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3 years ago

If 4 tsp of salt are needed for 5 dozen cupcakes, how many tsp of salt are needed for 11 dozen cupcakes?

Mathematics

2 answers:

kenny6666 [7]3 years ago

5 0

Answer:

8.8 tsp

Step-by-step explanation:

4/5=x/11

cross multiply

44=5x

44/5=x

x=8.8

Lostsunrise [7]3 years ago

4 0

Answer:

8.8 tsp

Step-by-step explanation:

Write a ratio to solve

4 tsp x tsp

----------- = ---------------

5 dozen 11 dozen

Using cross products

4 *11 = 5x

44 = 5x

Divide by 5

44/5 =x

8.8 tsp

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Is a good economist always objective or

Mashutka [201]

anwer

yes good economist is always objective.

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3 years ago

(a) Find the unit tangent and unit normal vectors T(t) and N(t).

andrey2020 [161]

Answer:

a. i. (i + tj + 2tk)/√(1 + 5t²)

ii. (-5ti + j + 2k)/√[25t² + 5]

b. √5/[√(1 + 5t²)]³

Step-by-step explanation:

a. The unit tangent

The unit tangent T(t) = r'(t)/|r'(t)| where |r'(t)| = magnitude of r'(t)

r(t) = (t, t²/2, t²)

r'(t) = dr(t)/dt = d(t, t²/2, t²)/dt = (1, t, 2t)

|r'(t)| = √[1² + t² + (2t)²] = √[1² + t² + 4t²] = √(1 + 5t²)

So, T(t) = r'(t)/|r'(t)| = (1, t, 2t)/√(1 + 5t²) = (i + tj + 2tk)/√(1 + 5t²)

ii. The unit normal

The unit normal N(t) = T'(t)/|T'(t)|

T'(t) = dT(t)/dt = d[ (i + tj + 2tk)/√(1 + 5t²)]/dt

= -5ti/√(1 + 5t²)⁻³ + [-5t²j/√(1 + 5t²)⁻³] + [-10tk/√(1 + 5t²)⁻³]

= -5ti/√(1 + 5t²)⁻³ + [-5t²j/√(1 + 5t²)⁻³] + j/√(1 + 5t²)+ [-10t²k/√(1 + 5t²)⁻³] + 2k/√(1 + 5t²)

= -5ti/√(1 + 5t²)⁻³ - 5t²j/[√(1 + 5t²)]⁻³ + j/√(1 + 5t²) - 10t²k/[√(1 + 5t²)]⁻³ + 2k/√(1 + 5t²)

= -5ti/√(1 + 5t²)⁻³ - 5t²j/[√(1 + 5t²)]⁻³ - 10t²k/[√(1 + 5t²)]⁻³ + j/√(1 + 5t²) + 2k/√(1 + 5t²)

= -(i + tj + 2tk)5t/[√(1 + 5t²)]⁻³ + (j + 2k)/√(1 + 5t²)

We multiply by the L.C.M [√(1 + 5t²)]³ to simplify it further

= [√(1 + 5t²)]³ × -(i + tj + 2tk)5t/[√(1 + 5t²)]⁻³ + [√(1 + 5t²)]³ × (j + 2k)/√(1 + 5t²)

= -(i + tj + 2tk)5t + (j + 2k)(1 + 5t²)

= -5ti - 5²tj - 10t²k + j + 5t²j + 2k + 10t²k

= -5ti + j + 2k

So, the magnitude of T'(t) = |T'(t)| = √[(-5t)² + 1² + 2²] = √[25t² + 1 + 4] = √[25t² + 5]

So, the normal vector N(t) = T'(t)/|T'(t)| = (-5ti + j + 2k)/√[25t² + 5]

(b) Use Formula 9 to find the curvature.

The curvature κ = |r'(t) × r"(t)|/|r'(t)|³

since r'(t) = (1, t, 2t), r"(t) = dr'/dt = d(1, t, 2t)/dt = (0, 1, 2)

r'(t) = i + tj + 2tk and r"(t) = j + 2k

r'(t) × r"(t) = (i + tj + 2tk) × (j + 2k)

= i × j + i × 2k + tj × j + tj × 2k + 2tk × j + 2tk × k

= k - 2j + 0 + 2ti - 2ti + 0

= -2j + k

So magnitude r'(t) × r"(t) = |r'(t) × r"(t)| = √[(-2)² + 1²] = √(4 + 1) = √5

magnitude of r'(t) = |r'(t)| = √(1 + 5t²)

|r'(t)|³ = [√(1 + 5t²)]³

κ = |r'(t) × r"(t)|/|r'(t)|³ = √5/[√(1 + 5t²)]³

8 0

3 years ago

"three times a number is greater than or equal to 12 and less than 21"

Diano4ka-milaya [45]

Answer:

The required inequality is: 12 ≤ 3x < 21

Step-by-step explanation:

We are given: three times a number is greater than or equal to 12 and less than 21

We need to answer following questions:

1) The inequality translated in numerical form

Let number = x

12 ≤ 3x < 21

2) Your work solving the inequality

We need to find value of x. Divide the inequality by x

4 ≤ x < 7

3) The solution graphed on a number line

It is shown in figure attached.

4) The solution in set notation

The set notation is: Considering x belongs to natural numbers N

{∀ x|x∈N, 4 ≤ x < 7}

5) The solution in interval notation

The interval notation is: [4,7)

because we have 4 less than equal to x and x is less than 7

8 0

3 years ago

A relay race has 4 runners who run different parts of the race. There are 16

xz_007 [3.2K]

Your coach can select it 4 times I think

4 0

3 years ago

In the month of June, the temperature in Johannesburg, South Africa, varies over the day in a periodic way that can be modeled a

Art [367]

Answer:

The answer is " $\bold{T = - 7.5 \cos \frac{\pi}{12}( t - 4 )+ 10.5}$ "

Step-by-step explanation:

Given value:

Temp-maximum= $18^{\circ}$

Temp. minimum = $3^{\circ}$

It is halfway between 10 am and 10 pm to 4 am.

The sinus and cosine roles could be used throughout the year to predict fluctuations in climate models. Its type of formula that can be used to model such information is:

$T = A \cos B(t-C) + D,$ where parameters are A, B , C, D, T is the ° C temperature and t is the time (1-24)

$A = amplitude = \frac{(T_{max} - T_{min})}{2}\\\\$

$= \frac{(3 - 18)}{2}\\\\= - \frac{15}{2}\\\\ = -7.5$

$B = \frac{2 \pi}{24}\\\\$

$= \frac{\pi}{12}$

$C = \text{ units translated to the right}= 4$

$D = y_{min} + amplitude = units \ translated \ up\\\\$

D = 7.5 + 3 = 10.5

Its trigonometric function equation that model temperature T hours after midnight in Johannesburg t.

$T = - 7.5 \cos \frac{\pi}{12}( t - 4 )+ 10.5$

6 0

4 years ago