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kolbaska11 [484]
3 years ago
15

A particle moves along the curve below. y = √ 3 + x 3 y=3+x3 As it reaches the point ( 1 , 2 ) (1,2), the y y-coordinate is incr

easing at a rate of 3 cm/s 3 cm/s. How fast is the x x-coordinate of the point changing at that instant?
Mathematics
1 answer:
nydimaria [60]3 years ago
7 0

Answer:

The x-coordinate of the point changing at ¼cm/s

Step-by-step explanation:

Given

y = √(3 + x³)

Point (1,2)

Increment Rate = dy/dt = 3cm/s

To calculate how fast is the x-coordinate of the point changing at that instant?

First, we calculate dy/dx

if y = √(3 + x³)

dy/dx = 3x²/(2√(3 + x³))

At (x,y) = (1,2)

dy/dx = 3(1)²/(2√(3 + 1³))

dy/dx = 3/2√4

dy/dx = 3/(2*2)

dy/dx = ¾

Then we calculate dx/dt

dx/dt = dy/dt ÷ dy/dx

Where dy/dx = ¾ and dy/dt = 3

dx/dt = ¾ ÷ 3

dx/dt = ¾ * ⅓

dx/dt = ¼cm/s

The x-coordinate of the point changing at ¼cm/s

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Factor 64 - P.<br> (8 - x(8 - x)<br> (8 + x (8 - x)<br> (X + 8)(x-8)
muminat

Question:

Factor 64-x^2

(8 - x)(8 - x)

(8 + x) (8 - x)

(X + 8)(x-8)

Answer:

Option B: (8+x)(8-x) is the factor

Explanation:

Given that the expression is 64-x^2

We need to find the factor of the given expression.

Let us rewrite the expression as 8^2-x^{2}

Since the expression is of the form a^2-b^2, let us use the identity a^2-b^2=(a+b)(a-b)

where a = 8 and b = x

Substituting the values in the identity, then the expression can be written as

8^2-x^{2}=(8+x)(8-x)

Thus, the factor of the expression is (8+x)(8-x)

Hence, Option B is the correct answer.

4 0
3 years ago
Please help me, math is so hard
Aneli [31]

Answer:

32 divided by 4 = 8,

8^2 + 8^2 = 128

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We are finding hypotenuse but first we find the length of all sides of the two squares to find the two sides of the triangle then we find hypotenuse.

8 0
2 years ago
Read 2 more answers
***PLEASE HELP***
Molodets [167]
Given:
250 sheep in a 40-acre pasture.
Number of sheep grazing in each acre.

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n = 6
sample proportion: signified by ρ
Sample 1: 4 → 4/6 = 0.67
Sample 2: 1 → 1/6 = 0.17
Sample 3: 9 → 9/6 = 1.50

multiply the sample proportion by 1-ρ
Sample 1: 0.67(1-0.67) = 0.67(0.33) = 0.2211
Sample 2: 0.17(1-0.17) = 0.17(0.83) = 0.1411
Sample 3: 1.50(1-1.5) = 1.5(-0.5) = -0.75

divide the result by n. n = 6
Sample 1: 0.2211/6 = 0.03685
Sample 2: 0.1411/6 = 0.02352
Sample 3: -0.75/6 = -0.125

square root of the quotient to get the standard error.
Sample 1: √0.03685 = 0.1919
Sample 2: √0.02352 = 0.1534
Sample 3: √-0.125 = invalid

z value 95% confidence 1.96.

Sample 1: 1.96 * 0.1919 = 0.3761 or 37.61% margin of error
Sample 2: 1.96 * 0.1534 = 0.3007 or 30.07% margin of error


8 0
3 years ago
Is there a mistake in this equation? if not please let me know!
Juli2301 [7.4K]

Answer:

no mistakes

Step-by-step explanation:

4 * 3^x = 324

Divide each side by 4

4/4 * 3^x = 324/4

3^x = 81

Rewriting 81 as a power of 3

3^x = 3^4

Since the bases are the same, the powers are the same

x=4

5 0
3 years ago
Read 2 more answers
What two numbers multiply to get -420 and add to get -32
netineya [11]

I'm not at my desk and can't check it out right now.
But I think you should try  10  and  -42 .

7 0
3 years ago
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