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LenKa [72]
3 years ago
12

A sunglassez store bought $5000 worth of sunglasses. The store made $9000, making a profit $20 per pair of sunglasses. There wer

e........ pairs of sunglasses involved.
Mathematics
1 answer:
julia-pushkina [17]3 years ago
3 0
200 because 5000/200 is 25 and add the profit to that to get 45. 9000/200 is 45. Sorry if that doesn't make sense :/
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Helen has 48 cubic inches of clay to make a solid square right pyramid with a base edge measuring 6 inches. Which is the slant h
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Answer: 5 inches


Step-by-step explanation:

Given: Volume of clay = 48 cubic inches

If we make a solid square right pyramid with a base edge a= 6 inches.

Then its base area = a^2=6^2=36\ inches^2

we know that volume of square right pyramid=\frac{1}{3}\times\ a^2h

Therefore, volume of square right pyramid made by all of clay=\frac{1}{3}\times\ a^2h=48 cubic inches

\Rightarrow\frac{1}{3}\times\ (36)\times\ h=48\\\Rightarrow12h=48\\\Rightarrow\ h=4\ inches.....\text{[Divide 12 on both sides]}

Now, slant height l=\sqrt{(\frac{a}{2})^2+h^2}

\\\Rightarrow\ l=\sqrt{3^2+4^2}\\\Rightarrow\ l=\sqrt{9+16}\\\rightarrow\ l=\sqrt{25}\\\Rightarrow\ l=5

The slant height of the pyramid if Helen uses all the clay=5 inches

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3 years ago
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Identify the variation as direct, inverse, joint or combined.
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a chef has a recipe that calls for 4 cups of flour. She wants to make 3/4 of the recipe instead of determining directly how many
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For each of these questions, you need to find the derivative y' or \dfrac{\mathrm dy}{\mathrm dx}. The slope of the tangent to these curves at the point (a,b) is the value of y' when x=a and y=b. It's also important to know that if the slope of a line is m\neq0, then the slope of any line normal/perpendicular to this line is -\dfrac1m.

###

y=\dfrac{6x+3}{3x^2+6x+4}

The derivative is

y'=\dfrac{(3x^2+6x+4)(6x+3)'-(6x+3)(3x^2+6x+4)'}{(3x^2+6x+4)^2}=\dfrac{6(3x^2+6x+4)-(6x+3)(6x+6)}{(3x^2+6x+4)^2}

y'=\dfrac{6-18x-18x^2}{(3x^2+6x+4)^2}

When x=1, we get a slope of

y'=\dfrac{6-18-18}{(3+6+4)^2}=-\dfrac{30}{169}

###

y=x^2+9x+16

The derivative is

y'=2x+9

and so the tangent line at (1, 9) has slope

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The line normal to this has slope -\dfrac1{11}. The point-slope and slope-intercept forms of this line are

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so the slope of any line tangent to the curve is 9. The line that passes through (3, 4) is

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