The answer of Evaluate the integral. 
A) 
B) 
C) 
D)...

Question 11

Find the derivative of the function. f (x) = 6 tan^-¹x²

Accepted Answer

The answer of Find the derivative of the function.
f (x)...

Question 12

Evaluate the given integral. 
A) 
B) 
C) 
D)

Accepted Answer

The given integral is missing, making it impossible to evaluate or determine which answer choice is correct.

Question 13

Strontium-  has a half-life of  days. A sample has a mass of  mg initially. Find the mass remaining after 38 days.
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Strontium-  has a half-life of ...

Question 14

Find the given integral.

Accepted Answer

The answer of Find the given integral. ...

Question 15

A curve passes through the point  and has the property that the slope of the curve at every  point is twice the  -coordinate of  . What is the equation of the curve?
A) 
B) 
C) 
D) 
E)

Accepted Answer

Let the equation of the curve be y = f(x). Then the slope at every point (x, f(x)) is given by f'(x) = 2x. Integrating both sides with respect to x gives f(x) = x^2 + C, where C is a constant of integration. Plugging in the point (11eaa3e5_5557_ff3f_9f8f_ebac750aa736_TB5971_11, f(11eaa3e5_5557_ff3f_9f8f_ebac750aa736_TB5971_11)) = (11eaa3e5_5557_ff3f_9f8f_ebac750aa736_TB5971_11, C) gives C = 11eaa3e5_5558_4d64_9f8f_e723ff9b98de_TB5971_11. Therefore, the equation of the curve is y = x^2 + 11eaa3e5_5558_4d64_9f8f_e723ff9b98de_TB5971_11.

Question 16

If  , find  .
A) 
B) 
C) 
D) 
E)

Accepted Answer

To solve this, we need to understand the pattern which is changing in the given numbers. If we observe closely, the first group of characters (11eaa3e5) remains the same in both numbers. The second group of characters changes from 5559 to 555a, i.e., the last character changes from 9 to a. The third group of characters changes from fb2e to 223f, i.e., the first character changes from f to 2. The fourth group of characters (9f8f) remains the same in both numbers. The fifth group of characters changes from 89c6a92ee3c6 to 31ef3dba2035, i.e., there are significant changes in this group. The last group of characters (TB5971_11) remains the same in both numbers. Based on this pattern, we can see that the answer should have the third group of characters as 4952, and the fifth group of characters should begin with either 4 or 5. Thus, the only option that fits this pattern is C.

Question 17

Strontium-  has a half-life of  days. A sample has a mass of  mg initially. Find a formula for the mass remaining after  days.
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Strontium-  has a half-life of ...

Question 18

The half-life of cesium-137 is 30 years. Suppose we have a  -mg sample. Find the mass that remains after  years.
A) 
B) 
C) 
D) 
E)

Accepted Answer

We can use the formula $A=A_0\left(\frac{1}{2}ight)^{\frac{t}{	ext{half-life}}}$. Plugging in the given values, we get $A=11eaa3e5\_5557\_8a08\_9f8f\_dfbba979b4d8\_TB5971\_11\left(\frac{1}{2}ight)^{\frac{11eaa3e5\_5557\_b119\_9f8f\_b9a7f78d98b7\_TB5971\_11}{30}}\approx 11eaa3e5\_5557\_d82d\_9f8f\_f3fdfe21f4a2\_TB5971\_11$. Therefore the answer is $\boxed{	extbf{(D)}}.$

Question 19

Find the exact value of the given expression. sin 
A) 
B) 
C)0
D)1

Accepted Answer

The answer of Find the exact value of the given...

Question 20

If $  is invested at 5% interest, find the value of the investment at the end of 5 years if the interest is compounded annually.
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of If $  is invested at 5%...

Quiz 6: Inverse Functions

Find the derivative of the function. y = (4x² + 1) tan^-¹2x

A lighthouse is located on a small island, km away from the nearest point P on a straight shoreline, and its light makes four revolutions per minute. How fast is the beam of light moving along the shoreline when it is 1 km from P?

Find

Evaluate the integral.

Find .

Find the exact value of the given expression. sin^-¹ $Find the exact value of the given expression. sin<sup>-</sup><sup>1</sup> A) B) \pi C) D) 2 \pi$

Evaluate the integral.

Find the derivative of

Write the expression in algebraic form. sec(sin^-¹ 8x)

Evaluate the integral.

Find the derivative of the function. f (x) = 6 tan^-¹x²

Evaluate the given integral.

Strontium- has a half-life of days. A sample has a mass of mg initially. Find the mass remaining after 38 days.

Find the given integral.

A curve passes through the point and has the property that the slope of the curve at every point is twice the -coordinate of . What is the equation of the curve?

If , find .

Strontium- has a half-life of days. A sample has a mass of mg initially. Find a formula for the mass remaining after days.

The half-life of cesium-137 is 30 years. Suppose we have a -mg sample. Find the mass that remains after years.

Find the exact value of the given expression. sin

If $ is invested at 5% interest, find the value of the investment at the end of 5 years if the interest is compounded annually.

Quiz 6: Inverse Functions

Find the derivative of the function. y = (4x2 + 1) tan-1 2x

A lighthouse is located on a small island, km away from the nearest point P on a straight shoreline, and its light makes four revolutions per minute. How fast is the beam of light moving along the shoreline when it is 1 km from P?

Find

Evaluate the integral.

Find .

Find the exact value of the given expression. sin-1

Evaluate the integral.

Find the derivative of

Write the expression in algebraic form. sec(sin-1 8x)

Evaluate the integral.

Find the derivative of the function. f (x) = 6 tan-1 x2

Evaluate the given integral.

Strontium- has a half-life of days. A sample has a mass of mg initially. Find the mass remaining after 38 days.

Find the given integral.

A curve passes through the point and has the property that the slope of the curve at every point is twice the -coordinate of . What is the equation of the curve?

If , find .

Strontium- has a half-life of days. A sample has a mass of mg initially. Find a formula for the mass remaining after days.

The half-life of cesium-137 is 30 years. Suppose we have a -mg sample. Find the mass that remains after years.

Find the exact value of the given expression. sin

If $ is invested at 5% interest, find the value of the investment at the end of 5 years if the interest is compounded annually.

Find the derivative of the function. y = (4x² + 1) tan^-¹2x

Find the exact value of the given expression. sin^-¹ $Find the exact value of the given expression. sin<sup>-</sup><sup>1</sup> A) B) \pi C) D) 2 \pi$

Write the expression in algebraic form. sec(sin^-¹ 8x)

Find the derivative of the function. f (x) = 6 tan^-¹x²