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1 year ago

At what points does the helix r(t) = sin t, cos t, t intersect the sphere x2 + y2 + z2 = 65? (round your answers to three decima

l places. if an answer does not exist, enter dne.)

Mathematics

1 answer:

Firdavs [7]1 year ago

7 0

$\mathbf r(t)=\langle x(t),y(t),z(t)\rangle=\langle\sin t,\cos t,t\rangle$

$x^2+y^2+z^2=\sin^2t+\cos^2t+t^2=65$
$\implies t^2=64$
$\implies t=\pm8$

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ella [17]

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Hence, comparing all the three costs per wing, we can see that Buffalo Mild Wings is serving chicken wings at lowest price of $0.833 per wing.

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1 year ago

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If r=[x,y,z] and r0=[x0,y0,z0], describe the set of all points (x,y,z) such that Ir-r0I =1.

sdas [7]

Answer:

The points (x,y,z) that respond to Ir-r0I =1, are all that describes the form $(x-x_0)^2+(y-y_0)^2+(z-z_0)^2=1$ with:

-1+x₀<x<1+x₀

-1+y₀<y<1+y₀

-1+z₀<z<1+z₀

Step-by-step explanation:

All points required in this problem came from applying the definition of modulus of a vector:

Ir-r0I =1.

$|(x,y,z)-(x_{0},y_{0},z_{0})|=|(x-x_{0},y-y_{0},z-z_{0})|=\sqrt{(x-x_{0})^2+(y-y_{0})^2+(z-z_{0})^2}=1\\(x-x_{0})^2+(y-y_{0})^2+(z-z_{0})^2=1^2=1$

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2 years ago

The polynomial function f (x) = 5 x Superscript 5 Baseline + sixteen-fifths x minus 3 is graphed below. On a coordinate plane, p

olya-2409 [2.1K]

Answer:

3/5

Step-by-step explanation:

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1 year ago

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A car with 15 gallons of gasoline drives 420 miles until the tank is empty. Write a linear equation that describes the amount of

DedPeter [7]

Answer:

g = 15 - m/28

Step-by-step explanation:

let g = gasoline

let m = miles

g = 15 - m/28

since you can drive 420 miles with 15 gallons of gas, you can drive 28 miles with one gallon (= 420/15 = 28)

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you drive 100 miles, then you will have:

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2 years ago

The fish population in a pond with carrying capacity 1200 is modeled by the following logistic equation where N(t) denotes the n

MArishka [77]

9514 1404 393

Answer:

(dN)/(dt) = (0.4)/(1200)N(1200-N) -50

142 fish

Step-by-step explanation:

A) The differential equation is modified by adding a -50 fish per year constant term:

(dN)/(dt) = (0.4)/(1200)N(1200-N) -50

B) The steady-state value of the fish population will be when N reaches the value that makes dN/dt = 0.

(0.4/1200)(N)(1200-N) -50 = 0

N(N-1200) = -(50)(1200)/0.4) . . . . rewrite so N^2 has a positive coefficient

N^2 -1200N + 600^2 = -150,000 +600^2 . . . . complete the square

(N -600)^2 = 210,000 . . . . . simplify

N = 600 + √210,000 ≈ 1058

This steady-state number of fish is ...

1200 - 1058 = 142 . . . . below the original carrying capacity

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