Which of the following correctly expresses the number below in scientific notation?

Convert 22 2/5% into decimal

Vera_Pavlovna [14]

Answer:

0.224

Step-by-step explanation:

2/5% = 0.004

22% = 0.22

22% + 2/5% = 0.224

5 0

2 years ago

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A circle has an arc of length 20π that is intercepted by a central angle of 180°. What is the radius of the circle?

Bond [772]

Answer:

10π

Step-by-step explanation:

RULE: The angle measure of the central angle is congruent to the measure of the intercepted arc.

RULE: Central Angle = Arc length

Given:

Arc length (20 π) = central angle (180)

we know 180 degrees is a straight line, thus a semi-circle is created. This would be the diameter.

1/2 diameter is the radius. 20π/2 is the radius.

10π

8 0

3 years ago

Let L be a tangent line to the hyperbola x y = 2 at x = 9 . Find the area of the triangle bounded by L and the coordinate axes.

mafiozo [28]

Answer:

$A = 4$

Step-by-step explanation:

The equation of the slope of the tangent line L is obtained by deriving the equation of the hyperbola:

$y = \frac{2}{x}$

$y'=-2\cdot x^{-2}$

The numerical value of the slope is:

$y' = -2 \cdot (9)^{-2}\\y' = -\frac{2}{81}$

The component of the y-axis is:

$y = \frac{2}{9}$

Now, the tangent line has the following mathematical model:

$y = m \cdot x + b$

The value of the intercept is found by isolating it within the equation and replacing all known variables:

$b = y - m \cdot x$

$b = \frac{2}{9}-(-\frac{2}{81} )\cdot (9)\\b = \frac{4}{9}$

Thus, the tangent line is:

$y = -\frac{2}{81}\cdot x + \frac{4}{9}$

The vertical distance between a point of the tangent line and the origin is given by the intercept.

$d_{y} = \frac{4}{9}$

In order to find horizontal distance between a point of the tangent line and the origin, let equalize y to zero and clear x:

$-\frac{2}{81}\cdot x + \frac{4}{9}=0$

$-\frac{2}{9}\cdot x + 4 = 0$

$x = 18$

$d_{x} = 18$

The area of the triangle is computed by this formula:

$A = \frac{1}{2}\cdot d_{x}\cdot d_{y}$

$A = \frac{1}{2}\cdot (18)\cdot (\frac{4}{9} )$

$A = 4$

4 0

3 years ago

The graph of y=x^2 -7x+ 12 is a parabola with x-intercepts at

vesna_86 [32]

Answer:

Step-by-step explanation:

$\text{x-intercept is for y = 0}.\\\\\text{We have the function:}\ y=x^2-7x+12.\\\\\text{Put y = 0 and calculate the value(s) of x.}\\\\x^2-7x+12=0\\\\x^2-3x-4x+12=0\\\\x(x-3)-4(x-3)=0\\\\(x-3)(x-4)=0\iff x-3=0\ \vee\ x-4=0\\\\x-3=0\qquad\text{add 3 to both sides}\\\boxed{x=3}\\\\x-4=0\qquad\text{add 4 to both sides}\\\boxed{x=4}$

6 0

2 years ago

Mark went to costco and bought 12 cans of albacore for $15.96. what is the cost per can?

Law Incorporation [45]

Answer:

$1.33

Step-by-step explanation:

15.96 divided by 12 = $1.33

3 0

2 years ago