Answer:
∠A= 45°....
Step-by-step explanation:
To find ∠A first we have to find the length of side B by cosine law:
b^2 = a^2 + c^2 – 2 a c cos B
b^2=(2)^2 +(√3 + 1)^2 - 2(2)(√3 + 1) cos 60
b^2 = 6
Taking square root at both sides:
√b^2 = √6
b= 2.45
Now we can calculate ∠A by sine law:
b / sin B = a / sin A
2.45 / sin 60 = 2 / sin A
sin A= 2* √3/2 /2.45
sin A = 2√3/2 * 1/2.45
sinA = 2√3/ 4.9
sin A = 0.7069
sin A = 0.707
A=45°
Thus ∠A= 45°....
Answer:
x²+5x - 150 = 0
Step-by-step explanation:
Let the length be y and width be x
If the length of a swimming pool is 10 more than 2 times the width, then;
y = 2x+10 ...1
Since the Area is 300m²
A = xy
300 = xy .... 2
Substitute 1 into 2
300 = x(2x+10)
300 = 2x²+10x
Rearrange
2x²+10x - 300 = 0
Divide through by 2
x²+5x - 150 = 0
This gives the required quadratic expression
By definition of <em>linear</em> functions and the comparison with the attached figure, the function that represents the graph is y = (7/15) · x + 4, - 6 ≤ x ≤ 9.
<h3>What kind of function represents the graph?</h3>
Graphically speaking, <em>linear</em> functions represent lines and we see that the line seen in the figure presents two bounds, the points (- 6, 0) and (9, 7). <em>Linear</em> functions are characterized by slope and intercept:
y = m · x + b (1)
Slope
m = (7 - 0)/[9 - (- 6)]
m = 7/15
Intercept
b = 4
By definition of <em>linear</em> functions and the comparison with the attached figure, the function that represents the graph is y = (7/15) · x + 4, - 6 ≤ x ≤ 9.
To learn more on linear functions: brainly.com/question/14695009
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X-intercept is -1 implies line passes through (-1,0).
So point slope form is
y - 0 = -2 (x -(-1) )
>> y = -2 (x +1) <----- FINAL ANSWER
Answer:
Step-by-step explanation:
V, r, h are the volume, radius, and height, respectively.
V = πr²h = 9πr²
The only error in your previous answers was that you forgot the π.
if r = 1, V = 9π1² = 9π ≅ 28 in³
if r = 2, V = 9π2² = 36π ≅ 113 in³
if r = 3, V = 9π3² = 81π ≅ 254 in³
