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vichka [17]
3 years ago
13

The coordinates of three points are A(- 1, - 3) , B(2, 3) and C(6, k) . If AB is perpendicular to BC find (i) the value of k, (i

i) the gradient of AC (iii) the acute angle that AC makes with the x-axis.​
Mathematics
1 answer:
padilas [110]3 years ago
6 0

9514 1404 393

Answer:

  (i) k = 1

  (ii) 4/7

  (iii) arctan(4/7) ≈ 29.7°

Step-by-step explanation:

(i) A graph of the given points is helpful. It shows us the slope of AB is ...

  mAB = rise/run = 2/1 = 2

so the slope of BC must be the opposite reciprocal, -1/2.

Point C is 6-2 = 4 units to the right of point B, so will be (-1/2)(4) = -2 units from point B in the vertical direction. That is, ...

  k = 3 -2

  k = 1

__

(ii) The gradient of AC is found from the slope formula:

  m = (y2 -y1)/(x2 -x1)

  m = (1 -(-3))/(6 -(-1))

  mAC = 4/7

__

(iii) The angle that line AC makes with the +x axis is the arctangent of the slope:

  arctan(4/7) ≈ 29.7° . . . angle between AC and +x axis

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Which equation is equivalent to 2 Superscript 4 x Baseline = 8 Superscript x minus 3?
marshall27 [118]

Answer:

2 Superscript 4 x Baseline = 2 Superscript 3 x minus 9

8^(x-3) = 2^(3x-9)

Step-by-step explanation:

2⁴ × 8^(x - 3)

2⁴ × (2³)^(x-3)

2⁴ × 2^(3x - 9)

Since the bases are same now, powers can be added

2^(4 + 3x - 9)

2^(3x - 5)

4 0
3 years ago
Read 2 more answers
Write the equation for the inverse of y=4arccot(
garri49 [273]
I think you meant "y = 4 arccot (x)."  

This is equivalent to:

 y
---- = arccot x
 4

and so cot (y/4) = x
8 0
2 years ago
Olaf earned $416.03 commission on his sales of $9245.00. What was his rate of commission?
Crank

Answer:

$1 per $22.22 sold.

Step-by-step explanation:

To find this answer, I divided his sales by his amount earned.

9245.00/416.03=22.22

This shows the for every 22.22 dollars sold, he recieved one dollar in commission.

Hope this helped! Thanks for posting your question! If correct, please award brainliest!

8 0
2 years ago
A basketball-player scores a free-throw with probability 0.9. What is the probability that her first miss occurs on the 6th shot
-BARSIC- [3]

Answer:

Pr = 0.059049

Step-by-step explanation:

Given

p = 0.9 --- probability of scoring

Required

Probability that his first miss is his 6th shot

Let q represent the event that he did not score.

Using complement rule:

q = 1 - p = 1 - 0.9 = 0.1

The event that his first miss is his 6th is represented as:

p p p p p q ---- That he scoress the first 5 attempts

So, the probability is:

Pr = p^5 * q

Pr = 0.9^5 * 0.1

Pr = 0.059049

7 0
3 years ago
We are interested in the dimensions of a certain rectangle. this rectangle has length twice the side of the square and width thr
Mila [183]
Area of square = s^2
Area of Rectangle = lw
l = 2s

w+3 = s
solve for w, w=s-3
Now we have l and w.
Plug both into area of rectangle formula so: (2s)(s-3)
Since both areas are equal set both equations equal to each other:
(2s)(s-3)=s^2
Now simplify
2s^2-6s=s^2
s^2-6s=0, Solve for s.
Factor polynomial. s(s-6)=0 , s can be equal to 0 or 6. HOWEVER, you cannot have a side length of 0 therefore the side length has to be 6.
Now plug in s for the length formula for the rectangle:
l = 2s so... l = 2(6) so length of rectangle = 12.
Now plug in s for the width formula for the rectangle:
w+3=s so... w+3=6 so width of rectangle = 3.
Now the dimensions of the rectangle are 12 by 3. 12 being length and 3 width.
To CHECK:
Find area of rectangle:
A=lw so A=3 times 12 so A=36
Find area of square:
We know the side is equal to 6 so
A=s^2 so 6^2 = 36
The areas are equal that verifies the answer of 12 by 3.
8 0
3 years ago
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