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4 years ago

Find the rectangular coordinates of the point that has polar coordinates , 4, −3π/4

1 answer:

6 0

Hello :
x= r cosθ
y= r sinθ
r = 4 and θ = −3π/4
cos( −3π/4 ) = cos( 3π/4 ) = cos ( π - π/4) = - cos (π/4)= - √2/2
sin( −3π/4 ) = - sin( 3π/4 ) = - sin ( π - π/4) = -sin (π/4)= - √2/2
x = - 2 √2
y = - 2 √2

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Four brothers have ages which are consecutive even integers. If the product of the ages of the two middle brothers is 528, how o

exis [7]

Answer:

The oldest brother is of age $26$ years.

Step-by-step explanation:

As the age of four brothers are consecutive even integers.

We assume that the ages are $x,(x+2),(x+4),(x+6)$ as their respective ages.

And the age of the youngest brother $x$ yrs.

Age of the oldest brother $(x+6)$ yrs.

According to the question

Product of two middle brother that is $(x+2)(x+4) =528$

So we will arrange this in our equation and solve the quadratic.

$(x+2)(x+4) =528$

$x^{2}+4(x)+2(x)+8 =528$

$x^{2}+4(x)+2(x)+8-528=0$

$x^{2}+6(x)-520=0$

Solving the quadratic by using middle term splitting or directly with quadratic formula we can find the value of 'x' .

Here it is solved with quadratic formula:

Comparing with standard equation $ax^{2}+b(x)+c=0$ ,here $a=1,b=6\ and\ c=-520$ .

$x= \frac{-b \pm \sqrt{b^2-4ac} }{2a} = \frac{-6 \pm \sqrt{6^2-4\times \ (-520)} }{2\times 1}$

$x=20,-26$

We will work with the positive value of (x) so the the age of the youngest brother $=(x)=20$ yrs.

And the age of the the oldest brother $=(x+6)=(20+6)=26$ years.

The age difference is of $(26-20)=6$ years.

4 0

4 years ago

At the coffee shop, two coffees and one latte cost $10.50. Three coffees and two lattes cost $17.00. What is the cost of one cof

EastWind [94]

To solve this problem, we can set two equations.

Let x be the cost of coffee and y be the cost of latte.

Two coffees and one latte: 2x + y = 10.50

y=10.50 - 2x ...(1)

Three coffees and two lattes: 3x + 2y = 17.00...(2)

Put (1) into (2), we have:

3x + 2(10.50-2x) = 17.00

3x + 2(10.50) - 2(2x) = 17.00

3x + 21 - 4x = 17

Put the unknown to one side:

3x -4x = 17 - 21

-x = -4

When there are negative numbers on both sides, we can take the negative signs away:

x= 4

Therefore, cost of one coffee is A. $4.00.

Hope ot helps!

3 0

4 years ago

Please help. I’ll mark you as brainliest if correct!

EastWind [94]

13 bikes
You would do 65 divided by 5 because there are 5 times as many new bikes compared to used ones

3 0

3 years ago

Three equivalent ratios are shown on the graph

kvasek [131]

To plot more the points, we move up one and right two.

<h3>How to plot more the points?</h3>

The ratios are given as:

(1, 0.5), (2, 1), and (5, 2.5)

Calculate the slope (m) using:

$m = \frac{y_2 -y_1}{x_2 -x_1}$

So, we have:

$m = \frac{1 - 0.5}{2 - 1}$

Evaluate

$m = \frac{0.5}{1}$

This gives

$m = \frac{1}{2}$

The above means

Vertical : Horizontal = 1 : 2

This means a vertical movement of 1, followed by an horizontal movement of 1

Hence, to plot more the points, we move up one and right two.

Read more about equivalent ratios at:

brainly.com/question/13513438

#SPJ1

Complete question

Three equivalent ratios are shown on the graph. On a coordinate plane, points (1, 0.5), (2, 1), and (5, 2.5) are plotted. Starting on one of the plotted points, how can you plot more equivalent ratio points?

5 0

2 years ago

What does the n stand for in n×$3.25=$325.00?

AlladinOne [14]

N would be the variable that we are solving for.

Lets solve:-

n * 3.25 = 325
3.25/3.25 = 325/3.25
n = 100

Answer: n = 100

6 0

4 years ago