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3 years ago

14

There are 51 students in the orchestra and twice that number in band. There are 19 boys and 13 girls in the choir. If each stude

nt only participates in one group how many students total are there in the orchestra, band & choir

1 answer:

Marizza181 [45]3 years ago

6 0

Their are 175 students total

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The triangle T has vertices at (-2, 1), (2, 1) and (0,-1). (It might be an idea to

Firdavs [7]

Rewrite the boundary lines <em>y</em> = -1 - <em>x</em> and <em>y</em> = <em>x</em> - 1 as functions of <em>y </em>:

<em>y</em> = -1 - <em>x</em> ==> <em>x</em> = -1 - <em>y</em>

<em>y</em> = <em>x</em> - 1 ==> <em>x</em> = 1 + <em>y</em>

So if we let <em>x</em> range between these two lines, we need to let <em>y</em> vary between the point where these lines intersect, and the line <em>y</em> = 1.

This means the area is given by the integral,

$\displaystyle\iint_T\mathrm dA=\int_{-1}^1\int_{-1-y}^{1+y}\mathrm dx\,\mathrm dy$

The integral with respect to <em>x</em> is trivial:

$\displaystyle\int_{-1}^1\int_{-1-y}^{1+y}\mathrm dx\,\mathrm dy=\int_{-1}^1x\bigg|_{-1-y}^{1+y}\,\mathrm dy=\int_{-1}^1(1+y)-(-1-y)\,\mathrm dy=2\int_{-1}^1(1+y)\,\mathrm dy$

For the remaining integral, integrate term-by-term to get

$\displaystyle2\int_{-1}^1(1+y)\,\mathrm dy=2\left(y+\frac{y^2}2\right)\bigg|_{-1}^1=2\left(1+\frac12\right)-2\left(-1+\frac12\right)=\boxed{4}$

Alternatively, the triangle can be said to have a base of length 4 (the distance from (-2, 1) to (2, 1)) and a height of length 2 (the distance from the line <em>y</em> = 1 and (0, -1)), so its area is 1/2*4*2 = 4.

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3 years ago

What is the reciprocal of 8 8/5 ?

Ksenya-84 [330]

Answer:

$\frac{5}{48}$

Step-by-step explanation:

The reciprocal of a number n is $\frac{1}{n}$

Given 8 $\frac{8}{5}$ , change to an improper fraction

= $\frac{5(8)+8}{5}$ = $\frac{48}{5}$ , thus

reciprocal = $\frac{1}{\frac{48}{5} }$ = $\frac{5}{48}$

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3 years ago

The formula f= 1.8 + 32 is used to convert temputure from degrees celsius ºC to degrees

Svetach [21]

Answer:

The Formula F=1.8C+32 gives the temperature in degrees Celsius (C). There is one temperature for which a number of degrees Fahrenheit is equal to the number of degrees Celsius.

Step-by-step explanation:

20ºC = 68ºF i think this is equation.;-;

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2 years ago

Find the slope of the line from the table below

bezimeni [28]

Answer:

m = -10

Step-by-step explanation:

m = y2 - y1 / x2 - x1

m = 60-50 / -2 - -1

m = 10/ -1

m = -10

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2 years ago

Read 2 more answers

Anna007 [38]

Answer:

1) The correct option is C. (2) The correct option is D. (3) The correct option is B. (4) The correct option is D. (5) The correct option is D.

Step-by-step explanation:

The slope formula is

$m=\frac{y_2-y_1}{x_2-x_1}$

(1)

Two points are (-2,5) and (1,4).

$m=\frac{4-5}{1-(-2)}=\frac{-1}{3}tex]Therefore option C is correct.(2)Use the above mentioned formula for each pair of coordinates.[tex]m=\frac{10-13}{17-12}=\frac{-3}{5}$

$m=\frac{10-15}{13-16}=\frac{-5}{-3}=\frac{5}{3}$

$m=\frac{10-7}{3-0}=\frac{3}{3}=1$

$m=\frac{18-13}{8-11}=\frac{5}{-3}=\frac{-5}{3}$

Therefore option D is correct.

(3)

The pair of points (6, y) and (10, -1). The slope is $\frac{1}{4}$ .

$\frac{1}{4}=\frac{-1-y}{10-6}$

$\frac{1}{4}=\frac{-1-y}{4}$

$1=-1-y$

$y=-2$

Therefore option B is correct.

(4)

For vertical line the x coordinates always remains the same. Therefore when we subtract the same number we get zero in the denominator, therefore the value of slope is undefined for a vertical line.

Therefore option D is correct.

(5)

Two points from the table are (2,110) and (3,165).

$m=\frac{165-110}{3-2}=\frac{55}{1}$

Therefore option D is correct.

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3 years ago

Read 2 more answers