Just number 1 please and explain

Answer:

(a)  144 ft

(b)  2 s

(c)  5 s

(d)  128 ft

Step-by-step explanation:

[tex]h(t) = -16t^2 + 64t + 80[/tex]

Part (a)

To find the turning point of the parabola:

1. differentiate the function:

[tex]\implies h'(t) = -32t + 64[/tex]

2. Set it to zero and solve for t:

[tex]\implies h'(t) =0[/tex]

[tex]\implies -32t + 64=0[/tex]

[tex]\implies 32t = 64[/tex]

[tex]\implies t=2[/tex]

3. Input found value of t back into the function and solve for h:

[tex]\implies h(2) = -16(2)^2 + 64(2) + 80=144[/tex]

Therefore, the maximum height reached by the ball is 144 ft

Part (b)

As found in part (a), the maximum height is reached when t = 2, so the ball reached its maximum height at 2 seconds.

Part (c)

The ball will hit the ground when h(t) = 0

1. Set the function to zero

[tex]\implies h(t)=0[/tex]

[tex]\implies -16t^2 + 64t + 80=0[/tex]

2. Solve for t:

Divide both sides by 16

[tex]\implies -t^2 + 4t + 5=0[/tex]

[tex]\implies t^2 - 4t - 5=0[/tex]

Factor:

[tex]\implies t^2 +t-5t - 5=0[/tex]

[tex]\implies t(t+1)-5(t+1)=0[/tex]

[tex]\implies (t+1)(t-5)=0[/tex]

Therefore:

[tex](t+1)=0 \implies t=-1[/tex]

[tex](t-5)=0 \implies t=5[/tex]

As time is positive, t = 5

So the ball will hit the ground at 5 seconds.

Part (d)

To find the height of the ball after 1 second, input t = 1 into the function and solve for h:

[tex]\implies h(1) = -16(1)^2 + 64(1) + 80=128[/tex]

Therefore, the height of the ball after 1 second is 128 ft

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Parts (a) & (b) - alternative method

Rewrite the function in vertex form by completing the square.

Set the function to zero:

[tex]\implies-16t^2 + 64t + 80=0[/tex]

Subtract 144 from both sides:

[tex]\implies -16t^2+64t-64=-144[/tex]

Factor out -16:

[tex]\implies -16(t^2 - 4t +4)=-144[/tex]

Factor expression in brackets:

[tex]\implies -16(t-2)^2=-144[/tex]

Add 144 to both sides:

[tex]\implies -16(t-2)^2+144=0[/tex]

Therefore:

[tex]\implies h(t)=-16(t-2)^2+144[/tex]

The maximum height is the y-value of the vertex.

The vertex is (2, 144) so the maximum height is 144 ft.

The time the ball reached the max height is the x-value of vertex.

So the time then the ball reached the maximum height is 2 s

There isn't any piece of data during Taylor's experiment which can be taken as  qualitative. Thus, correct choice is: Option D: None are qualitative.

Qualitative data tells about the quality or characteristic. It is tough to express it numerically or not at all expressible numerically. They are usually catagorical.

In contrast, there is quantitative data which can be expressed numerically.

The problem is missing its option, which are:

Mass can be measured (in kgs, grams etc), degree of inclination can be measured (in radians, degree etc), time can be measured (in seconds, minutes etc).

Thus, there isn't any piece of data during Taylor's experiment which can be taken as  qualitative. Thus, correct choice is: Option D: None are qualitative.

Learn more about qualitative and quantitative data here:

https://brainly.com/question/12929865

Answer:

It is squash

Step-by-step explanation:

This is because for every 3 tomatoes there is one squash. 1 squash times 3 is 3. 3 tomatoes times 3 is 9.

Answer:

7/11

Step-by-step explanation:

This is the only fraction without a 1 in its numerator.

Answer:7/11

Step-by-step explanation: unit fractions have 1 unit like 1/2 1/3 1/100 but 7/11 is not have 1 numerator

Answer:

Center: (1,−4)

Radius: 2

Step-by-step explanation:

Answer:

[tex]A=2000e^{0.085t}[/tex]

Step-by-step explanation:

Make sure you understand the formula for continuous compounding first. The formula is:

[tex]A=Pe^{rt}[/tex] where

A= Total

P= Principal (or the amount invested at beginning)

r= Interest rate (as a decimal)

t= Time (in years)

Note: e is an irrational mathematic number similar to π. Its value is around 2.72, but for these problems, you’ll need to use the version already on your calculator that will be called “[tex]e^{x}[/tex].” On most calculators, it can be accessed by 2nd → ln.

Find the values that you are given:

A= What you are looking for

P= 2000

r= 8.5% as a decimal = 0.085

t= What you change

Plug these into the equation:

[tex]A=2000e^{0.085t}[/tex]

This is the answer!

Answer:

See below ↓

Step-by-step explanation:

14.

15.

Answer:

has the app crashed, if not i dont know

Answer:549.81

Step-by-step explanation:because that is thhe answer you get

Answer:

$549.81

Step-by-step explanation:

Price

Money in hand

Money needed

Answer:

yes your answer is 45 degree

Answer:

105°

Step-by-step explanation:

There 360° in a circle, so...

