A ball is thrown from an initial height of 3 feet with an initial upward velocity of 21 ft/s. The ball height h (in feet) after t seconds is given by the following. h=3+21t-16t^2 find all values of t for which the balls height is 9 feet.

Answer:

A

Step-by-step explanation:

I believe this is correct, if not feel free to let me know and I will fix it. I'm sorry in advance if it is incorrect.

Answer:

Angle a is not the same as angle y

Step-by-step explanation:

I think

Answer:

37

Step-by-step explanation:

296÷8=37

Hope this helps! :)

Answer:

37 apples will be in 9 boxes

Step-by-step explanation:

296 ÷ 8 = 37

Answer:

a. i. (i + tj + 2tk)/√(1 + 5t²)

ii.  (-5ti + j + 2k)/√[25t² + 5]

b. √5/[√(1 + 5t²)]³

Step-by-step explanation:

a. The unit tangent

The unit tangent T(t) = r'(t)/|r'(t)| where |r'(t)| = magnitude of r'(t)

r(t) = (t, t²/2, t²)

r'(t) = dr(t)/dt = d(t, t²/2, t²)/dt = (1, t, 2t)

|r'(t)| = √[1² + t² + (2t)²] = √[1² + t² + 4t²] = √(1 + 5t²)

So, T(t) = r'(t)/|r'(t)| = (1, t, 2t)/√(1 + 5t²)  = (i + tj + 2tk)/√(1 + 5t²)

ii. The unit normal

The unit normal N(t) = T'(t)/|T'(t)|

T'(t) = dT(t)/dt = d[ (i + tj + 2tk)/√(1 + 5t²)]/dt

= -5ti/√(1 + 5t²)⁻³ + [-5t²j/√(1 + 5t²)⁻³] + [-10tk/√(1 + 5t²)⁻³]

= -5ti/√(1 + 5t²)⁻³ + [-5t²j/√(1 + 5t²)⁻³] + j/√(1 + 5t²)+ [-10t²k/√(1 + 5t²)⁻³] + 2k/√(1 + 5t²)

= -5ti/√(1 + 5t²)⁻³ - 5t²j/[√(1 + 5t²)]⁻³ + j/√(1 + 5t²) - 10t²k/[√(1 + 5t²)]⁻³ + 2k/√(1 + 5t²)

= -5ti/√(1 + 5t²)⁻³ - 5t²j/[√(1 + 5t²)]⁻³ - 10t²k/[√(1 + 5t²)]⁻³ + j/√(1 + 5t²) + 2k/√(1 + 5t²)

= -(i + tj + 2tk)5t/[√(1 + 5t²)]⁻³ + (j + 2k)/√(1 + 5t²)

We multiply by the L.C.M [√(1 + 5t²)]³  to simplify it further

= [√(1 + 5t²)]³ × -(i + tj + 2tk)5t/[√(1 + 5t²)]⁻³ + [√(1 + 5t²)]³ × (j + 2k)/√(1 + 5t²)

= -(i + tj + 2tk)5t + (j + 2k)(1 + 5t²)

= -5ti - 5²tj - 10t²k + j + 5t²j + 2k + 10t²k

= -5ti + j + 2k

So, the magnitude of T'(t) = |T'(t)| = √[(-5t)² + 1² + 2²] = √[25t² + 1 + 4] = √[25t² + 5]

So, the normal vector N(t) = T'(t)/|T'(t)| = (-5ti + j + 2k)/√[25t² + 5]

(b) Use Formula 9 to find the curvature.

The curvature κ = |r'(t) × r"(t)|/|r'(t)|³

since r'(t) = (1, t, 2t), r"(t) = dr'/dt = d(1, t, 2t)/dt  = (0, 1, 2)

r'(t) = i + tj + 2tk and r"(t) = j + 2k

r'(t) × r"(t) =  (i + tj + 2tk) × (j + 2k)

= i × j + i × 2k + tj × j + tj × 2k + 2tk × j + 2tk × k

= k - 2j + 0 + 2ti - 2ti + 0

= -2j + k

So magnitude r'(t) × r"(t) = |r'(t) × r"(t)| = √[(-2)² + 1²] = √(4 + 1) = √5

magnitude of r'(t) = |r'(t)| = √(1 + 5t²)

|r'(t)|³ = [√(1 + 5t²)]³

κ = |r'(t) × r"(t)|/|r'(t)|³ = √5/[√(1 + 5t²)]³

Answer:

The slope of the tangent line at x = 1 is -25.

