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d1i1m1o1n [39]
3 years ago
12

Car b is 250 miles east from car a, car b is traveling west 60mph while car a is traveling north 80mph. What is the minimum dist

ance between the two cars? What time does the minimum distance occur?​
Mathematics
1 answer:
Bogdan [553]3 years ago
8 0

Answer:

d = 200 miles

t = 1.5 hrs after start

Step-by-step explanation:

Set the origin at car a starting point.

equation for distance to car b

x = 250 - 60t

equation for distance to car a

y = 80t

distance between car a and car b

d = √((250 - 60t)² + (80t)²)

d = √(62500 - 30000t + 3600t² + 6400t²)

d = √(62500 - 30000t + 10000t²)

d = 100√(6.25 - 3t + t²)

setting the derivative to zero

0 = 100t - 150 / √(t² - 3t - 6.25)

The denominator cannot be zero, so the numerator must

0 = 100t - 150

150 = 100t

t = 1.5 hrs

d = √((250 - 60(1.5))² + (80(1.5))²)

d = √(160² + 120²)

d = 200 miles

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C. (0,2) if you plot these points correctly on a graph, the center is at 0,2. hope this helped.
6 0
3 years ago
Seventy concert tickets were sold for $550. each adult ticket cost $9 and each childrens ticket cost $5. find the number of adul
PilotLPTM [1.2K]

Answer:

Total tickets = 70

Total cost = $550

Adult's ticket = $9

Child's ticket = $5

Difference = 9 - 5 = $4

Assume all 70 are child's tickets

5 x 70 = 350

But the total cost was 550

550 - 350 = $200

The $200 must have come from Adult's tickets, which has a difference of $4.

200 ÷ 4 = 50

So there are 50 adult's tickets.

70 - 50 = 20

And there are 20 child's tickets.

Hope this helps - Itz.Jordan

5 0
2 years ago
Find the measure of each internal angle of the triangle!!!!!​
defon

Answer:

x=35

'x-10'=25 degrees

'x'=35 degrees

The last one is 120 degrees

Step-by-step explanation:

A straight line is 180 degrees

180-60=120

2x+110=180

2x=70

x=35

8 0
3 years ago
The number of cases of a new disease can be modeled by the quadratic regression equation y = -2x^2 + 40x + 8. What is the best p
Stels [109]

Answer:

158 cases

Step-by-step explanation:

Given tbe quadratic regression model :

y = -2x^2 + 40x + 8

y = number of cases of a new disease

x = number of years

The predicted number of cases of a new disease in 15 years can be calculated thus ;

Put x = 15 in the equation ;

y = -2(15)^2 + 40(15) + 8

y = - 2 * 225 + 600 + 8

y = - 450 + 600 + 8

y = 158

158 cases

5 0
2 years ago
Determine the number of possible triangles, ABC, that can be formed given A = 30°, a = 7, and b = 18.
zzz [600]

Answer:

none

Step-by-step explanation:

We are given a triangle ABC with ∠A = 30°, sides a = 4 and b = 10.

According to the 'Law of Sines- Ambiguous Case', we have,

If a < b×sinA, then no triangle is possible.

If a = b×sinA, only one triangle is possible

If a > b×sinA, two triangles are possible.

So, we have,

b×sinA = 10 × sin30 = 10 × 0.5 = 5.

Now, as

4 = a < bsinA = 5.

We get, according to the rule, no triangle is possible.

8 0
2 years ago
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