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3 years ago

6x - 5y = 15, x=y+3 what does x and y equal

Mathematics

1 answer:

Natasha_Volkova [10]3 years ago

3 0

Answer:

Step-by-step explanation:

6x - 5y = 15....... (1)

x=y+3..........(2)

Putting (2) in (1)

6(y + 3) - 5y = 15

6y + 18 - 5y = 15

6y - 5y = 15 - 18

y = -3

And x = y + 3

x = -3 + 3

x = 0

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Prove that 1+cosθ+sinθ/1+cosθ-sinθ = 1+sinθ/cosθ

marusya05 [52]

Step-by-step explanation:

(1 + cos θ + sin θ) / (1 + cos θ − sin θ)

Multiply by the reciprocal:

(1 + cos θ + sin θ) / (1 + cos θ − sin θ) × (1 + cos θ + sin θ) / (1 + cos θ + sin θ)

(1 + cos θ + sin θ)² / [ (1 + cos θ − sin θ) (1 + cos θ + sin θ) ]

(1 + cos θ + sin θ)² / [ (1 + cos θ)² − sin² θ) ]

Distribute and simplify:

(1 + cos θ + sin θ)² / (1 + 2 cos θ + cos² θ − sin² θ)

[ 1 + 2 (cos θ + sin θ) + (cos θ + sin θ)² ] / (1 + 2 cos θ + cos² θ − sin² θ)

(1 + 2 cos θ + 2 sin θ + cos² θ + 2 sin θ cos θ + sin² θ) / (1 + 2 cos θ + cos² θ − sin² θ)

Use Pythagorean identity:

(2 + 2 cos θ + 2 sin θ + 2 sin θ cos θ) / (sin² θ + cos² θ + 2 cos θ + cos² θ − sin² θ)

(2 + 2 cos θ + 2 sin θ + 2 sin θ cos θ) / (2 cos² θ + 2 cos θ)

(1 + cos θ + sin θ + sin θ cos θ) / (cos² θ + cos θ)

Factor:

(1 + cos θ + sin θ (1 + cos θ)) / (cos θ (1 + cos θ))

(1 + cos θ)(1 + sin θ) / (cos θ (1 + cos θ))

(1 + sin θ) / cos θ

3 0

3 years ago

A manufacturer is designing a flashlight. For the flashlight to emit a focused beam, the bulb needs to be on the central axis of

aalyn [17]

From the problem, the vertex = (0, 0) and the focus = (0, 3)
From the attached graphic, the equation can be expressed as:
(x -h)^2 = 4p (y -k)
where (h, k) are the (x, y) values of the vertex (0, 0)
The "p" value is the difference between the "y" value of the focus and the "y" value of the vertex.
p = 3 -0
p = 3
So, we form the equation
(x -0)^2 = 4 * 3 (y -0)
x^2 = 12y
To put this in proper quadratic equation form, we divide both sides by 12
y = x^2 / 12

Source:
http://www.1728.org/quadr4.htm

5 0

3 years ago

Which sample has a greater variability, or spread?

avanturin [10]

Answer:

The orange sample

Step-by-step explanation:

The higher the interquartile range the bigger the variance as it the difference between the 0.25 and 0.75 quantiles which basically means if the difference between the 25 percent and 75 percent is higher then there is more variety as they are further away

Would be amazing if you marked brainliest and feel free to comment any follow up questions :)

8 0

3 years ago

Read 2 more answers

Attached as photo. Please help

Effectus [21]

By Euler's method the numerical approximate solution of the definite integral is 4.189 648.

<h3>How to estimate a definite integral by numerical methods</h3>

In this problem we must make use of Euler's method to estimate the upper bound of a definite integral. Euler's method is a multi-step method, related to Runge-Kutta methods, used to estimate integral values numerically. By integral theorems of calculus we know that definite integrals are defined as follows:

∫ f(x) dx = F(b) - F(a) (1)

The steps of Euler's method are summarized below:

Define the function seen in the statement by the label f(x₀, y₀).
Determine the different variables by the following formulas:

xₙ₊₁ = xₙ + (n + 1) · Δx (2)
yₙ₊₁ = yₙ + Δx · f(xₙ, yₙ) (3)
Find the integral.

The table for x, f(xₙ, yₙ) and y is shown in the image attached below. By direct subtraction we find that the numerical approximation of the definite integral is:

y(4) ≈ 4.189 648 - 0

y(4) ≈ 4.189 648

By Euler's method the numerical approximate solution of the definite integral is 4.189 648.

To learn more on Euler's method: brainly.com/question/16807646

#SPJ1

7 0

2 years ago

Who can help me with this entire page?

trasher [3.6K]

Answer:

I'm not entirely sure what the question is but every thing under 12.5 is closer to 12, everything 12.5 and upwards like 12.87 would be closer to 13

8 0

2 years ago