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vodka [1.7K]
3 years ago
8

In quadrilateral PQRS, the coordinates are (0,0), R(a +c, b), and S(a, b). How can you use coordinate geometry to show that the

diagonals are perpendicular
Mathematics
1 answer:
aliina [53]3 years ago
6 0

Answer:By definition, perpendicular line are two lines that intersect at right angles. In other words, the angle made by two lines should be 90°. Therefore, the use of distance formula does not help because it only tells you if the sides are equal. It does not tell you about the intercepted angle.

A technique that can help you to know if two straight lines are perpendicular is is you find their slopes. Let's say the slope of line 1 is m1 and the slope of line 2 is m2. If m1*m2 yields a product of -1, then the lines are perpendicular. This is because if m1 is the negative reciprocal of m2, the lines are perpendicular. But if m1=m2, the lines are parallel, meaning they don't intersect at all.

Therefore, the answer is: Find the slopes and show that their product is -1.

hope it help

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10x+2 = 3x + 30 Find x (please)
Ganezh [65]
Answer: x=4

10x-3x=30-2
7x=28
X=4
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3 years ago
I don’t understand this so can I get help
solniwko [45]

Answer:

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Step-by-step explanation:

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3 years ago
What is the volume of a right circular cone that has a height of 18.8 m and a base with a radius of 19.3 m
12345 [234]

Answer: 7,333.32 m3

Step-by-step explanation:

Hi, to answer this question we have to apply the next formula:

Volume of a cone = 1/3 x π x radius^2 x height

Replacing with the values given:

V = 1/3 π (19.3)^2 (18.8) = 7,333.32 m3

The volume of the right circular cone is 7,333.32 cubic meters.

Feel free to ask for more if needed or if you did not understand something.  

7 0
3 years ago
Read 2 more answers
Suppose that we don't have a formula for g(x) but we know that g(3) = −5 and g'(x) = x2 + 7 for all x.
Leni [432]

Answer:

a)

g(2.9) \approx -6.6

g(3.1) \approx -3.4

b)

The values are too small since g'' is positive for both values of x in. I'm speaking of the x values, 2.9 and 3.1.

Step-by-step explanation:

a)

The point-slope of a line is:

y-y_1=m(x-x_1)

where m is the slope and (x_1,y_1) is a point on that line.

We want to find the equation of the tangent line of the curve g at the point (3,-5) on g.

So we know (x_1,y_1)=(3,-5).

To find m, we must calculate the derivative of g at x=3:

m=g'(3)=(3)^2+7=9+7=16.

So the equation of the tangent line to curve g at (3,-5) is:

y-(-5)=16(x-3).

I'm going to solve this for y.

y-(-5)=16(x-3)

y+5=16(x-3)

Subtract 5 on both sides:

y=16(x-3)-5

What this means is for values x near x=3 is that:

g(x) \approx 16(x-3)-5.

Let's evaluate this approximation function for g(2.9).

g(2.9) \approx 16(2.9-3)-5

g(2.9) \approx 16(-.1)-5

g(2.9) \approx -1.6-5

g(2.9) \approx -6.6

Let's evaluate this approximation function for g(3.1).

g(3.1) \approx 16(3.1-3)-5

g(3.1) \approx 16(.1)-5

g(3.1) \approx 1.6-5

g(3.1) \approx -3.4

b) To determine if these are over approximations or under approximations I will require the second derivative.

If g'' is positive, then it leads to underestimation (since the curve is concave up at that number).

If g'' is negative, then it leads to overestimation (since the curve is concave down at that number).

g'(x)=x^2+7

g''(x)=2x+0

g''(x)=2x

2x is positive for x>0.

2x is negative for x.

That is, g''(2.9)>0 \text{ and } g''(3.1)>0.

So 2x is positive for both values of x which means that the values we found in part (a) are underestimations.

6 0
4 years ago
Describe an algorithm for finding the smallest integer in a finite sequence of natural numbers.
Crazy boy [7]

Answer:

min = a_1

for i:= 2 to n:

      if a_i < min then min = a_i

return min

Step-by-step explanation:

We call the algorithm "minimum" and a list of natural numbers a_1, a_2, \cdot\cdot\cdot, a_n.

So lets first set the minimum to a_1

min = a_1

now we want to check all the other numbers.

We can use a simple for loop, to find the minimum

min = a_1

for i:= 2 to n:

      if a_i < min then min = a_i

return min

5 0
1 year ago
Read 2 more answers
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