Step-by-step explanation:

We are given the function:

[tex]f(x)=-7x^3-8x+2x^2[/tex]

And we want to find the slope of the tangent line at x = 1.

The slope of the tangent line at a point for a function is given by its derivative. Find the derivative of the function:

[tex]f'(x)=-21x^2+4x-8[/tex]

Then the slope of the tangent line at x = 1 is:

[tex]f'(1)=-21(1)^2+4(1)-8=-25[/tex]

Answer:

[tex]\sqrt{3}[/tex]

Step-by-step explanation:

x^2 + 1 = 4

x^2 = 3

[tex]\sqrt{3}[/tex]

Answer:

The radius is 10

Step-by-step explanation:

Given

[tex]x^2 + y^2 + 21 = 40 + 18y.[/tex]

Required

The radius

Rewrite as:

[tex]x^2 + y^2 - 18y = 40-21[/tex]

Subtract 81 from both sides

[tex]x^2 + y^2 - 18y +81= 40-21+81[/tex]

Expand

[tex]x^2 + y^2 - 9y - 9y +81= 40-21+81[/tex]

Factorize

[tex]x^2 + y( y- 9) - 9(y -9)= 40-21+81[/tex]

Factor out y - 9

[tex]x^2 + (y- 9) (y -9)= 40-21+81[/tex]

Express as squares

[tex]x^2 + (y- 9)^2= 100[/tex]

[tex]x^2 + (y- 9)= 10^2[/tex]

The equation of a circle is:

[tex](x - a)^2 + (y- b)= r^2[/tex]

By comparison:

[tex]r^2=10^2[/tex]

[tex]r = 10[/tex]

Answer:

I hope this helps

the outcomes are the compulsory 6, and 1 or 2

Step-by-step explanation:

[tex] \frac{3}{6} \\ \frac{1}{2} or \: 0.5[/tex]

Answer:

C 0.90

Step-by-step explanation:

Add 0.10 and 0.80=0.90

Answer:

D

Step-by-step explanation:

P(A and B)=P(A)×P(B)=0.80×0.10=0.08

Answer:

[tex]\frac{5105}{22}[/tex]

Step-by-step explanation:

Used Python function to get all the numbers and add them, then I divided it by 22, which is the number of numbers in the array.

The mean of the data is 232.045.

To find the mean of the data.

Mean is the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers. Mean = (Sum of all the observations/Total number of observations). Mean is the most commonly used measure of central tendency. There are different types of mean, viz. arithmetic mean, weighted mean, geometric mean (GM) and harmonic mean (HM).

Given that:

The data are:

217 + 253 + 214 + 247 + 217 + 253 + 232 + 246 + 223 + 227 + 229 + 247 + 206 + 241 + 239 + 223 + 222 + 216 + 252 + 209 + 236 + 256 = 5105

=5105 / 22 = 232.045

So, the mean of the data is 232.045.

Learn more about mean here:

https://brainly.com/question/24072290

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The option is missing:

A. 230.811

B. 231.045

C. 232.045

D. 232.811

[tex]m(2m+2n)+3mn+2m^2\implies \stackrel{\textit{distributing}}{2m^2+2mn}+3mn+2m^2 \\\\\\ 2m^2+2m^2+2mn+3mn\implies \stackrel{\textit{adding like-terms}}{4m^2+5mn}[/tex]

Answer:

83 or a

Step-by-step explanation:

if angle 6 is 97 then the total would be 180 meaning that 83 would be the answer to 5s angle

"83 degrees" is correct.

On a line, it can be assumed that all the angles must add up to 180 degrees. If you have two angle on a line and don't know the value of one of them, you can subtract that angle from 180 to find the missing angle. Considering this, 180 - 97 = 83.

Answer:

[tex]log_5 \ 125 = 3[/tex]

Step-by-step explanation:

[tex]log_5 \ 125 = log_2 \ 5^3 = 3 \times log_5 \ 5 = 3 \times 1 = 3[/tex]

The value of [tex]$\log _{5} 125$[/tex] can be estimated utilizing the logarithm rule. The value of [tex]$\log _{5} 125$[/tex] exists 3.

The logarithm stands for the inverse function of exponentiation. In logarithm base must be raised to yield a given number for an exponent.

Given:

[tex]$\log _{5} 125$[/tex]

Estimate the value of the given logarithm, we get

[tex]$\log _{5} 125=\log _{5}(5)^{3}$[/tex]

[tex]$\log _{5} 125=3 \log _{5} 5$[/tex]

From logarithm rule [tex]$\log m^{n}=n \log m$[/tex], we get

[tex]$\log _{5} 125=3 \times 1$[/tex]

[tex]$\log _{5} 125=3$[/tex]

Therefore, the value of [tex]$\log _{5} 125$[/tex] is 3.

