Answer: I think its C
Step-by-step explanation:
A car and a truck leave the same intersection, the truck heading north at 60 mph and the car heading west at 55 mph. At what rate is the distance between the car and the truck changing when the car and the truck are 30 miles and 40 miles from the intersection, respectively?
Answer: -81
Step-by-step explanation:
Let x = the car moving towards west = 30
Let y = truck moving towards north = 40
dx/dt = -55
dy/dt = -60
We the use Pythagoras theorem to solve further where,
s² = x² + y²
s² = 30² + 40²
s² = 900 + 1600
s² = 2500
s =✓2500
s = 50
We then differentiate with respect to t, then we will have:
s² = x² + y²
2s ds/dt = 2x ds/dt + 2y dy/dt
50 ds/dt = (30 × -55) + (40 × -60)
50 ds/dt = -1650 - 2400
50 ds/dt = - 4050
ds/dt = -4050/50
ds/dt = -81
(1 pt)What is the vertex of the graph of
the function f(x) = x2 + 6x + 9?
Answer:
(-3,0)
Step-by-step explanation:
A wave is traveling with a speed of 500 m/sec and has a wavelength of 10 m. Determine its frequency.
Answer:
I'm gonna get more people here
Answer:
50 hz yw pplz
Step-by-step explanation:
What is f(4) for the function f(x)= 6x+7?
Answer:
31
Step-by-step explanation:
f(4) = 6x4 + 7
= 24 + 7
= 31
Sarah earns $9 an hour at a Mort’s Pizza Palace, working 20 hours per week. She spends $3 each week for snacks at work, but saves all her other earnings. How many hours must Sarah work to buy a new phone that costs $150?
Answer:
15h
Step-by-step explanation:
Answer:
17 hours
Step-by-step explanation:
she needs 150, she spends 3 and she makes 9 per hour
153/9 = 17
If (4,-3) is the midpoint of the line segment ST and the coordinates of S are (1,5), find the
coordinates of T.
Answer:
[tex](7,-11)[/tex]
Step-by-step explanation:
Given
[tex]S = (1,5)[/tex]
[tex]M = (4,-3)[/tex]
Required
Determine the coordinates of T
Midpoint is calculated as:
[tex]M(x,y) = \frac{1}{2}(x_1 +x_2,y_1+y_2)[/tex]
Where:
[tex](x,y) = (4,-3)[/tex]
[tex](x_1,y_1) = (1,5)[/tex]
Substitute these values in the above formula:
[tex](4,-3) = \frac{1}{2}(1 + x_2,5+y_2)[/tex]
Multiply through by 2
[tex]2 * (4,-3) = 2 * \frac{1}{2}(1 + x_2,5+y_2)[/tex]
[tex](8,-6) = (1 + x_2,5+y_2)[/tex]
By direct comparison:
[tex]1 + x_2 = 8[/tex] and [tex]5 + y_2 = -6[/tex]
Solving for x2
[tex]1 + x_2 = 8[/tex]
[tex]x_2 = 8 - 1[/tex]
[tex]x_2 = 7[/tex]
Solving for y2
[tex]5 + y_2 = -6[/tex]
[tex]y_2 = -6 - 5[/tex]
[tex]y_2 = -11[/tex]
Hence, the coordinates of T is: [tex](7,-11)[/tex]
A communications tower is supported by two wires, connected at the same point on the ground. One is attached to the tower at D and the long-on at C. The angle AD makes with the ground is 30 ° and the angle between the two wires is 10 °. How much below the top of the tower is the shorter one attached?
Answer:
10.99 m
Step-by-step explanation:
✍️What we are basically asked to solve here is to find the distance between C and D.
To find CD, find the length of BC, and BD. Their difference will give us CD.
Thus, BC - BD = CD.
✍️Finding BC using trigonometric ratio formula:
[tex] \theta = 30 + 10 = 40 [/tex]
Opposite side = BC = ??
Adjacent side = 42 m
Thus:
[tex] tan(\theta) = \frac{opposite}{adjacent} [/tex]
Plug in the values
[tex] tan(40) = \frac{BC}{42} [/tex]
Multiply both sides by 42
[tex] tan(40) \times 42 = \frac{BC}{42} \times 42 [/tex]
[tex] 35.24 = BC [/tex]
BC = 35.24 m
✍️Finding BD using trigonometric ratio formula:
[tex] \theta = 30 [/tex]
Opposite side = BD = ??
Adjacent side = 42 m
Thus:
[tex] tan(\theta) = \frac{opposite}{adjacent} [/tex]
Plug in the values
[tex] tan(30) = \frac{BD}{42} [/tex]
Multiply both sides by 42
[tex] tan(30) \times 42 = \frac{BD}{42} \times 42 [/tex]
[tex] 24.25 = BD [/tex]
BD = 24.25 m
✍️How much below the top of the tower is the shorter one attached:
Thus,
BC - BD = CD
35.24 m - 24.25 m = 10.99 m