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2 years ago

What is the approximate circumference of a circle with a diameter of 300 feet

1 answer:

6 0

Circumference = 2πr

Since you know the diameter is 300, you divide it by 2 to find the radius. Therefore, the radius is 150.
Now plug it into the formula: C = 2(3.14)(150)
C = 942

Answer: Circumference is 942 feet

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In the metric system, multiplying by 1000 would be the same as moving the decimal point _____ place(s) to the right.

hodyreva [135]

It would be the same as moving the decimal three to the right, and that applies to everything, not just the metric system.

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2 years ago

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Consider the parabola r(t)equalsleft angle at squared plus 1 comma t right angle, for minusinfinityless thantless thaninfinity

kodGreya [7K]

Given:- $r(t)=< at^2+1,t>$ ; $-\infty < t< \infty$ , where a is any positive real number.

Consider the helix parabolic equation :

$r(t)=< at^2+1,t>$

now, take the derivatives we get;

$r{}'(t)=$

As, we know that two vectors are orthogonal if their dot product is zero.

Here, $r(t) and r{}'(t)$ are orthogonal i.e, $r\cdot r{}'=0$

Therefore, we have ,

$< at^2+1,t>\cdot < 2at,1>=0$

$< at^2+1,t>\cdot < 2at,1>=$

$=2a^2t^3+2at+t$

$2a^2t^3+2at+t=0$

take t common in above equation we get,

$t\cdot \left (2a^2t^2+2a+1\right )=0$

⇒ $t=0$ or $2a^2t^2+2a+1=0$

To find the solution for t;

take $2a^2t^2+2a+1=0$

The number $D = b^2 -4ac$ determined from the coefficients of the equation $ax^2 + bx + c = 0.$

The determinant $D=0-4(2a^2)(2a+1)$ $=-8a^2\cdot(2a+1)$

Since, for any positive value of a determinant is negative.

Therefore, there is no solution.

The only solution, we have t=0.

Hence, we have only one points on the parabola $r(t)=< at^2+1,t>$ i.e <1,0>

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2 years ago

Which exponential functions have been simplified correctly check all that apply

Fittoniya [83]

Principle: Law of Exponents - Combination of product to a power & power to a power. The first is when raising a product of two integers to a power, the power is distributed to each factor. In equation it is,

(xy)^a = (x^a)(y^a)

The latter is when raising the base with a power to a power, the base will remain the same and the powers will be multiplied. In equation it is,
(x^a)(x^b) = x^ab

Check:

f(x) = 5*(16)^.33x = 5*(8*2)^0.33x = 5*(8^0.33x)(2^0.33x) = 5*(2^x)*(2^0.33x) = 5*(2^1.33x)

f(x) = 2.3*(8^0.5x) = 2.3*(4*2)^0.5x = 2.3*(2^x)(2^0.5x) = 2.3*(2^1.5x)

f(x) = 81^0.25x = 3^x

f(x) = 0.75*(9*3)^0.5x = 0.75*(3^x)*(3^0.5x) = 0.75*3^1.5x

f(x) = 24^0.33x = (8*3)^0.33x = (2^x)*(3^0.33x)

Therefore, the answer is third equation.

<em>ANSWER: f(x) = 81^0.25x = 3^x</em>

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2 years ago

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R/3+2=21 solve for r

olchik [2.2K]

Answer:

r=63

Step-by-step explanation:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

r/3-(21)=0 r

Simplify —

— - 21 = 0

3 2.1 Subtracting a whole from a fraction

Rewrite the whole as a fraction using 3 as the denominator :

21 21 • 3

21 = —— = ——————

1 3

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

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2 years ago

Which graph represents the function f(x)= 1/x - 1<br> PLEASE ANSWER FAST IM TIMED

marusya05 [52]

Number 3, because if you replace x for 1 then you get zero. and because it is rise over run then the run is 0. it is the only line with a run of 0

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2 years ago

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