360°-150°-105°=105°

check: 150°+105°+105°= 360°

[Answer] 105°

Answer:

[tex]f^{-1}(x)[/tex] will be equal to 9y+18

Step-by-step explanation:

[tex]f^{-1}(x)[/tex] will be equal to 9y+18

Answer:

Rounded to the nearest whole number is 1

Step-by-step explanation:

when you divide 6 by 5 you get 1.2. Since 2 is not five or greater you round down.

Answer:

  24 square units

Step-by-step explanation:

There are a couple of ways you can figure the area of the frame:

__

The dimensions of the outer rectangle are twice the frame width plus the dimensions of the inner rectangle. That makes them 8 wide by 6 high. Then the difference of areas is ...

  A = (8)(6) -(6)(4) = 48 -24 = 24 . . . . square units frame area

__

The centerline of the frame is a rectangle with 1 unit greater length and width than the inner rectangle. It is 7 units by 5 units, so will have a perimeter of ...

  P = 2(L+W) = 2(7+5) = 24 . . . . units

Then the area of the frame is this length multiplied by the width of the frame:

  A = (24)(1) = 24 . . . . square units frame area

Answer:

12

Step-by-step explanation:

Laura makes 14 dollars an hour and it will take her 12 hours to make a total of $168!

Answer:

4.58257569 meters (Could probably get away with rounding it to 4.6 meters)

Step-by-step explanation:

Pythag theorem

a^2 +b^2 =c^2

Insert your numbers

10^2+b^2=11^2

Simplify squares

100+b^2=121

subtract 100 from both sides

b^2=21

sqrt both sides

sqrt(b^2)=sqrt(21)

simplify sqrts to get b

b= 4.58257569

[tex]__________________________[/tex]

Answer:

1,14,21,28,35,42,42,35,28,21,14,7

Step-by-step explanation:

Area of a circle = pi x r(squared)

= 3.14 x (15)2

= 3.14 x 225

=706.5cm2

Answer:

1. x + y = 180

2. x = 50 y= 130

Step-by-step explanation:

They're parallel.

We can label the unamed angle z.

So z = y

and 50 = x

There's 360 degrees in a circle, so x + y= 180 because it's half 360 and half a circle.

x=50

so 50 + 50 = 100.

360 - 100 = 260

so 260 ÷ 2 = 130

y = 130 because y and z are equal so they're the same number

Step-by-step explanation:

1. x+y=180

hope that helps

Answer:

ans is 10

Step-by-step explanation:

by using pythagoras theorm

26^2=a^2+24^2

a^2=100

a=10

Answer:

$7.13

Step-by-step explanation:

Very simple, we subtract 12.87 from 20 and the answer is 7.13.

So should get back $7.13 as her change

Answer:

  392.5 in²

Step-by-step explanation:

The area of a composite figure is found by decomposing it into areas that you have formulas for. This figure is easily decomposed to a trapezoid and a rectangle.

The base lengths of the trapezoid are 20 in and 9 in. Its height is the difference between the height of its top base (21 in) and the height of its bottom base (16 in). That difference is 5 in.

  A = 1/2(b1 +b2)h

  A = 1/2(20 in + 9 in)(5 in) = 72 1/2 in²

__

The area of a rectangle is the product of its base and height.

  A = bh

  A = (20 in)(16 in) = 320 in²

__

The area of the whole figure is the sum of the areas of its parts.

  area = trapezoid area + rectangle area

  area = 72 1/2 in² +320 in² = 392 1/2 in²

Answer: y=x-6

Step-by-step explanation:

5 quarts I think 4 cups per quart has 5 quarts and 2 cups I think

Answer:

1 quart = 4 cups

8 × 4 = 32

32 - 6 = 26

26 - 18 = 8

he has 2 quarts left

Answer:

(-0.5,-2.5)

Step-by-step explanation:

⇒ 2 + -3 = 5

⇒ 5 / 2 = -0.5

⇒ 4 + -9 = -5

⇒ -5 / 2 = -2.5

→ = (-0.5, -2.5)

Answer:

X = -0.5

Y = -2.5

Step-by-step explanation:

I found this by the forumla determine the X1 and X2 add the together then divide it by 2 for the value of X midpoint. Then add Y1 and Y2 and divide it by 2 together for the value of Y midpoint.

Answer:

42cm

Step-by-step explanation:

It's a rectangle so sides are 6, 6, 15, 15. Σs = 42.

Answer:

A

Step-by-step explanation:

the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

100° is an exterior angle of Δ MLN , then

∠ LMN + 60° = 100° ( subtract 60° from both sides )

∠ LMN = 40°

Answer:

1/17 mL of water

Step-by-step explanation:

5p = 85w

Divide both sides by 85.

5p/85 = 85w/85

p/17 = w

w = p/17

For 1 mL of papaya juice, p = 1.

w = 1/17

1/17 mL of water is used for 1 mL of papaya juice.