Answer:
91.8 ft
Step-by-step explanation:
So we can talk about the diagram, let's name a couple of points. The base of the tree is point T, and the top of the tree is point H. We want to find the length of TH given the length AB and the angles HAT and ABT.
The tangent function is useful here. By its definition, we know that ...
TA/BA = tan(∠ABT)
and
TH/TA = tan(∠HAT)
Then we can solve for TH by substituting for TA. From the first equation, ...
TA = BA·tan(∠ABT)
From the second equation, ...
TH = TA·tan(∠HAT) = (BA·tan(∠ABT))·tan(∠HAT)
Filling in the values, we get ...
TH = (24.8 ft)tan(87.3°)tan(9.9°) ≈ 91.8 ft
The height <em>h</em> of the tree is about 91.8 ft.
Answer:
1) y = (x + 8)² + 7; 5) y = (x - 6)² + 10; 7) y = (x - 3)² - 4
Step-by-step explanation:
Complete the square in order to figure these out. To complete the square, use the formula <em>[½B]</em><em>²</em><em>.</em><em> </em>Each time you do this, you get a perfect trinomial in the form of a product of two monomials [<em>h</em>], then you have to figure out how much more to deduct from or add on to your <em>C</em><em> </em>they gave you in each exercise [<em>k</em>].
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Answer:
Sipho catches up Jabu at 6:30 pm
Step-by-step explanation:
Jabu left town A to travel to town B at 6:00 a.m. he drove at an average speed of 80km/h.
At 8:30 am, when Sipho leaves, we will have traveled 2.5 hours at 80 km/h, so he will be 80*2.5 = 200 km ahead.
From then, his position will be given by:
Sipho left town A to travel to town B. He drove at an average speed of 100 km/h.
His position will be given by:
At what time will Sipho catch up jabu?
He will catch up in t hours, and t is found when:
So
He will catch up 10 hours after 8:30 am, that is, 6:30 pm.
Sipho catches up Jabu at 6:30 pm
9514 1404 393
Answer:
x
Step-by-step explanation:
There is already an expression given for x, so that is the easiest variable to substitute for.
Substituting for x using the second equation, you have ...
-3(-2y+14) +y = -14
6y -42 +y = -14
7y = 28
y = 4
x = -2(4) +14 = 6
The solution is (x, y) = (6, 4).
_____
Substitution for x is the easiest.
__
The first equation could be rearranged to give an expression for y:
y = 3x -14
Then that can be used to substitute for y in the second equation. My lazy brain judges that to be more work.
The answer would be 9.4 miles.
