Benjamin threw a rock straight up from a cliff that was 60 ft above the water. If the height of the rock​ h, in​ feet, after t seconds is given by the equation ​h=-16t^2+68t+60, how long will it take for the rock to hit the​ water?

Step-by-step explanation:

hope this helps you!

-s.

Answer:

C 377

Step-by-step explanation:

I simply typed in "surface area of cone calculator" in chrome and did it that way, since there is quite a complex formula for finding it out on your own.

(This is the formula : pi * r^2 + pi * r * sqrt (r^2+h^2)

Answer:

B) [tex]y=sin(x+\frac{\pi}{2})[/tex]

Step-by-step explanation:

Technically, since the function starts at its maximum, you could say the function is [tex]y=cos(x)[/tex], but the answer choices all use sine instead. Therefore, we will have to use the cofunction identity [tex]cos(x)=sin(x+\frac{\pi}{2})[/tex] and we can see that the correct answer is B.

The equation matches the function provided in the graph is y = sin(x + π/2) option (B) is correct.

It is defined as the function which is sinusoidal in nature, and it has a domain of all real numbers and lies between the [a, a] where is a amplitude of the function.

It is given that:

A graph of a trigonometric function is given:

As we know,

y = sinx has a sinusoidal graph

Based on the graph we can apply a transformation to get the required function.

Applying transformation:

x → x + π/2

The sin function will shift left side by π/2 unit

The equation of the function becomes:

y = sin(x + π/2)

The equation of the function shown in the graph is y = sin(x + π/2)

Thus, the equation matches the function provided in the graph is y = sin(x + π/2) option (B) is correct.

Learn more about the sin function here:

https://brainly.com/question/14397255

#SPJ5

Answer:

Step-by-step explanation:

Given equation:

Solve:

Answer:

area of the entire figure: 21 cm²

Step-by-step explanation:

bottom rectangle:

length * width

3 * 2

6 cm²

upper rectangle:

length * width

3 * 4

12 cm²

triangle area:

1/2 * base * height

1/2 * 2 * 3

3 cm²

Total area: 6 cm² + 12 cm² + 3 cm² = 21 cm²

Moving 2/3 to the other side, we get

x>1/4+2/3

Simplifying,

x>11/12

Answer:

Let W be the width of the rectangle. The length will then be 6W (six times the width). The area is length times width. if this equals 216, then you have an equation

(6W)(W) = 216

6W2 = 216

W2 = 36

W = 6.

The width is 6 ft and the length must then be 6W = 36 ft.

To find the perimeter, use the formula

P = 2L + 2W.

Plug in:

P = 2(36) + 2(6) = 72 + 12 = 84 ft.

The perimeter is 84 ft. (Remember that area has units length units squared and perimeter has units same as length.)

Step-by-step explanation:

Answer:

Find the area of the rectangle. Then, find the area of the circle. The diameter is given, so take half that to get the radius. Multiply the area of the circle by half. Subtract the area of the half circle from the area of the rectangle.

Step-by-step explanation:sample

Answer:

W/m²K                  by-step explanation:

Answer:

Step-by-step explanation:

106/4 = 26[tex]\frac{2}{4\\}[/tex] = 26[tex]\frac{1}{2}[/tex]

Hope this helps!

Answer:

x=72, y=108

Step-by-step explanation:

y-36=x

[tex]\left \{ {{y-x=36} \atop {y+x=180}} \right.[/tex]

⇒ 2y=216

108-36=x

Adding both

Put in eq(1)

Answer:

3x^2+11x+6

Step-by-step explanation:

          3x       +2

x       3x^2      2x  

+3       9x         6

3x^2+9x+2x+6
=

3x^2+11x+6

Answer:

less than 1 bag

Step-by-step explanation:

[tex] \sf{12 \: sq \: yds \: require = 7.5 \: bags}[/tex]

[tex] \implies\sf{1 \: sq \: yd \: will \: require = \frac{7.5}{12} \: bags} \\ = \sf{ \underline{0.625}}[/tex]

which is less than 1.

Implies that, each square yard requires about less than 1 bag of mulch.

