Which of the following could be the lengths of the sides of a 45°-45°-90° triangle?

Generate the nest three terms of each arithmetic sequence shown below.

o-na [289]

Answer:

A)2,6,10

B)2,-6,-18

C)-1,-3,-5

Step-by-step explanation:

A)a1=-2 and d=4

We know that the arithmetic sequence formula is

$a_{n}=a_{1}+(n-1)d$

Now

$a_{2}=a_{1}+(2-1)d$

$a_{2}=a_{1}+(1)d$

Substituting the given value we get

$a_{2}= -2+(1)4$

$a_{2}= -2+4$

$a_{2}= 2$

------------------------------------------

Similarly

$a_{3}=a_{1}+(3-1)d$

$a_{3}=a_{1}+(2)d$

Substituting the given value we get

$a_{3}= -2+(2)4$

$a_{3}= -2+8$

$a_{3}= 6$

-------------------------------------------------

$a_{4}=a_{1}+(4-1)d$

$a_{4}=a_{1}+(3)d$

Substituting the given value we get

$a_{4}= -2+(3)4$

$a_{4}= -2+16$

$a_{4}= 10$

-------------------------------------------------------------------------------------------

B $a_n=a_{(n-1)}-8$ with $a_1=10$

$a_2=a_{(2-1)}-8$

$a_2=a_{1}-8$

Substituting the given value

$a_2= 10-8$

$a_2=2$

---------------------------------------------------------------------

$a_3=a_{(3-1)}-8$

$a_3=a_{2}-8$

Substituting the value

$a_3=2-8$

$a_3= -6$

---------------------------------------------------------------------

$a_4=a_{(4-1)}-8$

$a_4=a_{3}-8$

Substituting the value

$a_4= -6-8$

$a_4= -14$

-------------------------------------------------------------------------------------------

C) $a_1=3, a_2=1$

Here the difference is -2

the arithmetic sequence formula is

$a_{n}=a_{1}+(n-1)d$

Now

$a_{3}=a_{1}+(3-1)d$

$a_{3}=a_{1}+(2)d$

Substituting the value we get

$a_{3}= 3+(2)-2$

$a_{3}= 3-4$

$a_{3}= -1$

------------------------------------------------------------------------------

$a_{4}=a_{1}+(4-1)d$

$a_{4}=a_{1}+(3)d$

Substituting the value we get

$a_{4}= 3+(3)-2$

$a_{4}= 3-6$

$a_{4}= -3$

----------------------------------------------------------------------------------

$a_{5}=a_{1}+(5-1)d$

$a_{5}=a_{1}+(4)d$

Substituting the value we get

$a_{5}= 3+(4)-2$

$a_{5}= 3-8$

$a_{5}= -5$

4 0

3 years ago

Find the extremum of f(x,y) subject to the given constraint, and state whether it is a maximum or a minimum. f(x,y)=4x2 2y2; 3x

nevsk [136]

For given f(x, y) the extremum: (12, 24) which is the minimum.

For given question,

We have been given a function f(x) = 4x² + 2y² under the constraint 3x+3y= 108

We use the constraint to build the constraint function,

g(x, y) = 3x + 3y

We then take all the partial derivatives which will be needed for the Lagrange multiplier equations:

$f_x=8x$

$f_y=4y$

$g_x=3$

$g_y=3$

Setting up the Lagrange multiplier equations:

$f_x=\lambda g_x$

⇒ 8x = 3λ .....................(1)

$f_y=\lambda g_y$

⇒ 4y = 3λ ......................(2)

constraint: 3x + 3y = 108 .......................(3)

Taking (1) / (2), (assuming λ ≠ 0)

⇒ 8x/4y = 1

⇒ 2x = y

Substitute this value of y in equation (3),

⇒ 3x + 3y = 108

⇒ 3x + 3(2x) = 108

⇒ 3x + 6x = 108

⇒ 9x = 108

⇒ x = 12

⇒ y = 2 × 12

⇒ y = 24

So, the saddle point (critical point) is (12, 24)

Now we find the value of f(12, 24)

⇒ f(12, 24) = 4(12)² + 2(24)²

⇒ f(12, 24) = 576 + 1152

⇒ f(12, 24) = 1728 ................(1)

Consider point (18,18)

At this point the value of function f(x, y) is,

⇒ f(18, 18) = 4(18)² + 2(18)²

⇒ f(18, 18) = 1296 + 648

⇒ f(18, 18) = 1944 ..............(2)

From (1) and (2),

1728 < 1944

This means, given extremum (12, 24) is minimum.

Therefore, for given f(x, y) the extremum: (12, 24) which is the minimum.

Learn more about the extremum here:

brainly.com/question/17227640

#SPJ4

6 0

2 years ago

2. In a school of 320 students, 85 students are in the band, 200 students are on sports teams, and 60 students

Alja [10]

Answer:

60 students are involved in either band or sports.

95 students are not involved in either sports or band.

Step-by-step explanation:

Given:

In a school of 320 students, 85 students are in the band, 200 students are on sports teams, and 60 students participate in both activities.

Now, to find the students are involved in either sports or band. And students who are not involved in either sports or band.

Total number of students = 320.

Number of students in the band = 85.

Number of students in the sports team = 200.

Number of students participate in both activities = 60.

Thus, 60 students are involved in either band or sports.

So, the number of students in the band adding number of students in the sports team we get:

200 + 85 = 285.

Then, to subtract the number of students participate in both activities we get:

285 - 60 = 225.

Thus, the remaining students are = 225.

Now, to get the students who are not involved in either sports or band we subtract the total number of students from the remaining students:

$320-225$

$=95.$

Therefore, 60 students are not involved in either band or sports. 95 students are not involved in either sports or band.

8 0

3 years ago

Scale a rectangle that has length 9 inches and width 17 inches by the scale factor determine the dimensions of the scaled rectan

emmasim [6.3K]

Answer:

The dimensions of the scaled rectangle are

$6.3\ in$ of length by $11.9\ in$ of width

Step-by-step explanation:

we know that

The scale factor is equal to $70\%$

Remember that

$70\%=70/100=0.70$

The scale factor is less than 1

so

the dilation is a reduction

To find the dimensions of the scaled rectangle multiply the dimensions of the original rectangle by the scale factor

$9*0.7=6.3\ in$

$17*0.7=11.9\ in$

4 0

3 years ago

8(2w-6)+4(-1-5w)=-8 Can you solve this and show work?

atroni [7]

I don’t have time to explain it but hopefully someone else will, he answer is -13!

4 0

4 years ago