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lidiya [134]
3 years ago
8

Jane buys some rocks for decorating her backyard. She uses a box full of rocks. The box is a rectangular container that is 1 yar

d long, 0.5 yard wide and 0.5 yard high. She buys rocks for $25 per cubic yard. How much does Jane spend to buy these rocks?
Mathematics
1 answer:
statuscvo [17]3 years ago
4 0
First, Jane must know the volume of the box.
Volume = l * w * h
Volume = 1 * 0.5 * 0.5
Volume = 0.25 yard^3

1 yard^3 = $25

So,
1 : 25 = 0.25 : x
x = 25 * 0.25
x = $6.25

So she need to spend $6.25
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A golfball is hit from the ground with an initial velocity of 200 ft/sec. The horizontal distance that the golfball will travel,
algol13

Answer:

The golfball launched with an initial velocity of 200ft/s will travel the maximum possible distance which is 1250 ft when it is hit at an angle of \pi/4.

Step-by-step explanation:

The formula from the maximum distance of a projectile with initial height h=0, is:

d(\theta)=\frac{v_i^2sin(2\theta)}{g}

Where v_i is the initial velocity.

In the closed interval method, the first step is to find the values of the function in the critical points in the interval which is [0, \pi/2]. The critical  points of the function are those who make d'(\theta)=0:

d(\theta)=\frac{v_i^2\sin(2\theta)}{g}\\d'(\theta)=\frac{v_i^2\cos(2\theta)}{g}*(2)\\d'(\theta)=\frac{2v_i^2\cos(2\theta)}{g}

d'(\theta)=0\\\frac{2v_i^2\cos(2\theta)}{g}=0\\\cos(2\theta)=0\\2\theta=\pi/2,3\pi/2,5\pi/2,...\\\theta=\pi/4,3\pi/4,5\pi/4,...

The critical value inside the interval is \pi/4.

d(\theta)=\frac{v_i^2sin(2\theta)}{g}\\d(\pi/4)=\frac{v_i^2sin(2(\pi/4))}{g}\\d(\pi/4)=\frac{v_i^2sin(\pi/2)}{g}\\d(\pi/4)=\frac{v_i^2(1)}{g}\\d(\pi/4)=\frac{(200)^2}{32}\\d(\pi/4)=\frac{40000}{32}\\d(\pi/4)=1250ft

The second step is to find the values of the function at the endpoints of the interval:

d(\theta)=\frac{v_i^2sin(2\theta)}{g}\\\theta=0\\d(0)=\frac{v_i^2sin(2(0))}{g}\\d(0)=\frac{v_i^2(0)}{g}=0ft\\\theta=\pi/2\\d(\pi/2)=\frac{v_i^2sin(2(\pi/2))}{g}\\d(\pi/2)=\frac{v_i^2sin(\pi)}{g}\\d(\pi/2)=\frac{v_i^2(0)}{g}=0ft

The biggest value of f is gived by \pi/4, therefore \pi/4 is the absolute maximum.

In the context of the problem, the golfball launched with an initial velocity of 200ft/s will travel the maximum possible distance which is 1250 ft when it is hit at an angle of \pi/4.

4 0
3 years ago
¿Qué es un sistema de ecuaciones de 2x2? ¿Para qué sirve y cuáles son sus usos en el área científica?
Tanya [424]

Answer:

4

Step-by-step explanation:

2x2=4

6 0
2 years ago
An oblique cylinder has a radius of 9 centimeters and a volume of 486 cubic centimeters. Use Cavalieri’s Principle to calculate
kotegsom [21]

Using Cavalieri’s Principle, the height of the oblique cylinder with the given volume and base radius is 6cm.

Option A) is the correct answer.

<h3>What is the height of the oblique cylinder?</h3>

From Cavalieri's principle, the volume of an oblique cylinder is expressed as;

V = base area × h

V = πr² × h

Given that;

  • Radius r = 9cm
  • Volume of the oblique cylinder V = 486πcm³
  • Height of the oblique cylinder h = ?

V = πr² × h

486πcm³ = π × ( 9cm )² × h

486πcm³ = π × 81cm² × h

486πcm³ = 81πcm² × h

h = 486πcm³ / 81πcm²

h = 6cm

Using Cavalieri’s Principle, the height of the oblique cylinder with the given volume and base radius is 6cm.

Option A) is the correct answer.

Learn more on volume of cylinder here: brainly.com/question/16788902

#SPJ1

6 0
2 years ago
I know it has to be b or d
densk [106]

It is C, however I might be wrong so you can visit this website.

Websites: https://www.varsitytutors.com/hotmath/hotmath_help/topics/converse-inverse-contrapositive

7 0
3 years ago
Dividing the polynomials by using long division
Andrew [12]

Answer:

x ) -x^2 + 8x ( -x + 8

-x^2

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0 + 8x

8x

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0

4 0
2 years ago
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