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3 years ago

Write a vector equation of the line that passes through P(4, 7) and is parallel to a = (3, 8).

Mathematics

1 answer:

love history [14]3 years ago

4 0

Answer:

Step-by-step explanation:

(x,y) = P + (a)t

(x,y) = (4,7) + t(3,8)

(x,y) - (4,7) = t(3,8)

(x-4, y-7) = t(3,8)

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Find two numbers the exact answer is between 6x7,381

sineoko [7]

I think the answer is 210.442

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3 years ago

Solve the equations in two different ways:6p=0.6(5p+15)

Damm [24]

Answer:

Step-by-step explanation:

1st way:

Solve directly

6p=0.6(5p+15)

Open bracket

6p = 3p + 9

Collecting like terms

6p - 3p = 9

3p = 9

Dividing by 3

p = 9/3

p = 3

2nd way:

6p=0.6(5p+15)

Convert the decimal to fraction

6p= 6/10(5p+15)

6p= 3/5(5p+15)

6p= 3/5(5p) +3/5(15)

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6p - 3p = 9

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Dividing by 3

p = 9/3

p = 3

6 0

4 years ago

Can y’all help me please? :))

german

Answer:

3.75

Step-by-step explanation:

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6 0

3 years ago

How many sides do 1 triangle, 4 octagons, 5 dodecagons, and 4 quadrilaterals have in all?

EleoNora [17]

Answer:

3+32+60+16= 111 sides.

Step-by-step explanation:

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6 0

3 years ago

Find the length of the curve. R(t) = cos(8t) i + sin(8t) j + 8 ln cos t k, 0 ≤ t ≤ π/4

arsen [322]

we are given

$R(t)=cos(8t)i+sin(8t)j+8ln(cos(t))k$

now, we can find x , y and z components

$x=cos(8t),y=sin(8t),z=8ln(cos(t))$

Arc length calculation:

we can use formula

$L=\int\limits^a_b {\sqrt{(x')^2+(y')^2+(z')^2} } \, dt$

$x'=-8sin(8t),y=8cos(8t),z=-8tan(t)$

now, we can plug these values

$L=\int _0^{\frac{\pi }{4}}\sqrt{(-8sin(8t))^2+(8cos(8t))^2+(-8tan(t))^2} dt$

now, we can simplify it

$L=\int _0^{\frac{\pi }{4}}\sqrt{64+64tan^2(t)} dt$

$L=\int _0^{\frac{\pi }{4}}8\sqrt{1+tan^2(t)} dt$

$L=\int _0^{\frac{\pi }{4}}8\sqrt{sec^2(t)} dt$

$L=\int _0^{\frac{\pi }{4}}8sec(t) dt$

now, we can solve integral

$\int \:8\sec \left(t\right)dt$

$=8\ln \left|\tan \left(t\right)+\sec \left(t\right)\right|$

now, we can plug bounds

and we get

$=8\ln \left(\sqrt{2}+1\right)-0$

so,

$L=8\ln \left(1+\sqrt{2}\right)$ ..............Answer

5 0

3 years ago