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3 years ago

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Pedro has 5 jars of marbles. Each jar is 2/3 filled with marbles. How many full jars of marbles does Pedro have? Write an equati

on to represent the problem. ______________________ Solve the equation. 1

1 answer:

Fynjy0 [20]3 years ago

4 0

Answer:

3 1/3 is the answer mark brainliest

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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

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3 years ago

Marie can find the volume of a cube by using the formula V = 53, where s represents the side length of the cube. If Marie's

dimulka [17.4K]

Answer:

The volume of her cube is 15.625cm^3

Step-by-step explanation:

The formula V = s³, where s represents the side length of the cube.

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3 years ago

A ball is dropped from a height of 5ft and bounces to 60% of I?ts previous height in each subsequent bounce

Gelneren [198K]

Answer:

Im assuming youre trying to answer what is the 60% height, it would be 3ft

Step-by-step explanation:

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4 years ago

The yearbook club had a meeting. The meeting had 24 people, which is three-fourths of the club. How many people are in the club?

Leto [7]

Answer:

32

Brainiest plz? :)

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3 years ago

A recipe calls for 18 ounces of cream cheese and 15 ounces of sugar.How many ounces of sugar are there per ounce of cream cheese

Pavlova-9 [17]

Step-by-step explanation:

MusicLeonard BernsteinLyricsStephen SondheimBookArthur LaurentsBasisRomeo and Juliet

by William ShakespeareProductions1957 Washington, D.C. (tryout)

1957 Philadelphia(tryout)

1957 Broadway

1958 West End

1959 US tour

1960 Broadway revival

1964 Broadway revival

1974 West End revival

1980 Broadway revival

1984 West End revival

1985 US tour

1995 US tour

1998 West End revival

2009 Broadway revival

2010 US tour

2020 Broadway revival

The story is set in the Upper West Sideneighborhood in New York City in the mid 1950s, a multiracial, blue-collar neighborhood. The musical explores the rivalry between the Jets and the Sharks, two teenage street gangsof different ethnic backgrounds. The members of the Sharks, from Puerto Rico, are taunted by the Jets, a white gang.[2] The young protagonist, Tony, a former member of the Jets and best friend of the gang's leader, Riff, falls in love with Maria, the sister of Bernardo, the leader of the Sharks. The dark theme, sophisticated music, extended dance scenes, and focus on social problems marked a turning point in American musical theatre. Bernstein's score for the musical includes "Jet Song", "Something's Coming", "Maria", "Tonight", "America", "Cool", "One Hand, One Heart", "I Feel Pretty", "Somewhere", "Gee, Officer Krupke" and "A Boy Like That".

The original 1957 Broadway production, conceived, directed and choreographed by Jerome Robbins and produced by Robert E. Griffith and Harold Prince, marked Sondheim's Broadway debut. It ran for 732 performances before going on tour. The production was nominated for six Tony Awards including Best Musical in 1958,[3] but the award for Best Musical went to Meredith Willson's The Music Man. Robbins won the Tony Award for his choreography and Oliver Smith won for his scenic designs. The show had an even longer-running London production, a number of revivals and international productions. A 1961 musical film adaptation, directed by Robert Wise and Robbins, starred Natalie Wood, Richard Beymer, Rita Moreno, George Chakirisand Russ Tamblyn. The film was nominated for eleven Academy Awards and won ten, including George Chakiris for Supporting Actor, Rita Moreno for Supporting Actress, and Best Picture.

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3 years ago

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