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3 years ago

Write the expanded form of 67.854

Mathematics

1 answer:

GREYUIT [131]3 years ago

6 0

Six tens, seven ones, and eight tenths, five hundredths,and four thousandths

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Find the average value fave of the function f on the given interval. f() = 5 sec2(/6), 0, 3 2

Inessa05 [86]

Answer:

$f_{ave}$ = ${\frac{10 }{3\pi }$

Step-by-step explanation:

To find - Find the average value fave of the function f on the given interval. f(x) = 5 sec²(x/6), [0, 3 $\pi$ /2]

Proof -

We know that,

Average value of f in the interval [a, b] is -

$f_{ave}$ = $\frac{1}{b - a}\int\limits^b_a {f(x)} \, dx$

Now,

Here a = 0, b = $\frac{3\pi }{2}$ , f(x) = $5sec^{2}(\frac{x}{6} )$

Now,

$f_{ave}$ = $\frac{1}{\frac{3\pi }{2} - 0}\int\limits^{\frac{3\pi }{2} }_0 {5sec^2 ({\frac{x}{6} }) } \, dx$

= ${\frac{2 }{3\pi }}\int\limits^{\frac{3\pi }{2} }_0 {5sec^2 ({\frac{x}{6} }) } \, dx$

= ${\frac{10 }{3\pi }}\int\limits^{\frac{3\pi }{2} }_0 {sec^2 ({\frac{x}{6} }) } \, dx$

= ${\frac{10 }{3\pi }}[\ {tan({\frac{x}{6} }) }|^{\frac{3\pi }{2} }_0 \, ]$

= ${\frac{10 }{3\pi }}[\ {tan({\frac{x}{6} }) - tan({0) } \, ]$

= ${\frac{10 }{3\pi }}[ {1 - 0 } ]$

= ${\frac{10 }{3\pi }$

⇒ $f_{ave}$ = ${\frac{10 }{3\pi }$

3 0

3 years ago

The ratio of the number of girls to the number of all students in the class is 4 to 9. Can there be 20 students in that class?

Masteriza [31]

Answer:

Step-by-step explanation:

20 ÷ 9 = 2.222222222
9 does not go evenly into 20, and there can't be a fraction of a student, so the answer is no.

I hope this helps!

3 0

3 years ago

What is the solution to the following system? 4x+3y-z=-6 6x-y+3z=12 8x+2y+4z=6

andrew-mc [135]

Answer:

Option B is correct.

Step-by-step explanation:

4x+3y-z= -6 eq(1)

6x-y+3z= 12 eq(2)

8x+2y+4z=6 eq(3)

We need to solve these equations and find the value of x, y and z.

Multiply equation 2 with 3 and then add equation 1 and 2

18x -3y +9z = 36

4x +3y -z = -6

_____________

22x + 8z = 30 eq(3)

Multiply equation 2 with 2 and add with equation 3

12x -2y + 6z = 24

8x +2y +4z = 6

____________

20x + 10 z = 30 eq(4)

Multiply equation 3 with 10 and equation 4 with 8 and then subtract

220x + 80z = 300

160x + 80z = 240

- - -

_________________

60x = 60

x= 60/60

x= 1

Putting value of x in equation 3

22x + 8z = 30

22(1) + 8z = 30

8z = 30 - 22

8z = 8

z = 8/8

z=1

Putting value of x and z in equation 1

4(1)+3y-(1)=-6

4 + 3y -1 = -6

3 + 3y = -6

3y = -6 -3

3y = -9

y = -3

so, Option B x=1, y=3 and z=1 is correct

8 0

3 years ago

Read 2 more answers

a chord subtend an angle of 72⁰ at the center of a circle with radius 24.5m. calculate the perimeter of the minor segment

andre [41]

The perimeter of the minor segment is 77. 4m

<h3>How to determine the perimeter</h3>

The formula for determining the perimeter of the minor segment is given as;

Perimeter = θ/360 × 2πr + 2r sin θ/2

where;

radius = 24. 5m

θ = 72

Substitute into the formula;

Perimeter = (72/360 × 2 × 3. 142 × 24. 5) +( 2 × 24. 5 × sin 72)

Perimeter = 30. 79 + 46. 60

Perimeter = 77. 4 m

Thus, the perimeter of the minor segment is 77. 4m

Learn more about segment of a circle here:

brainly.com/question/18603257

#SPJ1

5 0

2 years ago

The number of miles that a commuter travels a car per day for one seven day work week is as follows: 19, 28, 17, 39, 22, 44, 56.

olganol [36]

Car : (19 + 28 + 17 + 39 + 22 + 44 + 56) / 7 = 225/7 = 32.14
bus : (32 + 26 + 25 + 40 + 39 + 49 + 22)/7 = 233/7 = 33.29

bus has a higher commuter average

3 0

3 years ago