Answer:
1.5.80 miles
2.9.80ft
3.56 inches
4.5.20 units
5. 13 units
6.5.40 ft
Step-by-step explanation:
⇒These questions are on the Pythagorean relationship
⇒General expression is ;
a²+b²=c² where a and b are values for the legs and c is the hypotenuse
1. Isaiah waked 3 miles north and 5 miles east.
Finding the distance from starting point we apply the equation;
a²+b²=c² where a=5 miles and b=3miles
5²+3²=c²
25+9=c²
34=c²
c=√34 = 5.80 miles
2.The ladder is leaning against the wall to form the hypotenuse side of 10 ft.The distance from the base to the ladder forms side a= 2ft. The question requires you to calculate the height b.
a²+b²=c²
2²+b²=10²
4+b²=100
b²=100-4
b=√96
b=9.80 ft
3. The television has a diagonal of 70 inches to represent side c and a height of 42 inches to represent the side a. The question requires you to find the width of the television which represents the side b
a²+ b²=c²
42²+b²=70²
b²=70²-42²
b=√3136
c=56 inches
4. An equilateral triangle is one that has all its sides and angles equal. Here you have to introduce a perpendicular line from the apex point of the triangle to the base and get the distance a.The using the hypotenuse and the distance a, you can find the height/b.
c= 6 units and a=6/2= 3 units
a²+b²=c² 3²+ b²= 6²
9+b²=36
b²=36-9
b=√27 =5.20 units
5.In this question, you are given the height and the width of the right triangle thus apply the relationship as;
a²+b²=c²..........where a=5 and b=12
5²+12²=c²
25+144=c²⇒⇒⇒c=√169 =13 units
6. In this question, the height of the plant represents side b and the distance of the base from where the string is tied is side b.You are to find the length of the string which represents the hypotenuse side.
a²+b²=c²
5²+2²=c²
25+4=c²
29=c²
√29=c
c=5.40 ft
You know that 6x+3 equals 45 because the two sides are equal. So you first put the equation 6x+3=45. Then you use the subtraction property of equality and subtract 3 from both sides. This gives you 6x=42. Then you divide 6 from both sides to get you final answer, x=7
See the attached figure to better understand the problem
we know that
tan 29°=AC/CB--------> CB=AC/tan 29°
AC=110 ft
CB--------> <span>how far the man is from the helicopter landing pad
</span>so
CB=AC/tan 29°----------> CB=110/ tan 29°----------> CB=198.45 ft
the answer is
the man is 198.45 ft from the helicopter landing pad
We want to see how long will take a healthy adult to reduce the caffeine in his body to a 60%. We will find that the answer is 3.55 hours.
We know that the half-life of caffeine is 4.8 hours, this means that for a given initial quantity of coffee A, after 4.8 hours that quantity reduces to A/2.
So we can define the proportion of coffee that Jeremiah has in his body as:
P(t) = 1*e^{k*t}
Such that:
P(4.8 h) = 0.5 = 1*e^{k*4.8}
Then, if we apply the natural logarithm we get:
Ln(0.5) = Ln(e^{k*4.8})
Ln(0.5) = k*4.8
Ln(0.5)/4.8 = k = -0.144
Then the equation is:
P(t) = 1*e^{-0.144*t}
Now we want to find the time such that the caffeine in his body is the 60% of what he drank that morning, then we must solve:
P(t) = 0.6 = 1*e^{-0.144*t}
Again, we use the natural logarithm:
Ln(0.6) = Ln(e^{-0.144*t})
Ln(0.6) = -0.144*t
Ln(0.6)/-0.144 = t = 3.55
So after 3.55 hours only the 60% of the coffee that he drank that morning will still be in his body.
If you want to learn more, you can read:
brainly.com/question/19599469
