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3 years ago

11

Serena wants to create snack bags for a trip she's going on she has 6 granola bars and 10 piecies of dried fruit whats the great

est amount of bags she can make

1 answer:

Eduardwww [97]3 years ago

4 0

Answer:

6, if she wants one granola bar and one dried fruit in each bag

Step-by-step explanation:

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A local band is holding a concert. The price of a ticket to the concert is $15. The band must sell enough tickets to cover at le

Kamila [148]

15x is greater than or equal to 525

the answer is X is greater than or equal to 35

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2 years ago

Write an equation of the line in point slope form parallel to y=1/3x-5 through point (3,-7)

Mashcka [7]

Hmmm so, parallel lines have the same slope, so a line that's parallel to <span>y=1/3x-5, will also have the same slope as that one, what would that be anyway? </span> $\bf y=\stackrel{slope}{\cfrac{1}{3}}x-5$ , well, low and behold, since that equation is in slope-intercept form already, we can see is just 1/3.
<span>
so, what is the equation of a line whose slope is 1/3 and runs through 3, -7?

</span> $\bf \begin{array}{ccccccccc}
&&x_1&&y_1\\
% (a,b)
&&(~ 3 &,& -7~)
\end{array}
\\\\\\
% slope = m
slope = m\implies \cfrac{1}{3}
\\\\\\
% point-slope intercept
\stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-(-7)=\cfrac{1}{3}(x-3)\implies y+7=\cfrac{1}{3}(x-3)$ <span>
</span>

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2 years ago

Read 2 more answers

8 cm<br> 5 cm<br> 10 cm<br> 12 cm

lana66690 [7]

Answer:

35 cm

Step-by-step explanation:

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2 years ago

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

Rebeca spent $32.55 for a photo album and three identical candles. The photo album cost $17.50 and the sales tax was $1.55. How

Marina86 [1]

Answer: $4.50 per candle

Step-by-step explanation:

$32.55 - $17.50 - $1.55 = $13.50 for all the candles

To find the price of a single candle we divide our answer by 3

13.50/3 = $4.50

3 0

3 years ago