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3 years ago

Which of the following is equivalent to (81m^6)^1/2?

Mathematics

2 answers:

Wewaii [24]3 years ago

4 0

Answer:

A) 9m^3

Step-by-step explanation:

Raising something to the 1/2 power is the same as taking the square root.

The square root of 81 is 9. The square root of m^6 is m^3. Together, this gives us

9m^3.

ch4aika [34]3 years ago

3 0

That would be option A
because square root of 81 is 9 and square root m^6 is m^3.

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A plant cell is 0.00001267 meter wide.How is this number written in scientific notation?

MA_775_DIABLO [31]

<span>The answer is 0.00001267 m = 1.267 * 10^(-5) m. In scientific notation, the number is written as two factors - a number m from 0-10 and 10 raised to the n power: m x 10^n. 0.00001267 m = 1.267 x 0.00001 m. 0.00001 m = (0.1)^5 = 10^(-5). So: 0.00001267 m = 1.267 x 0.00001 m = 1.267 x (0.1)^5 m = 1.267 x 10^(-5) m.</span>

3 0

3 years ago

A golf player is trying to make a hole-in-one on the miniature golf green shown.

Flauer [41]

The path of the ball is an illustration of absolute equation.

The equation of the path is: $y =- \frac{12}7|x- 4.8| + 6.4$

The given parameters are:

$(h,k) = (4.8,6.4)$ --- the vertex (i.e. the point where the ball hits the wall)

$(x_1,y_1) = (2,1.6)$

$(x_2,y_2) = (7.6,1.6)$

An absolute function is represented as:

$y = a |x - h| + k$

Substitute $(h,k) = (4.8,6.4)$

$y = a |x - 4.8| + 6.4$

Substitute $(x_1,y_1) = (2,1.6)$ for x and y

$1.6 = a|2 - 4.8| + 6.4$

$1.6 = a|- 2.8| + 6.4$

Remove absolute bracket

$1.6 = 2.8a + 6.4$

Collect like terms

$2.8a = -6.4+1.6$

$2.8a =- 4.8$

Solve for a

$a =-\frac{4.8}{2.8}$

Simplify

$a =-\frac{12}{7}$

Substitute $a =-\frac{12}{7}$ in $y = a |x - 4.8| + 6.4$

$y =- \frac{12}7|x- 4.8| + 6.4$

Hence, the equation of the path is: $y =- \frac{12}7|x- 4.8| + 6.4$

See attachment for graph that models the path

Read more about absolute equations at:

brainly.com/question/2166748

5 0

2 years ago

Deluxe River Cruises operates a fleet of river vessels. The fleet has two types of vessels: A type-A vessel has 60 deluxe cabins

bixtya [17]

Answer: It should be used 2 for type-A and 3 for type-B to minimize the cost.

Step-by-step explanation: As it is stipulated, <u>x</u> relates to type-A and y to type-B.

Type-A has 60 deluxe cabins and B has 80. It is needed a minimum of 360 deluxe cabins, so:

60x + 80y ≤ 360

For the standard cabin, there are in A 160 and in B 120. The need is for 680, so:

160x + 120y ≤ 680

To calculate how many of each type you need:

60x + 80y ≤ 360

160x + 120y ≤ 680

Isolating x from the first equation:

x = $\frac{360 - 80y}{60}$

Substituing x into the second equation:

160( $\frac{360 - 80y}{60}$ ) + 120y = 680

-3200y+1800y = 10200 - 14400

1400y = 4200

y = 3

With y, find x:

x = $\frac{360 - 80y}{60}$

x = $\frac{360 - 80.3}{60}$

x = 2

To determine the cost:

cost = 42,000x + 51,000y

cost = 42000.2 + 51000.3

cost = 161400

To keep it in a minimun cost, it is needed 2 vessels of Type-A and 3 vessels of Type-B, to a cost of $161400

8 0

2 years ago

Given f(x) = (lnx)^3 find the line tangent to f at x = 3

kirill [66]

Explanation

We must the tangent line at x = 3 of the function:

$f(x)=(\ln x)^3.$

The tangent line is given by:

$y=m*(x-h)+k.$

Where:

• m is the slope of the tangent line of f(x) at x = h,

• k = f(h) is the value of the function at x = h.

In this case, we have h = 3.

1) First, we compute the derivative of f(x):

$f^{\prime}(x)=\frac{d}{dx}((\ln x)^3)=3*(\ln x)^2*\frac{d}{dx}(\ln x)=3*(\ln x)^2*\frac{1}{x}=\frac{3(\ln x)^2}{x}.$

2) By evaluating the result of f'(x) at x = h = 3, we get:

$m=f^{\prime}(3)=\frac{3}{3}*(\ln3)^2=(\ln3)^2.$

3) The value of k is:

$k=f(3)=(\ln3)^3$

4) Replacing the values of m, h and k in the general equation of the tangent line, we get:

$y=(\ln3)^2*(x-3)+(\ln3)^3.$

Plotting the function f(x) and the tangent line we verify that our result is correct:

Answer

The equation of the tangent line to f(x) and x = 3 is:

$y=(\ln3)^2*(x-3)+(\ln3)^3$

6 0

1 year ago

The expression, involving exponents , to represent the shaded area, in square inches, diagram. Then use that expression to calcu

mart [117]

Answer:

The shaded area is $23\ in^{2}$

Step-by-step explanation:

we know that

The shaded area is equal to the area of the large square minus the area of the two smaller squares

$A=6^{2} -(3^{2} +2^{2})\\ \\ A=(2*3)^{2} -(3^{2} +2^{2})\\ \\A=(2^{2})(3^{2}) -(3^{2} +2^{2})$

Calculate the shaded area

Remember that

$3^{2}=9\\ 2^{2}=4$

substitute

$A=(4)(9) -(9 +4)\\ \\A=36-13\\ \\A=23\ in^{2}$

5 0

3 years ago