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2 years ago

What's the difference quotient: F(x)=x^3

Mathematics

1 answer:

zaharov [31]2 years ago

5 0

$\dfrac{F(x+h)-F(x)}h=\dfrac{(x+h)^3-x^3}h=\dfrac{x^3+3x^2h+3xh^2+h^3-x^3}h=3x^2+3xh$

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Find (a) the slope of the curve at the given point P, and (b) an equation of the tangent line at P: y = 9x^2 + 5 ; P (2,41)

Flauer [41]

Answer:

(a) 36

(b) y = 36x-31

Step-by-step explanation:

(a) dy/dx = 18x

slope of tangent at (2, 41) = 18(2)

= 36

(b) using y-y1 = m(x-x1)

y-41 = 36(x-2)

y = 36x-31

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2 years ago

An experiment consists of choosing objects without regards to order. Determine the size of the sample space when you choose the

sdas [7]

Answer:

$n= 75, 582$

$n= 2300$

$n = 253$

Step-by-step explanation:

Generally the size of the sample sample space is mathematically represented as

$n = \left N } \atop {}} \right. C_r$

Where N is the total number of objects available and r is the number of objects to be selected

So for a, where N = 19 and r = 8

$n = \left 19 } \atop {}} \right. C_8 = \frac{19 !}{(19 - 8 )! 8!}$

$= \frac{19 *18 *17 *16 *15 *14 *13 *12 *11! }{11 ! \ 8!}$

$n= 75, 582$

For b Where N = 25 and r = 3

$n = \left 25 } \atop {}} \right. C_3 = \frac{25 !}{(19 - 3 )! 3!}$

$= \frac{25 *24 *23 *22 ! }{22 ! \ 3!}$

$n= 2300$

For c Where N = 23 and r = 2

$n = \left 23 } \atop {}} \right. C_2 = \frac{23 !}{(23 - 2 )! 2!}$

$= \frac{23 *22 *21! }{21 ! \ 3!}$

$n = 253$

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3 years ago

Angle Q measures 30 degrees. If angle Q is rotates 15 degrees, what is the measurement of angle Q?

wariber [46]

Angle Q will have the same measurement as it did before, 30°.
Just because the angle is rotated shouldn't change its angle measure.

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2 years ago

Christina paid $2 for 5/8 of a gallon of gas.How much does it cost per gallon

vladimir1956 [14]

Answer:

$3.20

Step-by-step explanation:

I divided the $2 by 8 to see how much 1/8 a gallon cost.

I got 0.40

Multiple this by 8 to get 8/8 or 1 gallon.

You get 3.2

so $3.20

Hope this helped. :)

5 0

2 years ago

write the standard form of the equation of the circle with endpoints of a diameter at the points (9,2) and (-7,5)

AnnyKZ [126]

Answer:

Step-by-step explanation:

Answer:

(x-1)²+(y-3.5)² = 265/4

Step-by-step explanation:

first find the midpoint (center of the circle)

(9+-7)/2, (2+5)/2

(1, 3.5) = center

then distance formula to find diameter

√(9- -7)²+(2-5)²=√256+9 = √265

The radius is half the diameter = (√265)/2

Formula for circle is (x-h)²+(y-k)²=r², where (h, k) is the center

Now you can plug everything in.

(x-1)²+(y-3.5)² = 265/4

4 0

3 years ago