You throw a baseball upward with an initial velocity of 35 feet per second. The height h (in feet) of the baseball relative to your glove is modeled by the position function
h(t) = −16t² + 35t,
where t is the time in seconds. How long does it take for the ball to reach your glove? (Round your answer to one decimal place.)

Step-by-step explanation:

use the law of sine :

a/sin(A) = b/sin(B) = c/sin(C)

and therefore also

sin(A)/a = sin(B)/b = sin(C)/c

where the lines and corresponding angles are always opposite of each other.

and remember, the sum of all angles in a triangle is always 180°.

and sin(x) = sin(180-x).

so, we have

sin(32)/43 = sin(B)/53

sin(B) = 53×sin(32)/43 = 0.653156302...

B = 40.77999844...° ≈ 41°

C = 180 - 32 - 40.77999844... = 107.2200016...° ≈ 107°

43/sin(32) = c/sin(107.2200016...)

c = 43×sin(107.2200016...)/sin(32) = 77.507143... ft

≈ 78 ft

B' = 180 - B = 139.2200016...° ≈ 139°

C' = 180 - 32 - 139.2200016... = 8.779998438...° ≈ 9°

43/sin(32) = c'/sin(8.779998438...)

c' = 43×sin(8.779998438...)/sin(32) = 12.38595519... ft

≈ 12 ft

To find the tangent line of the graph:

 ⇒ must find:

Let's find the point at which the tangent line touches the graph:

   At x = -1,

           [tex]y = ((-1)^3+2)^5=(-1+2)^5=1^5=1[/tex]

     Point: (-1,1)

Let's find the slope of the tangent line

  ⇒ get the derivation of function than plug (-1) in the x-position to get

       the exact slope

          [tex]\frac{d}{dx}(x^3+2)^5=5(x^3+2)^4*\frac{d}{dx}(x^3+2)=5(x^3+2)^4*3x^2\\ \\ 5((-1)^3)+2)^4*3(-1)^2=5(-1+2)^4*3*1=5*(1)^4*3=5*1*3=15[/tex]

    Slope of tangent line: 15

Now put all the calculated value into the point-slope form:

    [tex](y-y_{0})=m(x-x_{0} )[/tex]

   So:

     [tex](y-1)=15(x+1)\\y - 1= 15x + 15\\y = 15x + 15 + 1\\y = 15x + 16[/tex]

Thus the tangent line's equation is y = 15x + 16

Answer: y = 15x + 16

Hope that helps!

To simulate the probability in a spinner divide the spinner into colors depending on the probability each color represents.

This word refers to the likelihood for an event to occur. Moreover, it is often expressed either as a fraction, a percentage, or a number.

In this case, each of the colors represents a probability:

Due to this, the best is to divide the spinner by colors and considering the percentanges of each color. For example 40% of the spinner should be red, while 15% should be orange.

Learn more about spinner in: https://brainly.com/question/24280611

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Answer:

C. Distribution 3

Step-by-step explanation:

The more spread out a data distribution is, the greater its standard deviation.

To find the height of Replica,

Dialted scale factor=1in=20ft

So height of replica

Answer:

B) 77.5 square feet

Step-by-step explanation:

cut shape into rectangle and triangle

area of rectangle = x*y

area of rectangle = 5*13

area of rectangle = 65

area of triangle = (z-x)*(y-w)/2

area of triangle = 5*3/2

area of triangle = 7.5

Total area = 65 + 7.5

Total area = 77.5, B)

Answer:

77.5

Step-by-step explanation:

Cut the figure into a triangle and a rectangle

XxY=65

Z-x=5

Y-W=5

5x5=25

25/2=13.5

65+35.5=77.5

Answer:

the length of the rectangle is 50 ft

Step-by-step explanation:

A-LW

1,750=L(35)

divide both sides by 35

L= 50

Answer:

0.5km

[tex]1km = 1000m \\ x = 50m \\ \\ 50m \times 1km = 1000 \times x \\ x = 0.5km[/tex]

Use the Midpoint Rule Kelly travels 12m/s more than Chris does during the first ten seconds.

