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3 years ago

Find the slope of each line 5y = -2x + 15

Mathematics

1 answer:

Kipish [7]3 years ago

3 0

The slope of the line is -2/5x

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Evaluate the iterated integral 2 0 2 x sin(y2) dy dx. SOLUTION If we try to evaluate the integral as it stands, we are faced wit

nignag [31]

Answer:

Step-by-step explanation:

Given that:

$\int^2_0 \int^2_x \ sin (y^2) \ dy dx \\ \\ \text{Using backward equation; we have:} \\ \\ \int^2_0\int^2_0 sin(y^2) \ dy \ dx = \int \int_o \ sin(y^2) \ dA \\ \\ where; \\ \\ D= \Big\{ (x,y) | }0 \le x \le 2, x \le y \le 2 \Big\}$

$\text{Sketching this region; the alternative description of D is:} \\ D= \Big\{ (x,y) | }0 \le y \le 2, 0 \le x \le y \Big\}$

$\text{Now, above equation gives room for double integral in reverse order;}$

$\int^2_0 \int^2_0 \ sin (y^2) dy dx = \int \int _o \ sin (y^2) \ dA \\ \\ = \int^2_o \int^y_o \ sin (y^2) \ dx \ dy \\ \\ = \int^2_o \Big [x sin (y^2) \Big] ^{x=y}_{x=o} \ dy \\ \\= \int^2_0 ( y -0) \ sin (y^2) \ dy \\ \\ = \int^2_0 y \ sin (y^2) \ dy \\ \\ y^2 = U \\ \\ 2y \ dy = du \\ \\ = \dfrac{1}{2} \int ^2 _ 0 \ sin (U) \ du \\ \\ = - \dfrac{1}{2} \Big [cos \ U \Big]^2_o \\ \\ = - \dfrac{1}{2} \Big [cos \ (y^2) \Big]^2_o \\ \\ = - \dfrac{1}{2} cos (4) + \dfrac{1}{2} cos (0) \\ \\$

$= - \dfrac{1}{2} cos (4) + \dfrac{1}{2} (1) \\ \\ = \dfrac{1}{2}\Big [1- cos (4) \Big] \\ \\ = \mathbf{0.82682}$

5 0

3 years ago

the line with a slope of 1/3 and a y- intercept of - 15 intersects the line passing through which of these pairs of points?

stich3 [128]

Answer:

Options (C), (D) and (E)

Step-by-step explanation:

Slope of the given line = $\frac{1}{3}$

Any line having same slope will be parallel to the given line otherwise the lines will intersect.

Therefore, we will find the slope of the lines passing through two points given in the options.

Option A

Slope of the line passing through (12, -13) and (15, -12)

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

= $\frac{-13+12}{12-15}$

= $\frac{1}{3}$

Therefore, both the lines are parallel having no point of intersection.

Option B

Slope = $\frac{-9+7}{18-24}$

= $\frac{1}{3}$

Both the lines are parallel having no point of intersection.

Option C

Slope = $\frac{-20+21}{15-18}$

= $-\frac{1}{3}$

Therefore, both the lines will intersect.

Option D

Slope = $\frac{-15+14}{30-36}$

= $\frac{1}{6}$

Both the lines will intersect each other.

Option E

Slope = $\frac{-11+10}{24-30}$

= $\frac{1}{6}$

Both the lines will intersect each other at a point.

Options (C), (D) and (E) are the correct options.

6 0

3 years ago

Bill is a used car salesman. He sells a used automobile for $15,799. If he receives a 4%

Scrat [10]

Answer: 4 cents or .4

Step-by-step explanation:

Whenever in a problem like this where there is a fee, tax, and or bonus you move the decimal in front of the number and round to the nearest penny but if there is only one number in front of the decimal you don’t gotta do anything with it unless its .5 or higher but .4 and below you keep the same.

7 0

3 years ago

What is the binomial expansion of (x 2y)7? 2x7 14x6y 42x5y2 70x4y3 70x3y4 42x2y5 14xy6 2y7 x7 14x6y 42x5y2 70x4y3 70x3y4 42x2y5

AysviL [449]

You can take x = a, 2y = b and then can apply the binomial theorem.

The expansion of given expression is given by:

Option D: $x^7 + 14x^6y + 84x^5y^2 + 280x^4y^3 + 560x^3y^4 + 672x^2y^5 + 448xy^6 + 128y^7$ is

<h3>What is binomial theorem?</h3>

It provides algebraic expansion of exponentiated(integer) binomial.

According to binomial theorem,

$(a+b)^n = \sum_{i=0}^n ^nC_i a^ib^{n-i}$

<h3>How to use binomial theorem for given expression?</h3>

Taking a = x, and b =2y, we have n = 7, thus:

$(x+2y)^7 = \: ^7C_0x^0(2y)^7 + \: ^7C_1x^1(2y)^6 + \: ^7C_2x^2(2y)^5 + \: ^7C_3x^3(2y)^4 + \:^7C_4x^4(2y)^3 + \:^7C_5x^5(2y)^2 + \:^7C_6x^6y^1 + \: ^7C_0x^7y^0\\\\
(x+2y)^7 = 128y^7 + 448xy^6 + 672x^2y^5 + 560x^3y^4 + 280x^4y^3 + 84x^5y^2 + 14x^6y + x^7\\\\
(x+2y)^7 = x^7 + 14x^6y + 84x^5y^2 + 280x^4y^3 + 560x^3y^4 + 672x^2y^5 + 448xy^6 + 128y^7$

Thus, Option D: $x^7 + 14x^6y + 84x^5y^2 + 280x^4y^3 + 560x^3y^4 + 672x^2y^5 + 448xy^6 + 128y^7$ is correct.

Learn more about binomial theorem here:

brainly.com/question/86555

6 0

3 years ago

Lesson 4 Solving One Variable Equation

aleksandr82 [10.1K]

Answer:

b = -³¹⁄₃

Step-by-step explanation:

We can solve this Algebra equation by separating the variable and constants.

3b + 15 = -26 - 20

3b + 15 = -46

3b = -31

b = -³¹⁄₃

3 0

3 years ago