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3 years ago

13

At the beginning of the school year, there were three 4th grade classes. Mrs. Smith’s class had 19 children, Mr. Day’s class has

17 children, and Ms. Brown’s class had 20 children. At the end of the year there were still three classes, but 13 children had moved during the year. How many total students were left at the end of the year?

2 answers:

Blababa [14]3 years ago

7 0

43 19+17+20 = 56 - 13 = 43

MAVERICK [17]3 years ago

7 0

The answer is 43!!!

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Let f(x) = 1/x^2 (a) Use the definition of the derivatve to find f'(x). (b) Find the equation of the tangent line at x=2

Verdich [7]

Answer:

(a) $f'(x)=-\frac{2}{x^3}$

(b) $y=-0.25x+0.75$

Step-by-step explanation:

The given function is

$f(x)=\frac{1}{x^2}$ .... (1)

According to the first principle of the derivative,

$f'(x)=lim_{h\rightarrow 0}\frac{f(x+h)-f(x)}{h}$

$f'(x)=lim_{h\rightarrow 0}\frac{\frac{1}{(x+h)^2}-\frac{1}{x^2}}{h}$

$f'(x)=lim_{h\rightarrow 0}\frac{\frac{x^2-(x+h)^2}{x^2(x+h)^2}}{h}$

$f'(x)=lim_{h\rightarrow 0}\frac{x^2-x^2-2xh-h^2}{hx^2(x+h)^2}$

$f'(x)=lim_{h\rightarrow 0}\frac{-2xh-h^2}{hx^2(x+h)^2}$

$f'(x)=lim_{h\rightarrow 0}\frac{-h(2x+h)}{hx^2(x+h)^2}$

Cancel out common factors.

$f'(x)=lim_{h\rightarrow 0}\frac{-(2x+h)}{x^2(x+h)^2}$

By applying limit, we get

$f'(x)=\frac{-(2x+0)}{x^2(x+0)^2}$

$f'(x)=\frac{-2x)}{x^4}$

$f'(x)=\frac{-2)}{x^3}$ .... (2)

Therefore $f'(x)=-\frac{2}{x^3}$ .

(b)

Put x=2, to find the y-coordinate of point of tangency.

$f(x)=\frac{1}{2^2}=\frac{1}{4}=0.25$

The coordinates of point of tangency are (2,0.25).

The slope of tangent at x=2 is

$m=(\frac{dy}{dx})_{x=2}=f'(x)_{x=2}$

Substitute x=2 in equation 2.

$f'(2)=\frac{-2}{(2)^3}=\frac{-2}{8}=\frac{-1}{4}=-0.25$

The slope of the tangent line at x=2 is -0.25.

The slope of tangent is -0.25 and the tangent passes through the point (2,0.25).

Using point slope form the equation of tangent is

$y-y_1=m(x-x_1)$

$y-0.25=-0.25(x-2)$

$y-0.25=-0.25x+0.5$

$y=-0.25x+0.5+0.25$

$y=-0.25x+0.75$

Therefore the equation of the tangent line at x=2 is y=-0.25x+0.75.

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3 years ago

in a recent season NASCAR driver Jimmie Johnson won 6 of the 36 total races held to the nearest thousand ,find the part of races

castortr0y [4]

So, the fraction of races that he won was:

$\frac{6}{36}$ : you need ti divide the number of occurrences by the number of possibilities.

We can simplify this:
$\frac{1}{6}$ .

When we write it in decimals until the closest place, it's:

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3 years ago

Read 2 more answers

A bag cost 4 times as much as a dress if the bag cost $276 how much will Toni speed on the bag and 3 such dresses

timama [110]

276 divides by 4 = 69
So 3x69 = 207 + 276 = $483

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3 years ago

Evaluate 6 - 2(-1) + | -5 | =

tester [92]

Answer:

13

Step-by-step explanation:

The product of two negative numbers is positive. The absolute value of a number is its magnitude written with a positive sign.

6 -2(-1) +|-5|

= 6 + 2 + 5

= 13

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3 years ago

last week 24% of the campers at a state park were visiting from out of state this weekend additional 12% are from out of state i

lesya692 [45]

Work: x/175=12%/100
multiply 175 by 2 and then you divide it by 100
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3 years ago