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3 years ago

Please assist me with these problems

Mathematics

2 answers:

ololo11 [35]3 years ago

7 0

Answer: c) y₁ and y₃ are perpendicular

<u>Step-by-step explanation:</u>

Perpendicular (⊥) means the lines have opposite (change the sign) and reciprocal (flip the fraction) slopes.

y₁ = 2x - 6

↓

m= 2

m⊥= -(1/2)

y₂ = -3x + 4

↓

m= -3

m⊥= +(1/3)

y₃ = -(1/2)x + 4

↓

m= -(1/2)

m⊥= +2

y₁ and y₃ have opposite reciprocal slopes so they are perpendicular to each other.

Vinil7 [7]3 years ago

3 0

Part (a)

<h3>Answer: y1 and y3 are perpendicular</h3>

This is because the two slopes 2 and -1/2 multiply to -1. Perpendicular slopes multiply to -1 assuming neither line is vertical or horizontal.

=====================================================

Part (b)

Graph each line to see where they cross. The three points of intersection are

(0,4)

(2,-2)

(4,2)

The order of the points doesn't matter.

You could also form three systems of equations pairing up the equations, and solving each system. That way you can find the points of intersection. Graphing may be a better and faster route in my opinion. See the diagram below.

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What is the volume of the square pyramid with bad edges 12cm and height 12cm?

spayn [35]

The volume of a pyramid is found by multiplying the length, width and height together then dividing by 3.

length x width x height = 12 x 12 x 12 = 1728

volume = 1728 / 3 = 576 cubic cm

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3 years ago

A rectangular prism with length 12 m , width 8 m & height 15 m , find its surface area .

Irina-Kira [14]

Answer: $792\ m^2$

Step-by-step explanation:

Given

The length of the rectangular prism is $l=12\ m$

width of the rectangular prism is $w=8\ m$

height of the rectangular prism is $h=15\ m$

The surface area of the rectangular prism is $2[wl+lh+hw]$

Put the values

$\Rightarrow 2[8\times 12+15\times 12+15\times 8]\\\Rightarrow 2[96+180+120]=2\times 396\\\Rightarrow 792\ m^2$

The surface area of the rectangular prism is $792\ m^2$

7 0

3 years ago

Apply Gaussian quadrature with n = 4 to approximate integrate sin x^2dx from 1 to 5

maks197457 [2]

First, recall that Gaussian quadrature is based around integrating a function over the interval [-1,1], so transform the function argument accordingly to change the integral over [1,5] to an equivalent one over [-1,1].

$x=2t+3\iff t=\dfrac x2-\dfrac32\implies2\mathrm dt=\mathrm dx$
$x=1\implies t=\dfrac{2-6}4=-1$
$x=5\implies t=\dfrac{10-6}4=1$

So,

$\displaystyle\int_{x=1}^{x=5}\sin x^2\,\mathrm dx=\displaystyle2\int_{t=-1}^{t=1}\sin(2t+3)^2\,\mathrm dt$

Let $f(t)=2\sin(2t+3)^2$ . With $n=4$ , we're looking for coefficients $c_i$ and nodes $x_i$ , with $1\le i\le4$ , such that

$\displaystyle\int_{-1}^1f(t)\,\mathrm dt\approx c_1f(x_1)+\cdots+c_4f(x_4)$

You can either try solving for each with the help of a calculator, or look up the values of the weights and nodes (they're extensively tabulated, and I'll include a link to one such reference).

Using the quadrature, we then have

$\displaystyle\int_{-1}^1f(t)\,\mathrm dt\approx0.3749f(-0.8611)+0.6521f(-0.3400)+0.6521f(0.3400)+0.3749f-0.8611)$
$\displaystyle\int_{-1}^1f(t)\,\mathrm dt\approx0.5790$

4 0

3 years ago

How do you simplify 3(y-8)+3(2y)

SIZIF [17.4K]

Answer:

9y-24

Step-by-step explanation:

3(y-8)+3(2y)

3y-24+6y

9y-24

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3 years ago

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Nikitich [7]

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3 years ago

Please assist me with these problems​

Please assist me with these problems