Answer:

[tex] \boxed{\tt \: m = \boxed{\tt Undefined}}[/tex]

Step-by-step explanation:

Given Two Points are:

[tex] \sf \: \tt (6,-5) \: \sf and \: \tt (6,-4)[/tex]

We need to Find:

[tex] \longrightarrow \sf \: The \: Slope[/tex]

We know that,

[tex] \sf \: Slope = \tt \: Rise/Run \: , \: \sf \: i.e. \: \: \boxed{\tt\dfrac{y_2-y_1}{x_2-x_1}}[/tex]

[tex] \sf \: Slope= \boxed{\tt\dfrac{y_2-y_1}{x_2-x_1}}[/tex]

Where,

[tex] \tt \: y_2= -4[/tex]

[tex]\tt y_1= - 5[/tex]

[tex]\tt x_2=6[/tex]

[tex] \tt \: x_1=6[/tex]

So Substitute their values accordingly:

[Important Note: Slope is denoted as m generally.]

[tex] \tt\implies \: m = \cfrac{ - 4 -( - 5)}{6 - 6} [/tex]

Now Simplify it.[Follow BODMAS Rule strictly while simplifying]

[tex] \tt \implies m = \cfrac{ - 4 + 5}{0} [/tex]

[tex]\tt \implies m = \cfrac{ 1}{0} [/tex]

Here, We can find that 1 is divided by 0.

We know that any expressions divided by 0 is undefined .

Hence, the slope[m] would be undefined.

[tex] \rule{225pt}{2pt}[/tex]

I hope this helps!

Let me know if you have any questions! :)

[tex]SA=\pi rs+\pi r^2\\r=8\div2=4\\s=7 \\SA=3,14\times4\times7+3,14\times4^2=138,16\:\text{in}^2\approx138\:\text{in}^2[/tex]

Answer: 138 in²

Answer:

Negative

Step-by-step explanation:

From the number line we see that [tex]m[/tex] is negative and [tex]n[/tex] is positive

The expression in the parentheses, [tex](-m . n^2)[/tex] is positive since

[tex]-m[/tex] is the negative of a negative number and the sign of that is positive

[tex]n^2[/tex] is positive since a positive (or negative) number squared is always positive

[tex]\frac{m}{n}[/tex] is a negative number. If you divide a negative number, the sign of the result is negative

So evaluating the whole expression [tex]\frac{m}{n} .( m . n^2)[/tex]

gives us a negative number multiplied by a positive number and the result is a negative number

Answer:

  y = x² +10x -9

Step-by-step explanation:

A spreadsheet or suitable calculator can help you with this. All spreadsheets and most graphing calculators offer regression function capabilities. It is a good idea to learn to use these tools.

The attached graphing calculator output shows the equation to be ...

  y = x² +10x -9

_____

Additional comment

If you want to do this by hand, you recognize that there are only two coefficient values that need to be found. You can choose any two of the given points to use to create equations for those coefficients. I would choose the points with the x-values that are smallest in magnitude.

Using (-4, -33)

  y = x² +bx +c

  -33 = (-4)² +(-4)b +c

  -4b +c = -49 . . . . . . . . . subtract 16

Using (1, 2)

  2 = (1)² +(1)b +c

  b +c = 1 . . . . . . . . . . . . subtract 1

Now, we can subtract the first equation from the second ...

  (b +c) -(-4b +c) = (1) -(-49)

  5b = 50 . . . . . . . . simplify

  b = 10 . . . . . . . . . . divide by 5

Using the second equation, we get

  10 +c = 1

  c = -9 . . . . . . subtract 10

So, the desired quadratic is ...

  y = x² +10x -9

__

These equations are usually pretty easy to solve, because the 'c' variable has a coefficient of 1 in all of them. It can easily be eliminated by subtracting one equation from another. Here, we chose our subtraction so the coefficient of 'b' would end up being positive. (Not necessary, but can help prevent mistakes.)

If you don't know ahead of time that the coefficient of x² is 1, then you need to write 3 equations in the three coefficients.

Answer:

Slope = 3

y- intercept = (0, 10)

Step-by-step explanation:

the equation is given by y=mx+c where m is the slope

- At y-intercept, x is equal to 0

Therefore, y = 3(0) + 10

y = 0 + 10

y = 10

There needs to be   6     gallons of 35 % alcohol solution

and    3     gallons of 50 % solution.

======================================================

Explanation:

x = number of gallons of the 35% solution

y = number of gallons of the 50% solution

The two amounts must add to 9 gallons, so x+y = 9

This solves to y = 9-x

Since we want 9 gallons of 40% alcohol solution, this means we want 0.40*9 = 3.6 gallons of pure alcohol.

