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3 years ago

HELP ME PLSSSSSS THIS IS HARD

Mathematics

2 answers:

Kryger [21]3 years ago

8 0

It’s answer c and d it’s correct

Novosadov [1.4K]3 years ago

6 0

Step-by-step explanation:

Given:

Function 'f' with two variables 'x' and 'y'.

To find:

Function rule if the parent function 'f' is rotated by 270° clockwise.

Solution:

A function given with two variables 'x' and 'y',

f(x,y) → (x, y)

If this function is rotated by 270° clockwise, the function rule will become,

f(x, y) → (-y, x)

Therefore, Option A will be the correct option.

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riadik2000 [5.3K]

Let

$S_n = \displaystyle \sum_{k=0}^n r^k = 1 + r + r^2 + \cdots + r^n$

where we assume |r| < 1. Multiplying on both sides by r gives

$r S_n = \displaystyle \sum_{k=0}^n r^{k+1} = r + r^2 + r^3 + \cdots + r^{n+1}$

and subtracting this from $S_n$ gives

$(1 - r) S_n = 1 - r^{n+1} \implies S_n = \dfrac{1 - r^{n+1}}{1 - r}$

As n → ∞, the exponential term will converge to 0, and the partial sums $S_n$ will converge to

$\displaystyle \lim_{n\to\infty} S_n = \dfrac1{1-r}$

Now, we're given

$a + ar + ar^2 + \cdots = 15 \implies 1 + r + r^2 + \cdots = \dfrac{15}a$

$a^2 + a^2r^2 + a^2r^4 + \cdots = 150 \implies 1 + r^2 + r^4 + \cdots = \dfrac{150}{a^2}$

We must have |r| < 1 since both sums converge, so

$\dfrac{15}a = \dfrac1{1-r}$

$\dfrac{150}{a^2} = \dfrac1{1-r^2}$

Solving for r by substitution, we have

$\dfrac{15}a = \dfrac1{1-r} \implies a = 15(1-r)$

$\dfrac{150}{225(1-r)^2} = \dfrac1{1-r^2}$

Recalling the difference of squares identity, we have

$\dfrac2{3(1-r)^2} = \dfrac1{(1-r)(1+r)}$

We've already confirmed r ≠ 1, so we can simplify this to

$\dfrac2{3(1-r)} = \dfrac1{1+r} \implies \dfrac{1-r}{1+r} = \dfrac23 \implies r = \dfrac15$

It follows that

$\dfrac a{1-r} = \dfrac a{1-\frac15} = 15 \implies a = 12$

and so the sum we want is

$ar^3 + ar^4 + ar^6 + \cdots = 15 - a - ar - ar^2 = \boxed{\dfrac3{25}}$

which doesn't appear to be either of the given answer choices. Are you sure there isn't a typo somewhere?

7 0

2 years ago

What is 90 by 25% decreased

viva [34]

Answer:

- 22.5

Step-by-step explanation:

Answer:

90 decreased by 25% = 67.5

Absolute change (actual difference):

67.5 - 90 = - 22.5

8 0

2 years ago

Read 2 more answers

Find the surface area of the

katrin2010 [14]

Answer:

the surface of hexagonal prism is 12 cm

8 0

3 years ago

19 Kayla's car can hold 15 gallons of gas. She gets 20.5 miles per gallon The tank is full. About how far can Kayla drive if she

Nata [24]

Answer:

Step-by-step explanation:

6 0

3 years ago

Which of the following is the equation of the line that is parallel to y=35x+8 y = 3 5 x + 8 and goes through point (-10,4)?

xeze [42]

Slope-intercept form of a line is y=mx+b.

Where m= slope and b= y-intercept.

First step is to compare the given equation y=35x+8 with the above equation to get the value of m.

After comparing the two equations we will get m=35.

Slope of paralle lines always equal which means slope of a line which is parallel to the above line will also be 35.

Now the line is passing through (-10,4).

Point slope form of a line is :

$y-y_{1} =m(x-x_{1} )$

Next step is to plug in m=35, x1=-10 and y1=4 in the above equation. So,

y-4=35(x-(-10)

y-4=35(x+10)

y-4=35x+350

y=35x+350+4

y=35x+354.

So, the equation of the line is y=35x+354.

4 0

3 years ago