An arborist wants to prune an oak tree that has grown too tall. The arborist takes a 15-foot ladder and places it on a horizonta
l surface on the ground so it leans against the tallest part of the tree trunk. If the bottom part of the ladder makes an angle of 70 degrees with respect to the ground, what is the distance between the ladder and the tree trunk?
1 answer:
See the attached picture to better understand the problem
we know that
in the right triangle ABC
cos 70=adjacent side angle 70/hypotenuse
adjacent side angle 70=BC----> <span>distance between the ladder and the tree trunk
hypotenuse=AC------> 15 ft
cos 70=BC/AC-------> solve for BC
BC=AC*cos 70------> BC=15*cos 70-----> BC=5.13 ft
the answer is
the </span>distance between the ladder and the tree is 5.13 ft<span>
</span>
we know that
in the right triangle ABC
cos 70=adjacent side angle 70/hypotenuse
adjacent side angle 70=BC----> <span>distance between the ladder and the tree trunk
hypotenuse=AC------> 15 ft
cos 70=BC/AC-------> solve for BC
BC=AC*cos 70------> BC=15*cos 70-----> BC=5.13 ft
the answer is
the </span>distance between the ladder and the tree is 5.13 ft<span>
</span>
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<u>Corrected Question</u>
Is the function given by:
continuous at x=4? Why or why not? Choose the correct answer below.
Answer:
(D) Yes, f(x) is continuous at x = 4 because
Step-by-step explanation:
Given the function:
A function to be continuous at some value c in its domain if the following condition holds:
- f(c) exists and is defined.
exists.
At x=4
Therefore:
By the above, the function satisfies the condition for continuity.
The correct option is D.
1/4x - 2 = 3/8
First, to start solving this, we can rearrange our fraction. Let's take 1/4x and change it to x/4. Why? Well, a variable can also be considered as the number 1.
Second, now we can continue solving for our variable (x). Let's add 2 to each side.
Third, let's simplify 3/8 + 2. (3/8 + 2 = 2.375 =19/8)
Fourth, continue trying to get the variable by itself. Multiply each side by 4.
Fifth, let's simplify 19/8 × 4. This is simple. Leave the denominator be and just do 19 × 4, which equals 76.
Sixth, our final step is to simplify our fraction. To do so, we will need to list the factors of the numerator and denominator and find the greatest common factor (GCF).
Factors of 76: 1, 2, 4, 19, 38, 76
Factors of 8: 1, 2, 4, 8
Since 4 is our first common factor, it is considered our GCF.
Seventh, now let's divide. Divide both the numerator and denominator by the GCF (4) to create our new simplified fraction.
Answer in fraction form:
Answer in decimal form:
First, to start solving this, we can rearrange our fraction. Let's take 1/4x and change it to x/4. Why? Well, a variable can also be considered as the number 1.
Second, now we can continue solving for our variable (x). Let's add 2 to each side.
Third, let's simplify 3/8 + 2. (3/8 + 2 = 2.375 =19/8)
Fourth, continue trying to get the variable by itself. Multiply each side by 4.
Fifth, let's simplify 19/8 × 4. This is simple. Leave the denominator be and just do 19 × 4, which equals 76.
Sixth, our final step is to simplify our fraction. To do so, we will need to list the factors of the numerator and denominator and find the greatest common factor (GCF).
Factors of 76: 1, 2, 4, 19, 38, 76
Factors of 8: 1, 2, 4, 8
Since 4 is our first common factor, it is considered our GCF.
Seventh, now let's divide. Divide both the numerator and denominator by the GCF (4) to create our new simplified fraction.
Answer in fraction form:
Answer in decimal form: