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3 years ago

(Max Points) Do not answer if you’re not 100% sure. I’ll report if wrong.

Mathematics

2 answers:

scoray [572]3 years ago

7 0

Answer:

Step-by-step explanation:

Rocco: of the job per hour

Giulia: of the job per hour

Together: of the job per hour

Rocco + Giulia = Together

$\frac{1}{7} +\frac{1}{x} =\frac{1}{3}$

$\frac{1}{7} (21x)+\frac{1}{x}(21x) =\frac{1}{3}(21x)$

3x + 21 = 7x

21 = 4x

$x=\frac{21}{4}$

It will take Giulia $\frac{21}{4} =5\frac{1}{5}$ hours to paint the room by herself.

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Giulia: $r= \frac{1}{x} =\frac{4}{21\\}$

B) $\frac{3}{7} +3(\frac{4}{21})=1$

$\frac{3}{7} +\frac{4}{7} =1$

$\frac{7}{7} =1$

1=1

so it's true

CaHeK987 [17]3 years ago

6 0

Answer:

B. 3/7 + 3r = 1

Step-by-step explanation:

Job can be determines as:

Job = time*rate

We have:

Time 3 hours and
Rates 1/7 and r

Sum of the parts completed by both Rocco and Giulia gives the job, which is considered as a whole or 1:

1 = 3(1/7 + r)
1 = 3/7 + 3r

3/7 + 3r = 1

Correct choice is B

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Volleyball A volleyball is hit when it is 4 ft above the ground and 12 ft from a 6-ft-high net. It leaves the point of impact wi

Natali [406]

Answer:

a) the vector equation is r(x,y) = (35cos27°t, 16t^2 -35sin27° - 4)

b) Maximum height = 7.945ft

c) Time of flight = 1.201 secs and range = 37.45ft

d) when t = 0.74, the distance above the ground = 14.37ft

When t = 0.254, the distance above the ground = 26.53ft

e) if the ball is raised to 8ft, the ball won't be able to reach it. This is because the maximum height is 7.954ft

Step-by-step explanation:

a) From the diagram

x0 = 0

y0= 4

V0(initial velocity) = 35

α= 27°

y = 4 + 35sin27°t - 16t^2

y = -16t^2 + 35sin27°t+ 4

y = 16t^2 - 35sin27°t - 4

x = 35cos27°t

Vector equation for the path of the volleyball = r(x,y)

r(x,y) = (35cos27°t, 16t^2 -35sin27° - 4)

b) the ball reaches maximum when dy/dt = 0

y = 16t^2 - 35sin27°t - 4

dy/dt = 32 - 35sin27°

0 = 32 - 35sin27°t

-32 = -35sin27°t

t = -32 / -35sin27°

t = 0.4966 seconds

Put t = 0.4966 into y = 16t^2 - 35sin27°t - 4

y = 16(0.4966)^2 - 35sin27°(0.4966) - 4

y = 7.945 ft

The maximum height is 7.945 ft

c) To find the range and flight time, put y= 0

0 = 16t^2 - 35sin27°t - 4

0 = 16t^2 - 15.89t - 4

Using quadratic equation general formula,

[-b +/- √b^2 -4ac] / 2a

a = 16, b = -15.89, c = -4

= [-(-15.89) +/- √ (-15.89)^2 - 4(16)(-4)] /2(16)

= [15.89 +/- √(15.89)^2 + 256] / 32

= (15.59 +/- 22.55) / 32

= (15.89 + 22.55) / 32 or (15.89 - 22.55) / 32

= 1.201 or -0.208

Time of flight = 1.201 secs

Range = x = 35cos27°t

Range = 32cos27°(1.201)

= 37.45 ft

d) when the volley is 7ft above ground, y = 7

Recall that y = 16t^2 - 35sin27°t - 4

7 = 16t^2 - 35sin27°t - 4

0 = 16t^2 - 35sin27°t - 4 +7

0 = 16t^2 - 35sin27°t + 3

0 = 16t^2 - 15.89t + 3

Using quadratic equation general formula,

[-b +/- √b^2 -4ac] / 2a

a = 16, b = -15.89, c = 3

= [-(-15.89) +/- √ (-15.89)^2 - 4(16)(3)] /2(16)

= [15.89 +/- √(15.89)^2 - 192] / 32

= (15.59 +/- 7.7778) / 32

= (15.89 + 7.7778) / 32 or (15.89 - 7.7778) / 32

= 0.74 or 0.254

When t = 0.74,

x = 35cos27°t

x = 35cos27°(0.74)

x = 23.08 ft

Therefore , R - x(0.74)

= 37.45 - 23.08

= 14.37ft

When t = 0.254,

x = 35cos27°t

x = 35cos27°(0.254)

x = 7.92 ft

Therefore R - x(0.254) =

37.45 - 7.92 = 29.53ft

e) if the ball is raised to 8ft, the ball won't be able to reach it. This is because the maximum height is 7.954ft

7 0

3 years ago

Find the distance across the lake. Assume the triangles are similar.\

allochka39001 [22]

Answer: A. 300 m

Work Shown:

L/100 = 15/5

5L = 100*15

5L = 1500

L = 1500/5

L = 300

3 0

3 years ago

Read 2 more answers

The crosssectional areas of triangular prism and a night cylinder are congruent. The triangular prism has a helght of 5 units, a

dmitriy555 [2]

Answer:

The volume of the triangular prism is not equal to the volume of the cylinder

Step-by-step explanation:

Given that:

The cross sectional area of triangular prism and a night cylinder are congruent. The term 'congruent' means when two objects or shapes are placed above each other , they should both overlap exactly.

It was given that:

The triangular prism has a height of 5 units

and the right cylinder height of 3 units

The conclusion that can be drawn from this is that:

The volume of the triangular prism is not equal to the volume of the cylinder.

This is because, they do not occur in the same family. A triangular prism is a three - dimensional shape that has identical, parallel ends and parallel faces.

A triangular prism has two triangles at it ends and three rectangular faces.

The volume of the triangular prism is calculate by using the formula:

$V= \dfrac{1}{2}\times b \times h\times l$

On the other hand, a cylinder is a shape with two circular ends and a curved surface.The two circular ends are congruent and both circular end posses the same cross section from one end to the other in the cylinder.

The volume of a cylinder is calculated by using the formula:

V = πr²h

Thus, we conclude that irrespective of the nature of their congruency, since the heights are different which will definitely affects their volume, the the volume of the triangular prism is not equal to the volume of the cylinder.

3 0

3 years ago

5(x + 1) - 8 = 5x(2-4) what is the value of x? a. -5 b. -1/5 c. 5 d. 1/5

Harlamova29_29 [7]

Answer:

d) 1/5

Step-by-step explanation:

5(x + 1) - 8 = 5x(2-4)

5x+5-8 = 5x(-2)

5x-3=-10x

15x = 3

x = 1/5

4 0

3 years ago

Read 2 more answers

How do you slove 3x+4y=8 in steps

gavmur [86]

3x+4y=8
Add -4y to both sides
3x+4y+−4y=8+−4y3x=−4y+8
Then you divide both sides by 3
3x/3=−4y+8/3x=−4/3y+8/3
And your answer is ...
x=−4/3y+8/3

7 0

3 years ago