To learn more about logarithm

https://brainly.com/question/26240264

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Answer:

x = 2 ± [tex]\frac{\sqrt{2} }{2}[/tex]

Step-by-step explanation:

Answer:

∅ = 83.9º

Step-by-step explanation:

tan = opp/adj

opp = 15 - 1 = 14

tan∅ = 14/1.5

∅ = arctan 14/1.5

use calculator

∅ = 83.884496433714593º

Rounded

∅ = 83.9º

Answer:

D

Step-by-step explanation:

the end result of a radical can never be negative unless the negative sign shows outside of the radical

Answer:

30 I suppose

Step-by-step explanation:

Step-by-step explanation:

the answer is in the above image

Answer:

my answer is 225/5 sorry comments for wrong

Answer:

[tex] \frac{8}{5} = \frac{4}{x} \\ 8x = 20 \\ x = 2.5[/tex]

Answer:

here the resize factor is 5/8

so we need to calculate

x = 4 *5/8

= 20/8

= 2.5

I assume you get the basic idea from the other question you posted.

Answer:

Answer:

we arrive at the conclusion that the new employee installs the vertical blinds faster on average.

Step-by-step explanation:

null hypothesis; m₁-m₂ =0

alternative hypothesis; m₁-m₂<0

Given the information in this question, we first have to solve for the t statistic

[tex]t=\frac{22-24.8}{\sqrt{\frac{0.90^{2} }{10}+\frac{0.75^{2} }{10} } }[/tex]

[tex]t=\frac{-2.6}{\sqrt{o.081+0.05625} }[/tex]

[tex]t=\frac{-2.6}{0.37047}[/tex]

t = -7.018

the degree of freedom = n₁+n₂-2

= 10+10-2

= 18

Alpha α = 0.05

from these results the t critical value = -1.734

because the test statistic -7.018 < -1.734,

at 0.05 level of testing, we arrive at the conclusion that the new employee installs the vertical blinds faster on average than the veteran.

9514 1404 393

Answer:

  3 units left

Step-by-step explanation:

Replacing x in a function with (x-h) translates the graph to the right by h units. Here, you have h = -3, so the graph is translated left 3 units.

Answer:

32.25

Step-by-step explanation:

1 quart = 32 fluid ounces

12 months = 1 year

86 quarts/1 month = 1032 quarts/12 months

1032/32 = 32.25 fluid ounces

Answer:

[tex]15,120[/tex]

Step-by-step explanation:

For the first symbol, there are 9 options to choose from. Then 8, then 7, and so on. Since each player chooses 5 symbols, they will have a total of [tex]9\cdot 8 \cdot 7 \cdot 6\cdot 5=\boxed{15,120}[/tex] permutations possible. Since the order of which they choose them matters (as a different order would be a completely different password), it's unnecessary to divide by the number of ways you can rearrange 5 distinct symbols. Therefore, the desired answer is 15,120.

Answer:15,120

Step-by-step explanation:

Notice how points T and Z are vertically aligned, or vertically lined up. This is where the graph fails the vertical line test.

The input x = 2 leads to the outputs y = 3 and y = 5 (which are the y coordinates of points Z and T in that order).

A function is only possible when any given input leads to exactly one output only. It would be like saying "the conversion function from Celsius to Fahrenheit has 0 degrees C convert to both 32 degrees F and 50 degrees F at the same time". But such a statement makes no sense and it's not useful. So this is one example of why having one output makes sense for a function.

In short, we need one output for any given input. But the input x = 2 leads to more than one output. That's why we don't have a function.

Answer:

- 54

Step-by-step explanation:

11 c + 5 a - 8

11 × -6 + 5 × 4 - 8 (given :- a = 4 and b = -6)

- 66 + 20 - 8

- 54

Answer:

The equation of the new function is [tex]g(x) = 7x + 9[/tex]

Step-by-step explanation:

Vertically compress by a factor of 7.

Vertically compressing a function by a units is the same as:

[tex]g(x) = f(ax)[/tex]

In this question:

[tex]f(x) = x, a = 7[/tex]. So

[tex]g(x) = f(7x) = 7x[/tex]

Shift up 9 units.

Shifting a function up a units is the same thing as adding a to the function. In this case, [tex]a = 9[/tex], and then:

[tex]g(x) = 7x + 9[/tex]

The equation of the new function is [tex]g(x) = 7x + 9[/tex]