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1 year ago

Using point P, which point would form a line parallel to line AB?

Mathematics

1 answer:

geniusboy [140]1 year ago

8 0

Answer:

(3,2)

Step-by-step explanation:

The equation of the line graphed is

y = 2/3x + 2

Parallel lines have the same slope.

y = mx + b

y = 2/3x + 0 P tells me that the y-intercept is 0

y = 2/3 x Which point would make this true?

Point (3,2) We plug in 3 for x and 2 for y

2 = 2/3(3)

2 = 2 This is a true statement, so the point (3,2) is on the line.

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Zadanie optymalizacyjne z matematyki. Proszę o rozwiązanie i wyjaśnienie

Yakvenalex [24]

Volume of the pyramid:

$V=\dfrac{s^2h}3$

Perimeter of the cross-section:

$40=\sqrt2\,s+2\sqrt{\dfrac{s^2}2+h^2}=\sqrt2\left(s+\sqrt{s^2+2h^2}\right)$

$\implies h=\sqrt{\dfrac{(20\sqrt2-s)^2-s^2}2}=\sqrt{400-20\sqrt2\,s}$

Area of the cross-section:

$P=\dfrac12(\sqrt2\,s)h=\dfrac{sh}{\sqrt2}$

$\implies P=\dfrac{s\sqrt{400-20\sqrt2\,s}}{\sqrt2}=s\sqrt{200-10\sqrt2\,s}$

First derivative test:

$\dfrac{\mathrm dP}{\mathrm ds}=\dfrac{20\sqrt2-3s}{\sqrt{4-\dfrac{\sqrt2}5s}}=0\implies s=\dfrac{20\sqrt2}3$

Then the height of the cross-section/pyramid is

$h=\sqrt{400-20\sqrt2\,s}=\dfrac{20}{\sqrt3}$

The volume of the pyramid that maximizes the cross-sectional area $P$ is

$V=\dfrac{\left(\frac{20\sqrt2}3\right)^2\frac{20}{\sqrt3}}3=\dfrac{16000}{27\sqrt3}$

5 0

3 years ago

What is the value of a in the equation 304 b =54, when b =9? O 15 O 18 0 21 O 27

Serhud [2]

Step-by-step explanation:

I'm not sure where a is supposed to be in this equation, but I'm going to assume it's supposed to be written as either 3a x 4b = 54, or 304b = 54a. If it's something else, let me know, but I'll just answer these two for now.

1. 3a x 4b

So we know that b is equal to 9. Therefore, we can rewrite

$3a \times 4b = 54$

$3a \times 4(9) = 54$

To get rid of a multiplier on one side, divide both sides by the number you want gone. I'll use 4(9), which equals 36.

$3a = 54 \div 36 = 1.5$

Then we can divide by 3 to get

$a = 1.5 \div 3 = 0.5$

0.5 isn't a viable answer, so I'll try the second interpretation.

2. 304b = 54a

This one is a bit easier. All we need to do is divide both sides by 54 to get

$304b \div 54 = a$

304 x 9 = 2736

2736/54 = 50.66...

Again, not a viable answer. Please edit your question to include a and I'll give it another shot!

5 0

1 year ago

Write y=1/6x+7 in standard form using intergers.

Anna71 [15]

Answer:

–x + 6y = 42

Hope this answer is right!

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3 years ago

Adana has 4 skirts, 3 blouses, and

Bumek [7]

Adama can make 7 outfits

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3 years ago

Read 2 more answers

Given f(x)=x^2+1 and g(x)=x. Which expression is not a polynomial?

diamong [38]

Answer:

i think its not a polynomial

Step-by-step explanation:

7 0

2 years ago