5 > Chapter 2: Modeling with Quadratic Functions > Secti

Mathematics

2 answers:

Y_Kistochka [10]3 years ago

7 0

Answer:

(1,-2) is the correct answer

Nitella [24]3 years ago

5 0

Answer:

the awnser is 2,0

Step-by-step explanation:

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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°, <em>the line and plane must intersect</em>.

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

Write the decomposition that helps you, and then round to the given place value. Draw number lines to explain your thinking. Cir

egoroff_w [7]

Further explanation

There are general rules used in rounding numbers

1. Determine the rounded digit

2. Pay attention to the digits afterward (right). If the digit shows the numbers 0, 1, 2, 3 or 4, then the digit to be rounded is fixed, and the digit on the right is 0 all

3. If the digit on the right shows the numbers 5, 6, 7, 8 or 9, then the digit to be rounded is added to one, and the digit on the right side is made all 0

In rounding the nearest hundreds number, then we see the digit in the number tens (right of the digit hundreds), if it is worth 0, 1, 2, 3 or 4, then it remains, but if it shows numbers 5, 6, 7, 8 or 9, then the digit to be rounded is added one, and the right-hand side is 0

Calculated from the decimal point, the place on the right represents tents, hundredths, thousandths, etc.

a. 32.697

Decomposition

ten : 3

one : 2

tenth : 6

hundredth : 9

thousandths : 7

For the tenth number is 6, the value on the right is 9 then rounded become 32.7

For the hundredth number is 9, the value on the right is 7 then rounded become 32.70

for the one number is 2 , the value on the right is 6 then rounded become 33

b. 141.999