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alukav5142 [94]

4 years ago

7

What value(s) of ϑ, in radians make(s) x minimum?

1 answer:

iVinArrow [24]4 years ago

4 0

<span>He relationship between rectangular and rotational coordinates can be represented by the vector equation: r = xi +yj = rcos(theta)i+rsin(theta)j What values in radians makes x minimum y maximum and x = -y Ans : x minimum = -r when theta = 180 degrees + any multiple of 360 degrees y minimum = -r when theta = 270 degrees + any multiple of 360 degrees x = -y when theta = 135 degrees + any multiple of 180 degrees.</span>

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What is the value of 7P3?<br> 021<br> 35<br> 210<br> 840

MrRissso [65]

Answer:

210

Step-by-step explanation:

The answer for 7p3 is : 210. This can be solved in the following way: 7p3 is an expression for permutation which means the number of ways of arranging 3 items from a total of 7 items.

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3 years ago

Could someone help me rnnn?

GuDViN [60]

Answer:

vertex = (0, -4)

equation of the parabola: $y=3x^2-4$

Step-by-step explanation:

Given:

y-intercept of parabola: -4
parabola passes through points: (-2, 8) and (1, -1)

Vertex form of a parabola: $y=a(x-h)^2+k$

(where (h, k) is the vertex and $a$ is some constant)

Substitute point (0, -4) into the equation:

$\begin{aligned}\textsf{At}\:(0,-4) \implies a(0-h)^2+k &=-4\\ah^2+k &=-4\end{aligned}$

Substitute point (-2, 8) and $ah^2+k=-4$ into the equation:

$\begin{aligned}\textsf{At}\:(-2,8) \implies a(-2-h)^2+k &=8\\a(4+4h+h^2)+k &=8\\4a+4ah+ah^2+k &=8\\\implies 4a+4ah-4&=8\\4a(1+h)&=12\\a(1+h)&=3\end{aligned}$

Substitute point (1, -1) and $ah^2+k=-4$ into the equation:

$\begin{aligned}\textsf{At}\:(1.-1) \implies a(1-h)^2+k &=-1\\a(1-2h+h^2)+k &=-1\\a-2ah+ah^2+k &=-1\\\implies a-2ah-4&=-1\\a(1-2h)&=3\end{aligned}$

Equate to find h:

$\begin{aligned}\implies a(1+h) &=a(1-2h)\\1+h &=1-2h\\3h &=0\\h &=0\end{aligned}$

Substitute found value of h into one of the equations to find a:

$\begin{aligned}\implies a(1+0) &=3\\a &=3\end{aligned}$

Substitute found values of h and a to find k:

$\begin{aligned}\implies ah^2+k&=-4\\(3)(0)^2+k &=-4\\k &=-4\end{aligned}$

Therefore, the equation of the parabola in vertex form is:

$\implies y=3(x-0)^2-4=3x^2-4$

So the vertex of the parabola is (0, -4)

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Step-by-step explanation:

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4 years ago

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3 years ago

Dominic pays 7% interest on his $16,000 college loan and 12% interest on his $12,000 car loan. What average interest rate does h

Naya [18.7K]

The average interest rate is 8.57% paid on the total of $28,000

<h3>What is the percentage?</h3>

The percentage is defined as a ratio expressed as a fraction of 100.

Dominic pays 7% interest on his $16,000 college loan,

And 12% interest on his $12,000 car loan

To determine the average interest rate paid on the total $28,000 he owes

Calculating the total interest amount paid :

⇒ 7% of 16,000 + 12% of 12,000

⇒ (7/100)16,000 + (12/100)12,000

⇒ (0.07)16,000 + (0.12)12,000

⇒ (0.07)16,000 + (0.12)12,000

⇒ 960 + 1440

⇒ 2400

So the average interest rate paid on the total of $28,000 as

⇒ 2400/28,000 = 0.0857 ≈ 8.57%

Hence, the average interest rate is 8.57% paid on the total of $28,000

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1 year ago