The midpoint rule is the rule that follows the median of a set of values which is the middle value when the values are written in numerical order.

From the table above, the midpoint for the velocity of Chris car = 81, while the midpoint for the velocity of Kelly's car = 93

Therefore, the Kelly's car travelled 93-81 = 12 m/s farther than Chris does during the first ten seconds.

Learn more about median here:

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Answer:

Step-by-step explanation:

The hypotenuse is 16 and the adjacent angle is x.

So using SohCahToh

O is opposite, H is the hypotenuse, and A is adjacent.

Soh: sin(theta)= O/H

Cah: cos(theta)= A/H
Toh: tan(theta)= O/A

Any side length that is next to degree 60° is adjacent so x is adjecent.

Using Cah.

cos(theta)= A/H

cos(60°)= x/16

x=16*cos(60°)

x=16*1/2

x=8

Answer:

18

Step-by-step explanation:

The multiples of 9 are 9,18,27,36,45,54,63,...

The multiples of 6 are 6,12,18,24,30,36,42,...

The log base value is three.

Answer:

0.02 (the first option)

Step-by-step explanation:

This is because a proportion means there is division going on. If 5 out of the 250 students have red hair, this creates a fraction of [tex]\frac{5}{250}[/tex] and when you divide this out: 5 ÷ 250, you get 0.02

Answer: 25.12

Step-by-step explanation:

Circumference = πd or 2πr

Since the radius is given (which is 4) we will use 2πr

2× 3.14×4=

8 × 3.14 =

25.12

hence proved

hope it helps...!!!

Answer:

-2,1 and 3,-2 also -5,-1 and 0,2

Step-by-step explanation:

Answer:

1.) foxes
2.) lynxes
3.) bears
4.) minks
5.) squirrels

Step-by-step explanation: hope this helps ^^ pls mark me brainliest

Answer:

Step-by-step explanation:

The opposing side and the hypotenuse for the angle are given.

Remember, when the opposing side and the hypotenuse are given, take the cos ratio.

Answer:

The answer is 35/9

Step-by-step explanation:

Answer:

123.15

Step-by-step explanation:

Answer:24

Step-by-step explanation:

a^2+b^2=c^2

c^2 has to be 26 because it is the hypotinuce. 10 could take the place of a^2 or b^2, it dose not matter.

a^2+10^2=26^2

a^2+100=676

subtract 100 from both sides

a^2=576

sqrt576

a=24

x=a

x=24

Step-by-step explanation:

-4x – 2y= -18

Add 2y to both sides

-4x- 2y+ 2y = -18 + 2y

Simplify

-4x = -18 + 2y

Divide both sides by -4

-4x/-4= -18/-4+ 2y/-4

simplify

x= - -9+y/2

Answer:

1782 cm²

Step-by-step explanation:

the required surface area =1782

units= cm²

The answer is B because 6*2 = 12 + 11 = 23 !

Answer:

A

Step-by-step explanation:

108/24 finds you the ratio from people surveyed to population

gets you 1:4

so for the 6 who prefer candies you sub it it

6:(4*6)

6:24

so its 24 = A :)

Answer:

1,749

8,349

Step-by-step explanation:

We can multiply 6,600 by 1.265 to get 8,349. To get the percentage all we have to do is multiply 6,600 by .265 and get 1,749.

Hope this helps

Answer:

[tex]\sf{12^{8} }[/tex]

Step-by-step explanation:

12 × 12 × 12 × 12 × 12 × 12 × 12 × 12 = [tex]\sf{12^{8} }[/tex]

[tex]\sf{12^{8} }[/tex] = 429,981,696

An easy way to think of this is that there are 12 is being multiplied by itselg 8 times (there are 8 12s). Similar to how squared numbers work...

Hope this helps! If you need further explanation, let me know!

- profparis

Answer:

12⁸

Step-by-step explanation:

Index forms are used to show how many times a number or variable has been multiplied by itself. 

Here, 12 is being multiplied by itself eight (8) times.

The index form would be:

12⁸

Hope this helps!