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photoshop1234 [79]
2 years ago
5

During batting practice, two pop flies are hit from the same location, 2 s apart. The paths are modeled by the equations h = -16

t^2 + 56t and h = -16t^2 + 156t - 248, where t is the time that has passed since the first ball was hit. Explain how to find the height at which the balls meet. Then find the height to the nearest tenth.
Mathematics
1 answer:
Schach [20]2 years ago
4 0

Answer:

2.5 seconds since the first ball was hit.

Step-by-step explanation:

The equations that model the heights are:

  • h = -16t² + 56t
  • h = -16t² + 156t - 248

When the balls meet, both heights are equal, therefore:

-16t² + 56t = -16t² + 156t - 248

-16t² + 56t + 16t² - 156t + 248 = 0

- 100t + 248 = 0

248 = 100t

248/100 = t

t = 2.48 ≈ 2.5

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Hello there. =)

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1 year ago
The area of the surface of the swimming pool is 210 square feet. what is the lenght d of the deep end (in feet)?
madreJ [45]
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3 0
2 years ago
- In the following diagram of triangle QRS, QR = 8 and QS = 17. Determine the value of sin Q. Show how you
dimaraw [331]

Answer:

SinQ=\frac{15}{17}

Step-by-step explanation:

We draw the right triangle as shown in the image attached.

Δ QRS

Where R is the right angle

Given

QR = 8

QS = 17

Now, using Pythagorean Theorem, we can find RS:

QR^2+RS^2=QS^2\\8^2+RS^2=17^2\\RS^2=17^2-8^2\\RS^2=225\\RS=\sqrt{225}\\RS=15

Now, we know the ratio Sine as:

Sin(\theta)=\frac{Opposite}{Hyotenuse}

Where \theta is the angle (here angle Q)

Opposite side is RS (which is 15)

Hypotenuse is given as QS (which is 17)

So,

SinQ=\frac{15}{17}

This is the value of SinQ.

We don't want the angle, so we'll stop here.

5 0
2 years ago
Sum of positive roots of the equation (x2 - 12x + 35) (x2 + 10x + 24) = 504 is
Digiron [165]

Answer:

(3)11

Step-by-step explanation:

We are given that

(x^2-12x+35)(x^2+10x+24)=504

We have to find the sum of positive roots of the equation.

x^2(x^2+10x+24)-12x(x^2+10x+24)+35(x^2+10x+24)=504

x^4+10x^3+24x^2-12x^3-120x^2-288x+35x^2+350x+840=504

x^4-2x^3-61x^2+62x+840-504=0

x^4-2x^3-61x^2+62x+336=0

Factor of 336

2,3,4,6,8,7,

Let x=2

2^4-2^4-61(2^2)+62(2)+336\neq0

x=2 is not the root of equation

x=-2

(-2)^4-2(-2)^3-61(-2)^2+62(-2)+336=0

Hence x=-2 is the root of equation.

x+2 is a factor of equation.

x=3

3^4-2(3^3)-61(3^2)+62(3)+336=0

Therefore, x=3  is the root of equation.

(x+2)(x-3)(x^2-x-56)=0

(x+2)(x-3)(x^2-8x+7x-56)=0

(x+2)(x-3)(x(x-8)+7(x-8))=0

(x+2)(x-3)(x-8)(x+7)=0

x-8=0\implies x=8

x+7=0\implies x=-7

Positive roots are 3 and 8

Sum of positive roots=3+8=11

Option (3) is true.

4 0
2 years ago
What is the point of intersection when the system of equations below is graphed on the coordinate plane? (1, –3) (–1, 3) (1, 3)
Ainat [17]

( - 1 - 3)
it's lower
5 0
2 years ago
Read 2 more answers
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