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solniwko [45]
3 years ago
8

An amphitheatre has 24 seats in the first​ row, 28 in the​ second, 32 in the​ third, and so​ on, for 29 rows. How many seats are

in the​ amphitheatre?
Mathematics
1 answer:
melomori [17]3 years ago
3 0
The answer is 2,320 seats in the amphitheater. Since the seats are increasing at a rate of 4 more seats each row, then just add 4 to the number for each past row starting at 32 since that's where the rest is unknown. Once you find all he numbers just add them up to get your answer.
I hope I helped!
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Use implicit differentiation to find an equation of the tangent line to the curve at the given point. 7x2 + xy + 7y2 = 15, (1, 1
riadik2000 [5.3K]
Assume y=y(x).

7x^2+xy+7y^2=15
\dfrac{\mathrm d}{\mathrm dx}[7x^2+xy+7y^2]=\dfrac{\mathrm d}{\mathrm dx}[15]
14x+y+x\dfrac{\mathrm dy}{\mathrm dx}+14y\dfrac{\mathrm dy}{\mathrm dx}=0
\dfrac{\mathrm dy}{\mathrm dx}(x+14y)=-(14x+y)
\dfrac{\mathrm dy}{\mathrm dx}=-\dfrac{14x+y}{x+14y}

The slope of the tangent line to the curve at (a,b) is then -\dfrac{14a+b}{a+14b}, so the tangent to (1,1) has slope

\dfrac{\mathrm dy}{\mathrm dx}\bigg|_{x=1,y=1}=-\dfrac{15}{15}=-1

The point-slope form of the tangent line is then

y-1=-(x-1)\iff y=-x+2
7 0
3 years ago
The actual length of Lake Superior is 350 miles and the width is 160 miles. What's the length and width of the lake on a map if
pentagon [3]

The correct option is:   B.  length: 14 cm, width: 6.4 cm

<em><u>Explanation</u></em>

The actual length of Lake Superior is 350 miles and the width is 160 miles.

The scale is given as:  1 cm = 25 miles

Suppose, the length and width of the lake on the map are  x cm and y cm respectively.

First, the equation according to the <u>ratio of scaled length to the actual length</u> will be....

\frac{x}{350}=\frac{1}{25}\\ \\ 25x=350\\ \\ x=\frac{350}{25}=14

Now, the equation according to the <u>ratio of scaled width to the actual width</u> will be....

\frac{y}{160}=\frac{1}{25}\\ \\ 25y=160\\ \\ y=\frac{160}{25}=6.4

Thus, the length and width of the lake on the map will be 14 cm and 6.4 cm respectively.

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3 years ago
In the table below, 1:2, 2:4, 3:6, 4:8, and so on are all equivalent ratios.
Mazyrski [523]

Answer:

4

Step-by-step explanation:

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3 years ago
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Answer:

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Step-by-step explanation:

2.) 6 - 3 = 3

4 0
3 years ago
FIRST (CORRECT) ANSWER I WILL GIVE BRAINLIEST
LenaWriter [7]

Answer:

A

Explanation:

If you graph the points and connect them, you'll see the triangle they're asking about. Yhe base of the triangle is 9 and the height is 8. The area of a triangle is half of the base times the height. So multiply 8 by 9 and you get 72. This is twice the area. So divide it by 2 and you get 36, which is the area of the triangle. So the answer is A.

8 0
3 years ago
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