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2 years ago

Find the centroid for an area defined by the equations y = x² + 3 and y = - (x – 2)² + 7

1 answer:

6 0

First we need to find where the 2 graphs intercept.

x^2 + 3 = - (x^2 - 4x + 4) + 7
x^2 + 3 = -x^2 + 4x + 3
2x^2 - 4x = 0
2x(x - 2)

x = 0 , 2. are x coordinates of the 2 intercepts.

You might be interested in

The product of two consecutive even positive integers is 674 more than the sum of the two integers. Find the integers.

IrinaVladis [17]

$2n(2n+2)=2n+2n+2+674\\
4n^2+4n=4n+676\\
4n^2=676\\
n^2=169\\
n=-13 \vee n=13$
$-13\not\ \textgreater \ 0$

$n=13\\
2n=26\\
2n+2=28$

It's 26 and 28.

7 0

3 years ago

If ∠G is supplementary to ∠H and the measure of ∠G is 65° what is the measure of ∠H?

Elina [12.6K]

Solution:

Given:

∠G = 65°

Supplementary angles are a pair of angles that sum up to 180°.

It should be noted:

If ∠G and ∠H are a pair of supplementary angles, they both sum up to 180°.

Equation formed: ∠G + ∠H = 180

Substitute the values into the equation.

∠G + ∠H = 180
=> 65 + ∠H = 180

Subtract 65 both sides.

=> 65 - 65 + ∠H = 180 - 65
=> ∠H = 180 - 65 = 115°

7 0

2 years ago

Food and clothing are shipped to victims of a natural disaster. Each carton of food will feed 13 people, while each carton of c

lutik1710 [3]

Answer:

233 cartons of food; 467 cartons of clothing

Step-by-step explanation:

This linear programming problem can be formulated as two inequalities (in addition to the usual constraints that the variables be non-negative). One of these expresses the constraint on weight. Let f and c represent numbers of food and clothing containers, respectively.

40f +25c ≤ 21000

The other expresses the limit on volume.

20f + 5c ≤ 7000

_____

Feasible Region vertex

We can subtract the boundary line equation of the first inequality from that of 5 times the second to find f:

5(20f +5c) -(40f +25c) = 5(7000) -21000

60f = 14000

f = 233 1/3

The second boundary line equation can be rearranged to find c:

c = 1400 -4f = 466 2/3

The nearest integer numbers to these values are ...

(f, c) = (233, 467)

The other vertices of the feasible region are associated with one or the other variable being zero: (f, c) = (0, 840) or (350, 0).

Check of Integer Solution

Trying these in the constraint inequalities gives ...

40·233 +25·467 = 20,995 < 21000
20·233 +5·467 = 6995 < 7000

Selection of the Answer

The answer to the question will be the feasible region vertex that maximizes the number of people helped. That is, we want to maximize ...

p = 13f + 6c

The values of p at the vertices are ...

p = 13·233 + 6·467 = 5831

p = 13·0 + 6·840 = 5040

p = 13·350 + 6·0 = 2100

The most people are helped when the plane is filled with 233 food cartons and 467 clothing cartons.

7 0

2 years ago

Which ordered pair represents the solution to:

Serjik [45]

2x6=12
3x6=18
12+18=22

2x3=6
2x6=12

6+12=18

8 0

2 years ago

3. Are these ratios equivalent? 35:28 and 10:8 *

attashe74 [19]

Reduce each ratio to its minimum expression to find if they are equal.

35:28

$\begin{gathered} \frac{35}{28}=\frac{7\cdot5}{7\cdot4} \\ =\frac{5}{4} \end{gathered}$

10:8

$\begin{gathered} \frac{10}{8}=\frac{2\cdot5}{2\cdot4} \\ =\frac{5}{4} \end{gathered}$

Since both ratios reduce to 5:4, they are equivalent.

Another way to check a:b is equivalent to c:d, is that a*d = b*c

In this case, this will be true if 35 times 8 is equal to 10 times 28:

$\begin{gathered} 35\cdot8=280 \\ 10\cdot28=280 \end{gathered}$

Since both products are equal, then the ratios are equivalent.

4 0

10 months ago