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inna [77]
3 years ago
12

Match the numerical expressions to their simplest forms

Mathematics
2 answers:
BlackZzzverrR [31]3 years ago
4 0
 (a^6b^{12})^{1/3} ========> a^2b^4
\frac{(a^5b^3)^{1/2} }{(ab)^{- \frac{1}{2} } }  ======> a^3b^2
(\frac{a^{5} }{ a^{-3} b^{-4}  } )^{ \frac{1}{4}} ========> a^2b
( \frac{a^3}{ab^{-6} } )^{ \frac{1}{2} } ========> ab^3

sasho [114]3 years ago
4 0
The answers are the following:
(a^6b^12)^1/3 = a^2b^4
(a^5b^3)^1/2 / (ab)^-1/2 = a^3b^2
(a^5/a^-3b^-4)^1/4=a^2b
(a^3/ab^-6)^1/2 = ab^3
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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

so

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

so

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

so

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
Simplify 4+(9×2)÷(4-2)+1
kogti [31]

First we have to work out everything inside the parentheses (according to PEMDAS):

9 × 2 = 18

4 - 2 = 2

Now, we can rewrite the expression:

4 + 18 ÷ 2 + 1

According to PEMDAS, we should complete the division in the middle first:

18 ÷ 2 = 9

Now we can rewrite the expression again:

4 + 9 + 1

And now it's as simple as just adding the three numbers together:

4 + 9 + 1 = 14


Your final answer is 14. :)

3 0
3 years ago
Read 2 more answers
How can you use the x and y axis to help you determine unit rate?
leonid [27]

Answer:

x and y can help you show you the constant rate or the unit rate

Step-by-step explanation:

if you use a graph you can see that x mutipley my a certain number gets you y

6 0
3 years ago
Read 2 more answers
The cost of renting a bicycle from Dan's Bike Shop is $2 for 1 hour plus $1 for each additional hour of rental time. Which of th
Vlad [161]

option B

Explanation:

The cost of renting per hour = $2

For 1 hour = $2

For each additional hour, it is $1

For 2 hours = First hour + 1(additional hour)

For 2 hours = $2 + $1(1) = 2+1 = $3

For 3 hours = $2 + $1 (2) = 2+2 = $4

For 4 hours = $2 + $1(3) = 2+3 = $5

The graph which shows this rental cost as 2, 3, 4, 5 is option B

7 0
1 year ago
What is the solution to the system of linear equations below?<br> - 2x + 5y<br> 30
avanturin [10]
Answer: Infinite solutions

Step 1: Turn this into y=Mx+b form

The current equation is—

-2x+5y=30

Since we want to get y alone on the left side, let’s add 2x on both sides

-2x+5y=30
+2x +2x
____________
5y=2x+30

Step 2: Again, trying to get y alone, we need to divide 5 on both sides

5y=2x+30
/5 /5 /5
________
y=2/5x+6

Step 3: Now that we know how to find y, substitute that in where y is in the equation

-2x + 5(2/5x+6) = 30
-2x + 2x + 30 = 30
30=30

Seeing that you cannot get a specific answer for y when solving, there is an infinite number of solutions


Hope this is right and it helps comment below for more questions :)
5 0
3 years ago
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