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katen-ka-za [31]

2 years ago

5

Frankie is practicing for a 5 km race is normal time is 31 minutes 17 seconds yesterday it's a king only 29 minutes 49 seconds h

ow much faster was Frankie yesterday then his normal time

1 answer:

Rzqust [24]2 years ago

5 0

Answer: He was 1 minute 28 seconds faster.

Step-by-step explanation:

Hi, to answer this question we simply have to subtract Frankie's time yesterday (29 minutes 49 seconds) to his normal time (31 minutes 17 seconds)

Mathematically speaking:

31m 17s - 29m 49s =

(31m-29 m) (17s-49s)=

2m -32s=

1m 60s -32s=

1m 28s

He was 1 minute 28 seconds faster.

Feel free to ask for more if needed or if you did not understand something.

Feel free to ask for more if needed or if you did not understand something.

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Use the shell method to write and evaluate the definite integral that represents the volume of the solid generated by revolving

faust18 [17]

Answer:

$Volume = \frac{384}{7}\pi$

Step-by-step explanation:

Given (Missing Information):

$y = x^\frac{3}{2}$ ; $y = 8$ ; $x=0$

Required

Determine the volume

Using Shell Method:

$V = 2\pi \int\limits^a_b {p(y)h(y)} \, dy$

First solve for a and b.

$y = x^\frac{3}{2}$ and $y = 8$

Substitute 8 for y

$8 = x^\frac{3}{2}$

Take 2/3 root of both sides

$8^\frac{2}{3} = x^{\frac{3}{2}*\frac{2}{3}}$

$8^\frac{2}{3} = x$

$2^{3*\frac{2}{3}} = x$

$2^2 = x$

$4 =x$

$x = 4$

This implies that:

$a = 4$

For $x=0$

This implies that:

$b=0$

So, we have:

$V = 2\pi \int\limits^a_b {p(y)h(y)} \, dy$

$V = 2\pi \int\limits^4_0 {p(y)h(y)} \, dy$

The volume of the solid becomes:

$V = 2\pi \int\limits^4_0 {x(8 - x^{\frac{3}{2}}}) \, dx$

Open bracket

$V = 2\pi \int\limits^4_0 {8x - x.x^{\frac{3}{2}}} \, dx$

$V = 2\pi \int\limits^4_0 {8x - x^{\frac{2+3}{2}}} \, dx$

$V = 2\pi \int\limits^4_0 {8x - x^{\frac{5}{2}}} \, dx$

Integrate

$V = 2\pi * [{\frac{8x^2}{2} - \frac{x^{1+\frac{5}{2}}}{1+\frac{5}{2}}]\vert^4_0$

$V = 2\pi * [{4x^2 - \frac{x^{\frac{2+5}{2}}}{\frac{2+5}{2}}]\vert^4_0$

$V = 2\pi * [{4x^2 - \frac{x^{\frac{7}{2}}}{\frac{7}{2}}]\vert^4_0$

$V = 2\pi * [{4x^2 - \frac{2}{7}x^{\frac{7}{2}}]\vert^4_0$

Substitute 4 and 0 for x

$V = 2\pi * ([{4*4^2 - \frac{2}{7}*4^{\frac{7}{2}}] - [{4*0^2 - \frac{2}{7}*0^{\frac{7}{2}}])$

$V = 2\pi * ([{4*4^2 - \frac{2}{7}*4^{\frac{7}{2}}] - [0])$

$V = 2\pi * [{4*4^2 - \frac{2}{7}*4^{\frac{7}{2}}]$

$V = 2\pi * [{64 - \frac{2}{7}*2^2^{*\frac{7}{2}}]$

$V = 2\pi * [{64 - \frac{2}{7}*2^7]$

$V = 2\pi * [{64 - \frac{2}{7}*128]$

$V = 2\pi * [{64 - \frac{2*128}{7}]$

$V = 2\pi * [{64 - \frac{256}{7}]$

Take LCM

$V = 2\pi * [\frac{64*7-256}{7}]$

$V = 2\pi * [\frac{448-256}{7}]$

$V = 2\pi * [\frac{192}{7}]$

$V = [\frac{2\pi * 192}{7}]$

$V = \frac{\pi * 384}{7}$

$V = \frac{384}{7}\pi$

Hence, the required volume is:

$Volume = \frac{384}{7}\pi$

3 0

2 years ago

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katrin2010 [14]

Answer:

A=920 ft.

Step-by-step explanation:

Using the formulas

A=2AB+(a+b+c)h

AB=s(s﹣a)(s﹣b)(s﹣c)

s=a+b+c

2

Solving for A

A=ah+bh+ch+1

2﹣a4+2(ab)2+2(ac)2﹣b4+2(bc)2﹣c4=8·20+17·20+15·20+1

2·﹣84+2·(8·17)2+2·(8·15)2﹣174+2·(17·15)2﹣154=920

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2 years ago

5280x5 = ? record the product using expanded form to help

kotegsom [21]

5280•5= (5000•5) + (200•5) + (80•5) + (0•5) = 26400.

6 0

3 years ago

Tesfa is x years old his father is 4 times as old as tesfa his mother is 7 years younger than his father If their ages add up to

Sergio039 [100]

Step-by-step explanation:

his father's age= 4x

his mother's age= 4x- 7

his age= x

x+4x+4x-7=101

x+ 4x+ 4x= 101+ 7

9x= 108

$\frac{9x}{9}$ = $\frac{108}{9}$

x= 12

Tesfa is 12 years old

4 0

3 years ago

Read 2 more answers

Can you use a proportion to solve for a missing side length when given two similar triangles?

VARVARA [1.3K]

Answer:

yes you can.

Step-by-step explanation:

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I tried every way I could think of and got this 6.5 for the bottom A-B

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3 years ago