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Westkost [7]
3 years ago
7

SOLVE THE QUESTION BELOW ASAP

Mathematics
1 answer:
qwelly [4]3 years ago
8 0

Answer:

Part A) The graph in the attached figure (see the explanation)

Part B) 16 feet

Part C) see the explanation

Step-by-step explanation:

Part A) Graph the function

Let

h(t) ----> the height in feet of the ball above the ground

t -----> the time in seconds

we have    

h(t)=-16t^{2}+98

This is a vertical parabola open downward (the leading coefficient is negative)

The vertex is a maximum

To graph the parabola, find the vertex, the intercepts,  and the axis of symmetry

<em>Find the vertex</em>

The function is written in vertex form

so

The vertex is the point (0,98)

Find the y-intercept

The y-intercept is the value of the function when the value of t is equal to zero

For t=0

h(t)=-16(0)^{2}+98

h(0)=98

The y-intercept is the point (0,98)

Find the t-intercepts

The t-intercepts are the values of t when the value of the function is equal to zero

For h(t)=0

-16t^{2}+98=0

t^{2}=\frac{98}{16}

square root both sides

t=\pm\frac{\sqrt{98}}{4}

t=\pm7\frac{\sqrt{2}}{4}

therefore

The t-intercepts are

(-7\frac{\sqrt{2}}{4},0), (7\frac{\sqrt{2}}{4},0)

(-2.475,0), (2.475,0)

Find the axis of symmetry

The equation of the axis of symmetry in a vertical parabola is equal to the x-coordinate of the vertex

so

x=0 ----> the y-axis

To graph the parabola, plot the given points and connect them

we have

The vertex is the point (0,98)

The y-intercept is the point (0,98)

The t-intercepts are (-2.475,0), (2.475,0)

The axis of symmetry is the y-axis

The graph in the attached figure

Part B) How far is the artifact fallen from the time t=0 to time t=1

we know that

For t=0

h(t)=-16(0)^{2}+98

h(0)=98\ ft

For t=1

h(t)=-16(1)^{2}+98

h(1)=82\ ft

Find the difference

98\ ft-82\ ft=16\ ft

Part C) Does the artifact fall the same distance from time t=1 to time t=2 as it does from the time t=0 to time t=1?

we know that

For t=1

h(t)=-16(1)^{2}+98

h(1)=82\ ft

For t=2

h(t)=-16(2)^{2}+98

h(2)=34\ ft

Find the difference

82\ ft-34\ ft=48\ ft

so

The artifact fall 48 feet from time t=1 to time t=2 and fall 16 feet from time t=0 to time t=1

therefore

The distance traveled from t=1 to t=2 is greater than the distance traveled from  t=0 to t=1

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<h3>Given :-</h3>

  • Perimeter of triangle = 42

  • Side 1 of triangle = (x + 4)

  • Side 2 of triangle = (3x + 8)

  • Side 3 of triangle = (5x + 6)

<h3>To find:-</h3>

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<h3>Explanation:</h3>

So to find length of sides we have to find the value of x.We can find value of x , by this formula:

\\  \\

\bigstar \boxed{ \rm perimeter \: of \triangle \:  = side_1 + side_2 + side_3}

\\  \\

So:-

\\

\dashrightarrow \tt perimeter \: of \triangle \:  = side_1 + side_2 + side_3 \\

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\dashrightarrow \tt 42  = (x + 4) + (3x + 8)+( 5x + 6) \\

\\  \\

\dashrightarrow \tt 42  = x + 4+ 3x + 8+5x + 6 \\

\\  \\

\dashrightarrow \tt 42  = x + 3x+5x+ 4 + 8 + 6 \\

\\  \\

\dashrightarrow \tt 42  = 9x+ 4 + 8 + 6 \\

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\dashrightarrow \tt 42  = 9x+ 18\\

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\dashrightarrow \tt 42  - 18 = 9x \\

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\dashrightarrow \tt 24 = 9x \\

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\dashrightarrow \tt  9x = 24 \\

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\dashrightarrow \tt  x = \dfrac{24}{9}  \\

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\dashrightarrow \bf  x =2.67 \{approx \}\\

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  • Side 1 of triangle = (x + 4)
  • Side 1 of triangle =2.67 + 4
  • Side 1 of triangle = 6.67

  • Side 2 of triangle = 3x + 8
  • Side 2 of triangle = 3 × 6.67 + 8
  • Side 2 of triangle = 20.01 + 8
  • Side 2 of triangle = 28.01

  • Side 3 of triangle = 5x + 6
  • Side 3 of triangle = 5 × 2.67 + 6
  • Side 3 of triangle = 13.35 + 6
  • Side 3 of triangle = 19.35

━━━━━━━━━━━━━━━━

~WindyMint

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siniylev [52]
The answer is a: 80%
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What is the inverse of f(x)=3x-1
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Answer:

$ \frac{(y + 1)}{3} $

Step-by-step explanation:

Call $ f(x) = y = 3x - 1 $

Now, $ y + 1 = 3x $

$ \implies \frac{y + 1}{3} = x $

This is the inverse of the given function.

You can cross - verify it by substituting a point, say, $ (1,3) $

We see that the point satisfies both the equations.

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1. A school store sells pencils and erasers before school opens each day. On Monday, 13 pencils and
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Answer:

price of pencil is 0.74 and eraser is 0.72$

Step-by-step explanation:

Let, "p" represent pencils

and "e" represents erasers.

hence, according to question

13p+10e=16.75 ________(1)

and 25p+2e=19.85________(2)

Multiplying equation (2) by 5,

hence, 125p+10e=99.25________(3)

Substracting equation (3) and (1)

125p+10e-(13p+10e)=99.25-16.75

hence, 112p=82.5

p=0.74

substituting the value in equation (1),

13(0.74)+10e=16.75

9.57+10e=16.75

on solving,

e=0.72

hence, price of one pencil is 0.75$, and price of one eraser is $0.72

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