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user100
8 days ago
10

the equation of a curve is xy=12 and the equation of a line l is 2x+y=k where k is a constant .In the case where k=11 find the c

oordinates of the points of intersection of l and the curve.
Mathematics
1 answer:
tester [3.9K]8 days ago
7 0
The equations given are xy=12 and 2x+y=11.

To find the intersection points, you can isolate one of the variables, either x or y, and substitute into the other equation. I’ll choose to express x in terms of y.

Rearranging the first equation for y gives us y=12/x.

Substituting this y value into the second equation leads to an equation with a single variable to solve for x. This results in 2x + 12/x = 11.
To eliminate the fraction, multiply both sides by x, giving...
2x^2 - 11x + 12 = 0.
From here, we can factor to get (2x-3)(x-4).
By setting both factors to zero, we can solve for x values which yields x = 3/2 and x = 4.
Next, we substitute these x values back into the original equation xy=12 to find the corresponding y coordinates. This results in the points:
(3/2, 8) and (4, 3). The curves intersect at these two locations.
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We are given the triangle

△ABC, with m∠A=60° and m∠C=45°, and AB=8.

To start, we will calculate all angles and sides.

Finding angle B:

The total of all angles in a triangle equals 180.

m∠A + m∠B + m∠C = 180.

Substituting the known values,

60° + m∠B + 45° = 180.

This gives us m∠B = 75°.

Calculating BC:

Using the law of sines,

\frac{AB}{sin(C)}=\frac{BC}{sin(A)}

We can substitute in the values.

\frac{8}{sin(45)}=\frac{BC}{sin(60)}

BC=\frac{8}{sin(45)} \times sin(60)

BC=9.798

Finding AC:

\frac{AB}{sin(C)}=\frac{AC}{sin(B)}

Now we'll input the values.

\frac{8}{sin(45)}=\frac{AC}{sin(75)}

AC=\frac{8}{sin(45)} \times sin(75)

AC=10.928

Calculating Perimeter:

p=AB+BC+AC

We substitute values here as well.

p=10.928+8+9.798

p=28.726

Calculating Area:

Using the area formula,

A=\frac{1}{2}AB \times AC \times sin(A)

we can then insert values.

A=\frac{1}{2}8 \times 10.928 \times sin(60)

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Answer:

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Step-by-step explanation:

Since sales data for the second year is unavailable, we denote it as x million.

Year 3's total sales amount to 32 million.

Calculate the sales account for year 3 as follows:

\text{Percentage of sales for year 3}=\frac{\text{Total Sales in year 3}-\text{Total Sales in year 2}}{\text{Total Sales in year 2}}\times 100\%

                                                =\frac{32\ \text{mn}-x\ \text{mn}}{x\ \text{mn}}\times 100\%

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Another project on Kickstarter for an iPad stylus raised 1,253% of their goal, raising a total of $313,490 from 7,511 supporters
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Answer:

The initial goal was $25019.154.

Step by step Explanation:

Assuming the original goal is denoted as x.

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1253% can be expressed as a decimal.

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12.53 × x = 313490

12.53x = 313490

x = \frac{313490}{12.53}

x = $ 25019.154

This means the initial goal stands at $25019.154.

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