----------------

0.35x = amount of pure alcohol from the first batch

0.50y = amount of pure alcohol from the second batch

0.35x+0.50y = total amount of pure alcohol

Set that expression equal to the 3.6 figure calculated earlier (the total amount of pure alcohol we're after) and we get this equation

0.35x+0.50y = 3.6

----------------

Next, we replace y with 9-x and then solve for x.

0.35x+0.50y = 3.6

0.35x+0.50(9-x) = 3.6

0.35x+4.5-0.50x = 3.6

-0.15x+4.5 = 3.6

-0.15x = 3.6-4.5

-0.15x = -0.9

x = -0.9/(-0.15)

x = 6

We'll need 6 gallons of the 35% solution

Use this x value to find y

y = 9-x

y = 9-6

y = 3

We'll also need 3 gallons of the 50% solution

Answer:

1 + 4 = 5

Step-by-step explanation:

You did duplicates of all numbers, other than that one! :)

Hope this helps!!

Answer: 19 cents

Step-by-step explanation:

Let's say that the cost of a lemon be L and the cost of an orange is O

We get the equation

4L + 3O = 5.45

7L + 4O = 9.30

The first equation can be made into the equation

28L + 21O = 38.15

And the second be made into

28L + 16O = 37.20

The second equation - The first question

5O = 0.95

O = 0.19

Answer:

Step-by-step explanation:

Let,4x,3x, and 2x be the share .

Now we have,

[tex]4x+3x+2x=810000\\\\9x=810000\\\\x=\frac{810000}{9} \\\\x=90000[/tex]

Again,

Share of Sarah=4x=4×90000=360000

Share of John=3x=3×90000=270000

Share of Monica=2x=2×90000=180000

Answer:

The sample mean appears to be an unbiased estimator of the population mean.

Step-by-step explanation:

The sample means appear to be centered near 16

Solution:

Note that:

Using the equation (4x - 27 = 3x + 4), solve for x.

The measure of x is 31.

Solve for X ~

[tex] \bf4x - 27 = 3x + 4[/tex]

[tex] \bf \: 4x - 3x = 4 + 27[/tex]

[tex] \boxed{ \bf \: x = 31}[/tex]

[tex] \tt \: ∠1 = 2x + 21 \\ \tt \: = 2 \times 31 + 21 \\ \tt \: ∠1= 83 \degree[/tex]

[tex] \tt \: ∠2 = 4x + 27\\ \tt \: = 4\times 31 - 27 \\ \tt \: ∠2= 97 \degree[/tex]

[tex] \tt \: ∠3 = 3x + 4 \\ \tt \: = 3\times 31 + 4 \\ \tt \: ∠3= 97 \degree[/tex]

Answer:

a = 22

Step-by-step explanation:

[tex]cot \: 4a = tan \: (a - 20)....(given) \\ \\ \implies \: tan(90 - 4a) = tan \: (a - 20) \\ [\because \: cot \theta = tan(90 \degree - \theta) ]\\ \\ \implies (90 - 4a) = tan(a - 20) \\ \\ \implies \: 90 + 20 = 4a + a \\ \\\implies \: 110 = 5a \\ \\ \implies \: a = \frac{110}{5} \\ \\ \huge \red{ \boxed{\implies \: a = 22}}[/tex]

Answer:

53 Girls

Step-by-step explanation:

X is the number of girls and Y is the number of boys:
(X + 15) + Y = 91
91 - 15 = 76
76 ÷ 2 = 38
38 + 15 = X
X = 53

(38 + 15) + 38 + 91

Answer:

60 Km / hour

Step-by-step explanation:

average speed (S) is calculated as

S = [tex]\frac{D}{T}[/tex] ( D is distance and T time in hours )

here D = 180 and T = 3 , then

S = [tex]\frac{180}{3}[/tex] = 60 Km / hour

Answer:

(-6, 1)

Step-by-step explanation:

((-5) + (-7))/2 = -6

((-1) + 3)/2 = 1

so the answer is (-6, 1)

Answer:

D=35

Step-by-step explanation:

First, find a common multiple of both 15 and 6, we get 30, 14/6*5=70/6 meaning that 14/6=35/15