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3 years ago

58,927 in scientific notation

1 answer:

4 0

5.8927 x 10^4
it easy it must be a number between 1-10 (this time 5.8927) and then the 10^4 its because the decimal point moves 4 spaces

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Find the area of the shaded regions. Give your answer as a completely simplified exact value in terms of π (no approximations).

Elan Coil [88]

Answer:

(40/3)*pi

Step-by-step explanation:

lets first find the area of the little circle

A=pi*r^2

A=pi*3^2

A=9pi

Now, lets find the area of the big circle

A=pi*r^2

A=pi*(3+4)^2

A=pi*7^2

A=49pi

now lets subtract the area of the little circle from the area of the big circle

49pi-9pi=40pi, now we found the area of the "bagel)

lets find what portion of the bagel is the shaded region

120/360=1/3

now lets multiply the bagel area by the fraction

40pi*(1/3)=

(40/3)*pi or (40*pi)/3

4 0

3 years ago

Write an equation of a parabola that passes through (3,-30) and has x-intercepts of -2 and 18. Then find the average rate of cha

Nookie1986 [14]

Answer:

The equation of the parabola is $y = \frac{2}{5}\cdot x^{2}-\frac{32}{5}\cdot x -\frac{72}{5}$ . The average rate of change of the parabola is -4.

Step-by-step explanation:

We must remember that a parabola is represented by a quadratic function, which can be formed by knowing three different points. A quadratic function is standard form is represented by:

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

Where:

$x$ - Independent variable, dimensionless.

$y$ - Dependent variable, dimensionless.

$a$ , $b$ , $c$ - Coefficients, dimensionless.

If we know that $(3, -30)$ , $(-2, 0)$ and $(18, 0)$ are part of the parabola, the following linear system of equations is formed:

$9\cdot a +3\cdot b + c = -30$

$4\cdot a -2\cdot b +c = 0$

$324\cdot a +18\cdot b + c = 0$

This system can be solved both by algebraic means (substitution, elimination, equalization, determinant) and by numerical methods. The solution of the linear system is:

$a = \frac{2}{5}$ , $b = -\frac{32}{5}$ , $c = -\frac{72}{5}$ .