A _______ is a variable, an integer or a product of variables and integers.

Show that the plane and line with the given equations intersect, and then find the acute angle of intersection between them. (Gi

Reptile [31]

Answer:

angle of intersection: 5.2°

Step-by-step explanation:

The direction vector normal to the plane is ...

n = (1, 1, 3)

The direction vector of the line is ...

m = (1, -3, 1)

Then the angle θ between them can be found from the dot product:

n•m = |n|·|m|·cos(θ)

(1·1 +1(-3) +3·1) = 1 -3 +3 = 1 = √(1²+1²+3²)·√(1²+(-3)²+1²)·cos(θ)

1 = 11·cos(θ)

θ = arccos(1/11) ≈ 84.8°

This is the angle between the line and the normal to the plane, so the angle between the line and the plane will be the complement of this. Since this angle is not 90°, the line and plane must intersect.

acute angle = 90° -84.8° = 5.2°

_____

The attached graph shows the line and plane meet at a shallow angle, consistent with the above answer.

8 0

3 years ago

Paul's pizzeria sells 45 cheese pizzas and 20 pepperoni pizza every week. what is the ratio of cheese pizzas to pepperoni pizzas

Mkey [24]

9:4 would be the correct answer

6 0

3 years ago

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Write the equation of the line that passes through the points (-2,9) and (2,6). Put your answer in fully simplified point-slope

maw [93]

Answer:

4y = -3x +30

Firstly you have to look for the gradient or slope using the points given in the question.

Then substitute the gradient (m) into y= mx+ c

8 0

2 years ago

Define the term isomer

Tema [17]

Physics: each of two or more atomic nuclei that have the same atomic number and the same mass number but different energy states.

chemistry: each of two or more compounds with the same formula but a different arrangement of atoms in the molecule and different properties.

8 0

3 years ago

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What is the product? (5r + 2)(3r − 4)

bazaltina [42]

this is the answer 15r^2 − 14r − 8

Murda on the beat so it's not nice

For this life, I cannot change

Hidden Hills, deep off in the main

M&M's, sweet like candy cane

Drop the top, pop it, let it bang (pop it, pop it)

For this life, I cannot change

Hidden Hills, deep off in the main

M&M's, sweet like candy cane

Drop the top, pop it, let it bang (pop it, pop it)

Drop the top, play hide and seek

Jump inside, jump straight to the lake

Take a sip, feel just how I breathe

On freeway, but no, ain't nothin' free (straight up)

Bend laws, bend lanes

Been bustin' bills, but still ain't nothin' change

You in the mob soon as you rock the chain

She caught the waves just thumbin' through my braids (alright)

Heatin' up, baby, I'm just heatin' up (it's lit)

Fiji lover, now they need it is a must

Feelin' stuck, you know how to keep me up

Icy love, icy like a hockey puck

For this life, I cannot change

Hidden Hills, deep off in the main

M&M's, sweet like candy cane

Drop the top, pop it, let it bang (Pop it, pop it)

For this life, I cannot change

Hidden Hills, deep off in the main

M&M's, sweet like candy cane

Drop the top, pop it, let it bang

All the ones, all the chains piled on the mantle

All the dogs, all the dogs low creep right behind me in the Phantom

Never go, never go dip on the set, stayed Santana

Yeah, run it back, turn the lights on when I hit up Green Lantern

Yeah, fly the broads, fly the dogs down to Atlanta

Yeah, in the cut in Medusa, lay low I might be

Yeah, roll up, help me calm down when I move in high speed

Yeah, If I send one, need the text back 'cause you know what I need

Oh, please (oh please)

Oh me (oh me)

Oh my (oh my)

We been movin', we been movin' for some time (Alright!)

Flexin', flexin' try to exercise

(Exercise, exercise, exercise, exercise)

For this life, I cannot change

Hidden Hills, deep off in the main

M&M's, sweet like candy cane

Drop the top, pop it, let it bang (Pop it, pop it)

For this life, I cannot change

Hidden Hills, deep off in the main

M&M's, sweet like candy cane

Drop the top, pop it, let it bang

8 0

3 years ago

Read 2 more answers