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3 years ago

4,7,2,x,2,9,6: the median is 5

Mathematics

1 answer:

telo118 [61]3 years ago

6 0

Answer:

the median is 5

hope this helps

have a good day :)

Step-by-step explanation:

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The tangents to the curve with equation y = x^3-3x at the points A and B with x coordinates −1 and 4 respectively meet at the po

sladkih [1.3K]

Answer:

$\displaystyle C=\left(\frac{26}{9}, 2\right)$

Step-by-step explanation:

We need to find the equation of the tangent lines of Points A and B.

Differentiate the equation:

$\displaystyle \frac{dy}{dx}=3x^2-3$

Point A has an x-coordinate of -1. Hence, the slope of its tangent line is:

$\displaystyle \frac{dy}{dx}\Big|_{x=-1}=3(-1)^2-3=0$

Find the y-coordinate of Point A using the original equation:

$y(-1)=(-1)^3-3(-1)=2$

Hence, Point A is (-1, 2).

Thus, the tangent line at Point A is:

$y-2=0(x-(-1))$

Simplify:

$y=2$

Point B has an x-coordinate of 4. Hence, the slope of its tangent line is:

$\displaystyle \frac{dy}{dx}\Big|_{x=4}=3(4)^2-3=45$

Find the y-coordinate of Point B:

$y(4)=(4)^3-3(4)=52$

Thus, Point B is at (4, 52).

So, the tangent line at Point B is:

$y-52=45(x-4)$

Simplify:

$y=45x-128$

Point C occurs at the intersections of the tangent lines of Points A and B. Set the two equations equal to each other and solve for x:

$2=45x-128$

We acquire:

$\displaystyle x=\frac{26}{9}$

Since one of our equations is y = 2, the y-coordinate is 2.

Hence, Point C is:

$\displaystyle C=\left(\frac{26}{9}, 2\right)$

5 0

3 years ago

Read 2 more answers

What is the sixth term of the sequence an=-3•2n+1 a6=

muminat

Answer:

$a_6=-384$

Step-by-step explanation:

The $n^{th}$ term of the sequence is given as $a_n=-3\cdot 2^{n+1}$ .

To find the sixth term, which is denoted by $a_6$ , we substitute n=6 into the given rule.

This will give us:

$a_6=-3\cdot 2^{6+1}$

Simplify the exponent to get:

$a_6=-3\cdot 2^{7}$

We simplify further to get:

$a_6=-3\cdot 128$

This simplifies to

$a_6=-384$

8 0

3 years ago

On a factory floor, 30 out of every 140 toy robots is defective. What percent is defective?

yaroslaw [1]

Answer:

$21.43\%$

Step-by-step explanation:

we know that

To find out the percent of robots which are defective, divided the number of defective robots by the total number of robots and multiply the result by 100

Let

x ----> the number of defective robots

y ----> the total number of robots

p ---> percentage of robots which are defective

$p=\frac{x}{y} (100)$

we have

$x=30\\y=140$

substitute

$p=\frac{30}{140}(100)$

$p=21.43\%$

5 0

3 years ago

Tickets to the school dance cost $3.00 in advance or $5.00 at the door. There were a total of 184 tickets sold, raising $688. Ho

GenaCL600 [577]

Answer: They sold 68 tickets at the door
688-920= -2x= -232
2x=232/2=116
184-116=68

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2 years ago

Simplify fully 8 x 12 x 2 y

Talja [164]

Answer:

$8 \times 12 \times 2y = 96 \times 2y = 192y$

7 0

3 years ago

4,7,2,x,2,9,6: the median is 5​

4,7,2,x,2,9,6: the median is 5