Answer:
a. Emily should begin her turn as the third driver at point (1, -0.5).
b. Emily's turn to drive end at point (-2.5, -3.75).
Step-by-step explanation:
Let assume that the group of girls travels from their hometown to San Antonio in a straight line. We know that each location is, respectively:
Hometown
San Antonio
Then, we can determine the end of each girl's turn to drive by the following vectorial expression based on the vectorial equation of the line:
Steph
![S(x,y) = H(x,y) + \frac{1}{4}\cdot [T(x,y)-H(x,y)]](https://tex.z-dn.net/?f=S%28x%2Cy%29%20%3D%20H%28x%2Cy%29%20%2B%20%5Cfrac%7B1%7D%7B4%7D%5Ccdot%20%5BT%28x%2Cy%29-H%28x%2Cy%29%5D)
(1)
![S(x,y) = (8,6) + \frac{1}{4}\cdot [(-6,-7)-(8,6)]](https://tex.z-dn.net/?f=S%28x%2Cy%29%20%3D%20%288%2C6%29%20%2B%20%5Cfrac%7B1%7D%7B4%7D%5Ccdot%20%5B%28-6%2C-7%29-%288%2C6%29%5D)
Andra
![A(x,y) = H(x,y) + \frac{2}{4}\cdot [T(x,y)-H(x,y)]](https://tex.z-dn.net/?f=A%28x%2Cy%29%20%3D%20H%28x%2Cy%29%20%2B%20%5Cfrac%7B2%7D%7B4%7D%5Ccdot%20%5BT%28x%2Cy%29-H%28x%2Cy%29%5D)
(2)
![A(x,y) = (8,6) + \frac{2}{4}\cdot [(-6,-7)-(8,6)]](https://tex.z-dn.net/?f=A%28x%2Cy%29%20%3D%20%288%2C6%29%20%2B%20%5Cfrac%7B2%7D%7B4%7D%5Ccdot%20%5B%28-6%2C-7%29-%288%2C6%29%5D)
Emily
![E(x,y) = H(x,y) + \frac{3}{4}\cdot [T(x,y)-H(x,y)]](https://tex.z-dn.net/?f=E%28x%2Cy%29%20%3D%20H%28x%2Cy%29%20%2B%20%5Cfrac%7B3%7D%7B4%7D%5Ccdot%20%5BT%28x%2Cy%29-H%28x%2Cy%29%5D)
(3)
![E(x,y) = (8,6) + \frac{3}{4}\cdot [(-6,-7)-(8,6)]](https://tex.z-dn.net/?f=E%28x%2Cy%29%20%3D%20%288%2C6%29%20%2B%20%5Cfrac%7B3%7D%7B4%7D%5Ccdot%20%5B%28-6%2C-7%29-%288%2C6%29%5D)
a. <em>If the girls take turns driving and each girl drives the same distance, at what point should they stop from Emily to begin her turn as the third driver? </em>
Emily's beginning point is the Andra's stop point, that is, .
Emily should begin her turn as the third driver at point (1, -0.5).
b. <em>At what point does Emily's turn to drive end?</em>
Emily's turn to drive end at point (-2.5, -3.75).
Your answer would be 6cm by 48cm because if your ratio is 1:8 your second number would be eight times the cm of your first number. 6*8=48
The second condition tells you that
is half the size of
, so
, which could be rewritten in several ways. In standard form, that would be
.
Answer:
angle: 71
x = -3
Step-by-step explanation:
step 1: 180-(55+54) = 71
step 2: x+74=71 (subtract 74 from both sides)
step 3: x=-3
step 4: -3+74=71
Answer:
The length of s is 5.1 inches to the nearest tenth of an inch
Step-by-step explanation:
In Δ RST
∵ t is the opposite side to ∠T
∵ r is the opposite side to ∠R
∵ s is the opposite side to ∠S
→ To find s let us use the cosine rule
∴ s² = t² + r² - 2 × t × r × cos∠S
∵ t = 4.1 inches, r = 7.1 inches, and m∠S = 45°
→ Substitute them in the rule above
∴ s² = (4.1)² + (7.1)² - 2 × 4.1 × 7.1 × cos(45°)
∴ s² = 16.81 + 50.41 - 41.1677568
∴ s² = 26.0522432
→ Take √ for both sides
∴ s = 5.10413981
→ Round it to the nearest tenth
∴ s = 5.1 inches
∴ The length of s is 5.1 inches to the nearest tenth of an inch
