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3 years ago

What is the power to another power rule

Mathematics

2 answers:

Sholpan [36]3 years ago

7 0

Answer:

Step-by-step explanation:

USPshnik [31]3 years ago

4 0

Answer:

The power rule says that if we have an exponent raised to another exponent, you can just multiply the exponents together.

Step-by-step explanation:

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What is 30.12 rounded to one decimal place

leva [86]

it should be rounded to 30.1

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3 years ago

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Which ratio is higher 15:20 or 12:16. for 35 points

Margarita [4]

To find which ratio is higher, we can first convert the ratios into fractions (that makes it easier, at least for me) and then simplify the fractions and see which one is greater.

Since ratios are basically division, 15:20 = $\frac{15}{20}$ , and

12:16 = $\frac{12}{16}$

Now we simplify these fractions. 15 and 20 have a GCF of 5, so taking out the common number gives us the simplified fraction of $\frac{3}{4}$ .

12 and 16 have a GCF of 4, so taking out the common number gives us the simplified fraction of $\frac{3}{4}$ . Since $\frac{3}{4}$ = $\frac{3}{4}$ , these ratios are the same.

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3 years ago

The students in Mr. Wilson's Physics class are making golf ball catapults. The

Mnenie [13.5K]

Answer:

Part a) About 48.6 feet

Part b) About 8.3 feet

Part c) The domain is $0 \leq x \leq 48.6\ ft$ and the range is $0 \leq y \leq 8.3\ ft$

Step-by-step explanation:

we have

$y=-0.014x^{2} +0.68x$

This is a vertical parabola open downward (the leading coefficient is negative)

The vertex represent a maximum

where

x is the ball's distance from the catapult in feet

y is the flight of the balls in feet

Part a) How far did the ball fly?

Find the x-intercepts or the roots of the quadratic equation

Remember that

The x-intercept is the value of x when the value of y is equal to zero

The formula to solve a quadratic equation of the form

$ax^{2} +bx+c=0$

is equal to

$x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}$

in this problem we have

$-0.014x^{2} +0.68x=0$

$a=-0.014\\b=0.68\\c=0$

substitute in the formula

$x=\frac{-0.68(+/-)\sqrt{0.68^{2}-4(-0.014)(0)}} {2(-0.014)}$

$x=\frac{-0.68(+/-)0.68} {(-0.028)}$

$x=\frac{-0.68(+)0.68} {(-0.028)}=0$

$x=\frac{-0.68(-)0.68} {(-0.028)}=48.6\ ft$

therefore

The ball flew about 48.6 feet

Part b) How high above the ground did the ball fly?

Find the maximum (vertex)

$y=-0.014x^{2} +0.68x$

Find out the derivative and equate to zero

$0=-0.028x +0.68$

Solve for x

$0.028x=0.68$

$x=24.3$

<em>Alternative method</em>

To determine the x-coordinate of the vertex, find out the midpoint between the x-intercepts

$x=(0+48.6)/2=24.3\ ft$

To determine the y-coordinate of the vertex substitute the value of x in the quadratic equation and solve for y

$y=-0.014(24.3)^{2} +0.68(24.3)$

$y=8.3\ ft$

the vertex is the point (24.3,8.3)

therefore

The ball flew above the ground about 8.3 feet

Part c) What is a reasonable domain and range for this function?

we know that

A reasonable domain is the distance between the two x-intercepts

$0 \leq x \leq 48.6\ ft$

All real numbers greater than or equal to 0 feet and less than or equal to 48.6 feet

A reasonable range is all real numbers greater than or equal to zero and less than or equal to the y-coordinate of the vertex

we have the interval -----> [0,8.3]

$0 \leq y \leq 8.3\ ft$

All real numbers greater than or equal to 0 feet and less than or equal to 8.3 feet

8 0

2 years ago

Given: M(-4,-1), B(-5,-3) find the midpoint

Dmitry [639]

$\bf \textit{middle point of 2 points }\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
M&({{ -4}}\quad ,&{{ -1}})\quad 
% (c,d)
B&({{ -5}}\quad ,&{{ -3}})
\end{array}\qquad
% coordinates of midpoint 
\left(\cfrac{{{ x_2}} + {{ x_1}}}{2}\quad ,\quad \cfrac{{{ y_2}} + {{ y_1}}}{2} \right)
\\\\\\
\left(\cfrac{{{ -5}}-4}{2}\quad ,\quad \cfrac{-3-1}{2} \right)$

4 0

3 years ago

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6. Examine the prism shown below.

bulgar [2K]

It may be can be number 1 (a)

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2 years ago