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3 years ago

A baseball will reach heighth feet artert seconds, as

Mathematics

1 answer:

romanna [79]3 years ago

6 0

Answer:

1 and 37/8 feet

Step-by-step explanation:

We set h(t) to 76 because we want to know when the ball will be at 76 feet high.

So, we have 76=-16t^2+90t+2. When we subtract 76 from both sides, we get -16t^2+90t-74=0, and when you mutiply the equation by -1 (so that x^2 has a positive coefficient, which makes things easier), we get 16t^2-90t+74=0.

We notice that each separate monomial has a common factor, 2, so we can take that out and make it 2(8t^2-45t+37) = 0. Factoring the quantity in the parentheses gives us 2(t-1)(8t-37) = 0.

Using Zero Product Property, we can set the two factors in parentheses to 0 (the 2 isn't really relevant so we don't need to worry about it). This gives us t-1=0 and 8t-37=0. Solving these two equations gives us t = 1 foot or t = 37/8 feet.

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HELP NEEDED!!! WILL MARK BRAINLIEST!!!

erma4kov [3.2K]

Answer:

$x(x + 1)$

Step-by-step explanation:

$\frac{2x + 1}{ \frac{1}{x} + \frac{1}{x + 1} }$

Make denominators same:

$\frac{2x + 1}{ \frac{x + 1}{x(x + 1)} + \frac{x}{(x + 1)} }$

Add the numerators:

$\frac{2x + 1}{ \frac{x + 1 + x}{x(x + 1)} }$

$\frac{2x + 1}{\frac{2x + 1}{x(x + 1)} }$

Apply the rule:

$\frac{a}{ \frac{b}{c} } = \frac{a \times c}{b}$

Therefore,

$\frac{(2x + 1)\times x(x + 1))}{2x + 1}$

Cancel out common factor of 2x+1:

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6 0

3 years ago

Find the lateral surface area of this

Ksenya-84 [330]

Answer:

$A=157.07\ cm^2$

Step-by-step explanation:

Given that,

The radius of a cylinder, r = 5 cm

Height of the cylinder, h = 5 cm

We need to find the lateral surface area of the cylinder. The formula for the lateral surface area of the cylinder is given by :

$A=2\pi r h$

Put all the values,

$A=2\pi\times 5\times 5\\\\=157.07\ cm^2$

So, the lateral surface area of the cylinder is $157.07\ cm^2$ .

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3 years ago

What is the vertex of this parabola? y= 2x² + 4x +5

uranmaximum [27]

Answer:

vertex = (- 1, 3 )

Step-by-step explanation:

Given a parabola in standard form

y = ax² + bx + c ( a ≠ 0 )

Then the x- coordinate of the vertex is

$x_{vertex}$ = - $\frac{b}{2a}$

y = 2x² + 4x + 5 ← is in standard form

with a = 2, b = 4, then

$x_{vertex}$ = - $\frac{4}{4}$ = - 1

Substitute x = - 1 into the equation for corresponding value of y, that is

y = 2(- 1)² + 4(- 1) + 5 = 2 - 4 + 5 = 3

vertex = (- 1, 3 )

6 0

3 years ago

The wildflowers at a national park have been decreasing in numbers. There were 1200 wildflowers in the first year that the park

bonufazy [111]

Year New flowers

1 1200

2 300

3 75

There were 1200 wildflowers in the first year that the park started tracking them. Since then, there have been one fourth as many new flowers each year

Initially there are 1200 flowers and start decreasing by $\frac{1}{4}$

So first term is 1200 and common ratio is $\frac{1}{4}$ .

Its a geometric sequence so summation becomes

i =1∑ ∞ 1200( $\frac{1}{4})^{i-1}$

Now we find the sum

We use sum formula

$Sum = \frac{a}{1-r}$

Where a is the first term , a= 1200

r is the common ratio , r= 1/4

$Sum = \frac{1200}{1-(\frac{1}{4})}$

$Sum = \frac{1200}{\frac{3}{4}}$

Sum = 1600 wildflowers

4 0

3 years ago

Please help pls pls help pls belp

Delvig [45]

Answer:

After 1 second, the ball will reach a maximum height of 16 feet

Step-by-step explanation:

The height of the ball after t seconds: h(t) = -16t^2 + 32t

The graph of this quadratic function is parabola which opens downwards. The vertex of a quadratic equation is the maximum or minimum point on the equation's parabola

t = -b/2a = -(32)/2(-16) = -32/-32 = 1 second

then

h(t) = -16(1)^2 + 32(1) = -16 + 32 = 16

After 1 second, the ball will reach a maximum height of 16 feet

8 0

2 years ago