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LiRa
20 days ago
13

Explain why the following expression is false. |x| < -4

Mathematics
1 answer:
Zina [9.1K]20 days ago
8 0

Step-by-step explanation:

When a negative number is placed within a modulus function, the result will be positive. For instance, |-3| equals 3, |-6| equals 6, and |5| equals 5, etc.

A modulus function, expressed as |x|, is always positive unless x is zero, in which case it equals zero.

Consequently, |x| cannot be less than -4 because |x| is always non-negative. Thus, the statement is inaccurate.

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What number comes next in the series? 31, 1031, 402, 16, ____
lawyer [9240]

Answer:

Someone has previously provided an answer to this question, and I must attribute it to writersparadise. All credit goes to him/her.

Step-by-step explanation:

There can be various responses to this query. Usually, the next number following 16 has digits that add up to 8.

Explanation:

First number 31 – The digits add up to 3 + 1 = 4  

Second number 1031 – The sum of the digits is 1 + 0 + 3 + 1 = 5

Third number 402 – The digits sum to 4 + 0 + 2 = 6

Fourth number 16 – Adding the digits gives 1 + 6 = 7

Thus, the missing number could either be the single digit 8 or any of these two-digit options: 17, 26, 35, 44, 53, 62, 71, or 80. It may also include larger numbers consisting of the digits from the mentioned two-digit figures combined with 0, like 260 or 7001.

Read more.in - https://.in/question/3032926#readmore

4 0
20 days ago
Find the point on the circle x^2+y^2 = 16900 which is closest to the interior point (30,40)
Leona [9271]

Response-

(78,104) represents the point closest to the interior.

Explanation-

The equation defining the circle,

\Rightarrow x^2+y^2 = 16900

\Rightarrow y^2 = 16900-x^2

\Rightarrow y = \sqrt{16900-x^2}

Since the point lies on the circle, its coordinates must be,

(x,\sqrt{16900-x^2})

The distance "d" from the point to (30,40) can be calculated as,

=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}

=\sqrt{(x-30)^2+(\sqrt{16900-x^2}-40)^2}

=\sqrt{x^2+900-60x+16900-x^2+1600-80\sqrt{16900-x^2}}

=\sqrt{9400-60x-80\sqrt{16900-x^2}}

Next, we need to determine the value of x for which d is minimized. The minimum distance occurs when 9400-60x-80\sqrt{16900-x^2} is at its lowest value.

Let’s set up the equation,

\Rightarrow f(x)=9400-60x-80\sqrt{16900-x^2}

\Rightarrow f'(x)=-60+80\dfrac{x}{\sqrt{16900-x^2}}

\Rightarrow f''(x)=\dfrac{1352000}{\left(16900-x^2\right)\sqrt{16900-x^2}}

We find the critical points,

\Rightarrow f'(x)=0

\Rightarrow-60+80\dfrac{x}{\sqrt{16900-x^2}}=0

\Rightarrow 80\dfrac{x}{\sqrt{16900-x^2}}=60

\Rightarrow 80x=60\sqrt{16900-x^2}

\Rightarrow 80^2x^2=60^2(16900-x^2)

\Rightarrow 6400x^2=3600(16900-x^2)

\Rightarrow \dfrac{16}{9}x^2=16900-x^2

\Rightarrow \dfrac{25}{9}x^2=16900

\Rightarrow x=\sqrt{\dfrac{16900\times 9}{25}}=78

\Rightarrow x=78

Then,

\Rightarrow f''(78)=\dfrac{1352000}{\left(16900-78^2\right)\sqrt{16900-78^2}}=\dfrac{125}{104}=1.2

Since f''(x) is positive, the function f(x) achieves its minimum at x=78

When x is set to 78, the corresponding y value will be

\Rightarrow y = \sqrt{16900-x^2}=\sqrt{16900-78^2}=104

This leads us to conclude that the closest point is (78,104)

5 0
1 month ago
Mrs. Adams bought cans of pears and cans of mixed fruit.
Svet_ta [9500]

Answer: 5 Cans

Step-by-step explanation:

4 0
1 month ago
Jackie runs and dances for 75 minutes every day.
babunello [8412]
A. x + y = 75 B. She dedicates 25 minutes to running and 50 minutes to dancing daily. C. Yes, that's correct.
6 0
5 days ago
Read 2 more answers
Carla can choose two of her three pairs of sneakers to take to a track meet. If the pairs of sneakers are called A, B, and C, wh
lawyer [9240]
The formula for determining the number of ways to select two pairs of sneakers from three pairs labeled A, B, and C is represented by 3C2 (3 combinations of 2), which calculates as 3! / (2!(3 - 2)!) = 3! / (2! x 1!) = (3 x 2) / (2 x 1) = 3. Therefore, the sample space is S = {AB, AC, BC}.
5 0
1 day ago
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