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3 years ago

If n is the larger of the two consecutive numbers, write an expression for the sum of these two numbers.

Mathematics

1 answer:

iren [92.7K]3 years ago

4 0

Answer: 2n-1

Step-by-step explanation:

If n is the larger number, than the smaller number is n-1, because they are consecutive. So if you add them together, the answer is n+n-1= 2n-1.

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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

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

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

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

3 years ago

Help yall girl for 30 point

zhenek [66]

Answer:

cant help ya but if you go to math_way they help with all sorts of stuff like this

Step-by-step explanation:

sorry!

7 0

3 years ago

Use the drop-down menus to complete the statements about factoring 14x2 + 6x – 7x – 3 by grouping.

Stella [2.4K]

Answer:1. GCF of the group ( 6 x - 3 ) is 3.

2. The common binomial factor is 2 x - 1.

3. The factored expression is: ( 2 x - 1 ) ( 7 x + 3 ).

Step-by-step explanation:

14 x² + 6 x - 7 x - 3 =

= ( 14 x² - 7 x ) + ( 6 x - 3 ) =

= 7 x ( 2 x - 1 ) + 3 ( 2 x - 1 ) =

= ( 2 x - 1 ) ( 7 x + 3 )

4 0

3 years ago

Read 2 more answers

The larger square is composed of 16 smaller squares. Find the length of the sides of Square "a".

kondaur [170]

Answer:

2.5 ft.

Step-by-step explanation:

The area of the side of each smaller square = 100 / 16 sq ft.

= 6.25 sq feet.

So the length of each smaller square = square root of 6.25

= 2.5 ft.

6 0

3 years ago

Read 2 more answers

An American tourist visits South Africa with $3000. The exchange rate when she arrives is

algol [13]

9514 1404 393

Answer:

$2505.80

Step-by-step explanation:

After the first exchange, the tourist has ...

$3000(12.90 R/$) = R38,700

After 7 days, she has ...

R38,700 -7(R900) = R32,400

After the second exchange, she has ...

R32,400 × ($1/R12.93) = $2505.80

She gets $2505.80 at the second exchange.

8 0

3 years ago