Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

$已知集合 A={x∣sqrt(x-1) <= 2}*B={y∣-y^(2)+3y > 0}, 则 A nn B= C_(3) A. 8 B. (0.3) C. (0,5] D. [1,3)$

$1$ . 已知集合 $A=\{x \mid \sqrt{x-1} \leqslant 2\} \cdot B=\left\{y \mid-y^{2}+3 y>0\right\}$ , 则 $A \cap B=$ $\newline$ $\mathrm{C}_{3}$ $\newline$ A. $8$ $\newline$ B. $(0.3)$ $\newline$ C. $(0,5]$ $\newline$ D. $[1,3)$

View step-by-step help

View step-by-step help

Solve complex trigonomentric equations

Full solution

Q.

1

. 已知集合

A=\{x \mid \sqrt{x-1} \leqslant 2\} \cdot B=\left\{y \mid-y^{2}+3 y>0\right\}

, 则

A \cap B=

\newline

\mathrm{C}_{3}

\newline

A.

8

\newline

B.

(0.3)

\newline

C.

(0,5]

\newline

D.

[1,3)

Set A Solution: For set A, we have $\sqrt{x-1} \leq 2$ . Square both sides to get rid of the square root: $(\sqrt{x-1})^2 \leq 2^2$ . This gives us $x - 1 \leq 4$ . Add $1$ to both sides: $x \leq 5$ . So, $A = \{x | x \leq 5 \text{ and } x > 1\}$ because we can't take the square root of a negative number.
Set B Solution: For set B, we have $-y^2 + 3y > 0$ . $\newline$ Factor out $y$ : $y(-y + 3) > 0$ . $\newline$ This gives us two critical points, $y = 0$ and $y = 3$ . $\newline$ The inequality is satisfied between these points: $0 < y < 3$ . $\newline$ So, $B = \{y | 0 < y < 3\}$ .
Intersection of A and B: Now let's find the intersection $A \cap B$ . $\newline$ Since $A = \{x | 1 < x \leq 5\}$ and $B = \{y | 0 < y < 3\}$ , the intersection is the set of all numbers that are both greater than $1$ and less than or equal to $3$ . $\newline$ So, $A \cap B = \{x | 1 < x \leq 3\}$ .
Final Answer: Looking at the answer choices, we see that the correct answer is $D$ . $[1,3)$ .

More problems from Solve complex trigonomentric equations

Question

Find all solutions with

0^\circ \leq \theta \leq 180^\circ

. Give the exact answer(s) in simplest form. If there are multiple answers, separate them with commas.

\newline

\cos(\theta) = -1

\newline

\underline{\hspace{2em}}^\circ

Posted 2 months ago

Question

Kimi's school is

15

kilometers west of her house and

8

kilometers south of her friend Franklin's house. Every day, Kimi bicycles from her house to her school. After school, she bicycles from her school to Franklin's house. Before dinner, she bicycles home on a bike path that goes straight from Franklin's house to her own house. How far does Kimi bicycle each day?

\newline

\_\_\_\_\_

Posted 2 months ago

Question

Evaluate. Write your answer as an integer or as a decimal rounded to the nearest hundredth.

\newline

\cos 35^\circ =

Posted 2 months ago

Question

Find all solutions with

-90^\circ \leq \theta \leq 90^\circ

. Give the exact answer(s) in simplest form. If there are multiple answers, separate them with commas.

\newline

\csc(\theta) = -1

\newline

\_\_\_\_\,^\circ

Posted 2 months ago

Question

Evaluate. Write your answer in simplified, rationalized form. Do not round.

\newline

\cot 30^\circ =

Posted 2 months ago

Question

The terminal side of an angle

\theta

in standard position intersects the unit circle at

(\frac{84}{85}, \frac{13}{85})

\cos(\theta)

\newline

Write your answer in simplified, rationalized form.

\newline

Posted 2 months ago

Question

-90^\circ < \theta < 90^\circ

. Find the value of

\theta

\newline

\tan(\theta) = 0

\newline

Write your answer in simplified, rationalized form. Do not round.

\newline

\theta =

^\circ

\newline

Posted 2 months ago

Question

Evaluate. Write your answer in simplified, rationalized form. Do not round.

\newline

\csc 60^\circ =

Posted 2 months ago

Question

\theta

is an acute angle. Find the value of

\theta

\newline

\sec(\theta) = \sqrt{2}

\newline

\theta =

\degree

Posted 2 months ago

Question

Evaluate. Write your answer in simplified, rationalized form. Do not round.

\newline

\cos 90^\circ =

Posted 3 months ago