HA2 SEM1 practice 2

1. Question

Consider the polynomial function [math]f(x)=-x^2(x^2+1)(x^2-3)[/math], which of the following statements is true?

[math]f(x)\to\infty[/math] as [math]x\to\infty[/math]

Correct Incorrect Correct answer

[math]f(x)[/math] has 7 terms

Correct Incorrect Correct answer

[math]f(-1)=0[/math]

Correct Incorrect Correct answer

The coefficient of [math]x^3[/math] is 2

Correct Incorrect Correct answer

None of the above.

Correct Incorrect Correct answer

2. Question

Consider the scatter plot above. Suppose the coefficient of the correlation is [math]r[/math] and the slope of the regression line is [math]m[/math] which of the following statements is true?

[math]r<0[/math]

Correct Incorrect Correct answer

[math]r=m[/math]

Correct Incorrect Correct answer

[math]mr=-1[/math]

Correct Incorrect Correct answer

None of the above.

Correct Incorrect Correct answer

3. Question

Consider the function [math]f(x)=\begin{cases}x^2+1&x\geq1\\-x+k&x<1\end{cases}[/math] where [math]k[/math] is a constant. Which of the following statements is true?

The function has minimum when [math]x=0[/math]

Correct Incorrect Correct answer

[math]f(x)[/math] is a continuous function if [math]k=-1[/math]

Correct Incorrect Correct answer

[math]f(x)[/math] has at most 1 zero

Correct Incorrect Correct answer

[math]f(x)=2[/math] has 3 solutions

Correct Incorrect Correct answer

None of the above.

Correct Incorrect Correct answer

4. Question

Consider the linear equation system [math]\begin{cases}x+by=5\\ax+4y=c\end{cases}[/math] where [math]a, b[/math], and [math]c[/math] are constants. Which of the following statements is true?

If [math]a=-1[/math] and [math]b-4[/math], then the system has infinite solutions.

Correct Incorrect Correct answer

If [math]\dfrac{-1}{b}\times\dfrac{a}{4}=1[/math], then the system has only one solution.

Correct Incorrect Correct answer

If [math]a=\dfrac{-4}{b}=\dfrac{c}{5}=2[/math], then the system is inconsistent.

Correct Incorrect Correct answer

None of the above.

Correct Incorrect Correct answer

5. Question

Let [math]a[/math] and [math]b[/math] be complex numbers. Which of the following statements is true?

[math](a+b)^*=a^*+b^*[/math]

Correct Incorrect Correct answer

[math]a+a^*[/math] is always a pure imaginary number.

Correct Incorrect Correct answer

[math]bb^*[/math] is always negative.

Correct Incorrect Correct answer

[math]ab^*=ba^*[/math]

Correct Incorrect Correct answer

None of the above.

Correct Incorrect Correct answer

6. Question

Consider two matrices [math]A=\begin{bmatrix}0&2\\8&0\\0&-6\end{bmatrix}[/math] and [math]B=\begin{bmatrix}0&15&0\\3&0&1\end{bmatrix}[/math]. If [math]C=AB[/math], how many nonzero entries does [math]C[/math] have?

Fill in the blank 1 of 1

7. Question

Use RREF to solve the linear equation system [math]\begin{cases}x-3y+2z=5\\2x+5y-10=0\\-4x+12y-8z=-20\end{cases}[/math]

[math]x=5t[/math]
[math]y=[/math]Fill in the blank 1 of 4 [math]+[/math]Fill in the blank 2 of 4 [math]t[/math]
[math]z=[/math]Fill in the blank 3 of 4 [math]+[/math]Fill in the blank 4 of 4 [math]t[/math]
where [math]t[/math] is a real number.

8. Question

If the solution to the equation [math]x+1=x^2[/math] can be written as [math]x=\dfrac{a+\sqrt{b}}{2}[/math] where [math]a[/math] and [math]b[/math] are integers, what are [math]a[/math] and [math]b[/math]?

[math]a=[/math]Fill in the blank 1 of 2 , [math]b=[/math]Fill in the blank 2 of 2

9. Question

Solve the equation [math]x-\sqrt{4x}-8=0[/math]. If you have two or more solutions, write the smallest one.

Fill in the blank 1 of 1

10. Question

Consider a function [math]f(x)=\dfrac{x^2}{\sqrt{2x-3}}[/math]. After reflecting about the [math]y[/math]-axis, stretching vertically by a factor of 4 and then translating 3 units left, the function becomes [math]g(x)[/math]. If [math]g(a)[/math] is undefined, what is the maximum possible value of [math]a[/math]?

Fill in the blank 1 of 1

11. Question

(Calculator) Amanda is a cook. She bakes bread every day. She has a big oven which can bake 60 loaves of bread at a cost of $150. Since the business is very successful, she needs to bake more bread, but she has only one oven. Therefore, she has to decrease the price of her bread since the size of each bread is now smaller. For every additional loaf of bread she bakes, the price of each bread decreases by $2. What is Amanda’s maximum revenue?

Fill in the blank 1 of 1

12. Question

Franky throws a ball from [math](0,8)[/math], and then he shoots an arrow to the ball. The track function of the ball is [math]f(x)=ax^2+bx+c[/math] and the track function of the arrow is [math]g(x)=mx+k[/math]. Suppose the arrow touches the ball at [math](3,c+9)[/math]. Find [math]f(x)[/math] and [math]g(x)[/math].

[math]f(x)=[/math]Fill in the blank 1 of 5 [math](x-[/math]Fill in the blank 2 of 5 [math])^2+[/math]Fill in the blank 3 of 5
[math]g(x)=[/math]Fill in the blank 4 of 5 [math]x+[/math]Fill in the blank 5 of 5

13. Question

Let [math]p[/math] and [math]q[/math] be two numbers. If [math]p+q=7[/math] and [math]pq=11[/math], find

(a) [math](p-q)^2[/math]

(b) [math]p^3+q^3[/math]

(a) Fill in the blank 1 of 2

(b) Fill in the blank 2 of 2

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