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3 years ago

Help ASAP please :)) Image attached

Mathematics

1 answer:

NemiM [27]3 years ago

4 0

No Sophie made a mistake going from step one to two. (She should’ve multiplied 9*2 and 6*7 instead of dividing first, she didn’t follow PEMDAS)

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Find the area bounded by the given curves: y=2x−x2,y=2x−4

Andrej [43]

Answer:

$A = [\frac{32}{3}]$

Step-by-step explanation:

Given

$y_1 = 2x - x^2$

$y_2 = 2x - 4$

Required

Determine the area bounded by the curves

First, we need to determine their points of intersection

$2x - x^2 = 2x - 4$

Subtract 2x from both sides

$-x^2 = -4$

Multiply through by -1

$x^2 = 4$

Take square root of both sides

$x = 2$ or $x = -2$

This Area is then calculated as thus

$A = \int\limits^a_b {[y_1 - y_2]} \, dx$

Where a = 2 and b = -2

Substitute values for $y_1$ and $y_2$

$A = \int\limits^a_b {(2x - x^2) - (2x - 4)} \, dx$

Open Brackets

$A = \int\limits^a_b {2x - x^2 - 2x + 4} \, dx$

Collect Like Terms

$A = \int\limits^a_b {2x - 2x- x^2 + 4} \, dx$

$A = \int\limits^a_b {- x^2 + 4} \, dx$

Integrate

$A = [-\frac{x^{3}}{3} +4x](2,-2)$

$A = [-\frac{2^{3}}{3} +4(2)] - [-\frac{-2^{3}}{3} +4(-2)]$

$A = [-\frac{8}{3} +8] - [-\frac{-8}{3} -8]$

$A = [\frac{-8+ 24}{3}] - [\frac{8}{3} -8]$

$A = [\frac{-8+ 24}{3}] - [\frac{8-24}{3}]$

$A = [\frac{16}{3}] - [\frac{-16}{3}]$

$A = [\frac{16}{3}] + [\frac{16}{3}]$

$A = [\frac{16 + 16}{3}]$

$A = [\frac{32}{3}]$

Hence, the Area is:

$A = [\frac{32}{3}]$

7 0

4 years ago

Tom, Michael and Jane visit the same sport club. Tom visits the club every 5th day, Michael every 6th day and Jane every 8th day

Sedaia [141]

Answer: December 3rd.

Step-by-step explanation:

To solve this question, we have to calculate the multiples of 5, 6 and 8 and then choose the lowest common multiple. After then, we add the number chosen to the date earlier given to derive our answer.

For Tom:

Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120

For Michael:

Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96, 102, 108, 114, 120.

For Jane:

Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 120.

L. C. M = 120

It should be noted that when we use the calendar or calculate the number of days we have, August 5 will be 217 days.

The next day when the three of them will be at the sports club will be:

= August 5 + 120

= 217 days + 120 days

= 337 days

The 337th day will be December 3rd.

7 0

3 years ago

Find the coordinate that divides the directed line segment from A(-2,-4) to B(8,1) in the ratio of 2 to 3

zalisa [80]

We have that
A(-2,-4) B(8,1) 

let
M-------> the coordinate that divides the directed line segment from A to B in the ratio of 2 to 3

we know that

A--------------M----------------------B
2 3
distance AM is equal to (2/5) AB
distance MB is equal to (3/5) AB
so

step 1
find the x coordinate of point M
Mx=Ax+(2/5)*dABx
where
Mx is the x coordinate of point M
Ax is the x coordinate of point A
dABx is the distance AB in the x coordinate
Ax=-2
dABx=(8+2)=10
Mx=-2+(2/5)*10-----> Mx=2

step 2
find the y coordinate of point M
My=Ay+(2/5)*dABy
where
My is the y coordinate of point M
Ay is the y coordinate of point A
dABy is the distance AB in the y coordinate
Ay=-4
dABy=(1+4)=5
Mx=-4+(2/5)*5-----> My=-2

the coordinates of point M is (2,-2)

see the attached figure