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trasher [3.6K]
3 years ago
11

The sum of two numbers is 38. Their difference is 50. What are the numbers? 20 POINTS

Mathematics
1 answer:
enot [183]3 years ago
7 0
Let, the numbers = x,y
Now, x + y = 38
x - y = 50, x = 50 + y

Substitute it into first equation,
50 + y + y = 38
2y = 38 - 50
y = -12 / 2
y = -6

Substitute it into first equation,
x - 6 = 38
x = 38 + 6 = 44

So, your final answer is x = 44 & y = -6

Hope this helps!
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3 years ago
2. When Joey dives off a diving board, the equation of his pathway can be modeled by h = -16- + 15 + 12.
Sergeu [11.5K]

Answer:

a) The maximum height is approx 15.5 unit.

b) The time it will take for Joey to reach the water is 1.45 hour.

Step-by-step explanation:

Given : When Joey dives off a diving board, the equation of his pathway can be modeled by h(t)= -16t^2+15t + 12

To find : a) Find Joey's maximum height.

b) Find the time it will take for Joey to reach the water.

Solution :

Modeled  h(t)= -16t^2+15t + 12 ....(1)

a) To find maximum height

Derivate (1) w.r.t. t,

h'= -32t+15

For critical point put h'=0,

-32t+15=0

t=\frac{15}{32}

t=0.46875

Derivate again w.r.t. t,

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It is maximum at t=0.46875.

Substitute t in equation (1),

h(0.46875)= -16(0.46875)^2+15(0.46875)+12

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h(0.46875)= 15.515625

The maximum height is approx 15.5 unit.

b) To find the time it will take for Joey to reach the water.

Put h=0 in equation (1),

-16t^2+15t + 12=0

Apply quadratic formula, x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}

Here, a=-16 , b=15, c=12

t=\frac{-15\pm\sqrt{(15)^2-4(-16)(12)}}{2(-16)}

t=\frac{-15\pm\sqrt{225+768}}{-32}

t=\frac{-15\pm\sqrt{993}}{-32}

t=\frac{-15+\sqrt{993}}{-32},\frac{-15-\sqrt{993}}{-32}

t=−0.515,1.453

Reject negative value.

The time is t=1.45.

The time it will take for Joey to reach the water is 1.45 hour.

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3 years ago
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Fofino [41]

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