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2 years ago

,, 8.16,32,64 what is the arithmetic sequence?

Mathematics

1 answer:

seraphim [82]2 years ago

8 0

Answer:

2,4,8,16,32,64

Step-by-step explanation:

There are a couple of ways one could approach this. The goal is to find out the factor by which the numbers are increasing. Looking at going from 8 -> 16, we have either added 8, or doubled 8. So the factor is either +8 or x2. Going from 16 -> 32, adding 8 no longer holds true, while multiplying by 2 (doubling 16) does. To confirm what we have found, we can further check our math by using the final two numbers, 32 -> 64, to confirm that the sequence pattern is to double the current number to achieve the next number.

Working backwards, we can half each number to find out the first two numbers in the sequence. 64/2 = 32, 32/2 = 16, 16/2 = 8, 8/2 = 4, 4/2 = 2

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A long jumper lifts off 3 m after starting his run, and lands 6 m later. When he is 8 m from the start line, he is 5 cm above an

slega [8]

Answer:

The equation of the parabola that models the path of the long jumper through the air is $y = -x^{2}+12\cdot x -27$ .

Step-by-step explanation:

Mathematically, we know that parabolas are second-order polynomials and every second-order polynomials, also known as quadratic functions, can be constructed by knowing three different points of the curve. The standard form of the parabola is:

$y = a\cdot x^{2}+b\cdot x + c$

Where:

$x$ - Horizontal distance from the start line, measured in meters.

$y$ - Height of the long jumper, measured in meters.

$a$ , $b$ , $c$ - Polynomial constants, measured in $\frac{1}{m}$ , dimensionless and meters, respectively.

If we know that $(x_{1},y_{1}) = (3\,m, 0\,m)$ , $(x_{2},y_{2}) = (8\,m, 0.05\,m)$ and $(x_{3}, y_{3}) = (9\,m, 0\,m)$ , this system of linear equations is presented below:

$9\cdot a + 3\cdot b + c = 0$ (Eq. 1)

$81\cdot a + 9\cdot b + c = 0$ (Eq. 2)

$64\cdot a + 8\cdot b + c = 0.05$ (Eq. 3)

The coefficients of the polynomial are, respectively:

$a = -\frac{1}{100}$ , $b = \frac{3}{25}$ , $c = -\frac{27}{100}$

The equation of the parabola that models the path of the long jumper through the air is $y' = -\frac{1}{100}\cdot x^{2}+\frac{3}{25}\cdot x -\frac{27}{100}$ .

But we need $y$ measured in centimeters, then, we use the following conversion:

$y = 100\cdot y'$

Then, we get that:

$y = -x^{2}+12\cdot x -27$

Where $x$ and $y$ are measured in meters and centimeters, respectively.

The equation of the parabola that models the path of the long jumper through the air is $y = -x^{2}+12\cdot x -27$ .

4 0

2 years ago

When do we say that the computed solution or root of a quadratic equation is<br>extraneous?<br><br>

scoray [572]

Answer:

raising both sides of the equation to a certain power in order to eliminate radicals may result in the creation of extraneous roots

Step-by-step explanation:

7 0

2 years ago

Find the area of the composite figure in terms of the figure (use 3.14 for pi)

svp [43]

Answer:

105.12 ft²

Step-by-step explanation:

Let's first find the area of the rectangle.

$10\cdot8=80$ ft², so the rectangle has an area of 80ft².

To find the area of the semi-circle, we find the area of a whole circle and divide by two.

The formula to find the area of a circle is $\pi r^2$ . The radius is 4, as the diameter is 8.

$3.14\cdot4^2$

$3.14\cdot16$

$50.24\div2=25.12$

Add 80 and 25.12:

$80+25.12=105.12$

Hope this helped!

5 0

2 years ago

Jason had to replace the floor of a triangular portion of his dining room. The portion had a height that was twice as high as th

Eva8 [605]

Answer:

4 feet

Step-by-step explanation:

We know the the area of a triangle can be represented as $\frac{bh}{2}$ .

Since the height is twice the base, we can substitute the value $2b$ in as $h$ in the expression, making it $\frac{b\cdot2b}{2}$ . If the area is 16, we can make the equation