1. 5/ 8+root 7
A. 5/57
B. 5 root 7 /15
C. 5- root 7/8
D. 40- 5 root 7/ 57
My answer I had two was not sure A and D .
2. An object 8.1 feet tall casts a shadow that is 24.3 feet long. How long in feet would the shadow be for an object which is 17.4 feet tall?
A. 1.2 feet
B. 5.8 feet
C. 3.3 feet
D. 52.2 feet
I am not sure my answer was C and A.
5/(8+√7) = 5(8-√7)/(64-7) = (40-5√7)/57
So, (D). It should have been obvious that (A) was out, since it had no √√ involved.
Draw a diagram. Using similar triangles,
s/17.4 = 24.3/8.1
s = 52.2
(D)
All the others should have been easily eliminated since the given shadow was longer than the object casting it. Roughly 3 times as long. That ratio wojuld be the same for all objects at the same place.
Thanks Steve !!
To solve these questions, let's walk through the steps together!
1. To simplify the expression 5/8 + √7, we need to combine the terms. Since we cannot directly add a fraction to a square root, we will leave the answer in the form of a mixed expression.
To do this, we need to rationalize the denominator of the fraction. We can multiply both the numerator and denominator by the conjugate of the denominator, which is 8 - √7.
(5/8 + √7) * (8 - √7) / (8 - √7)
Multiplying the numerator and denominator using the distributive property, we get:
(40 - 5√7 + 8√7 - 7) / (64 - 7)
Simplifying the numerator, we get:
(33 + 3√7) / 57
So, the final answer is (C) 5 - √7/8.
2. To find the length of the shadow, we can use the concept of similar triangles. The ratio of the height of the object to the length of its shadow should be the same as the ratio of the height of the second object to the length of the second shadow.
Let's set up the following proportion:
8.1 feet / 24.3 feet = 17.4 feet / x feet
To find x, we can cross-multiply the proportion:
8.1 * x = 17.4 * 24.3
Dividing both sides by 8.1, we get:
x = (17.4 * 24.3) / 8.1
Simplifying the expression, we find:
x = 52.2
So, the length of the shadow for an object that is 17.4 feet tall would be 52.2 feet.
Therefore, the correct answer is (D) 52.2 feet.