2. A football is punted into the air. Its height h, in metres, after t seconds is given by the equation
h(t) = -4.91? + 24.5t + 1
a) How high is the ball after 1 second?

b) Find the maximum height of the ball to one decimal place.

c) When does the ball reach its maximum height?

d) When does the ball hit the ground?

Step-by-step explanation:

well, the approach is totally simple : we use (x+3) everywhere where we have "x" in the function expression.

so,

f(x+3) = 2(x+3)² - 3(x+3) + 4 =

= 2(x² + 6x + 9) - 3x - 9 + 4 =

= 2x² + 12x + 18 - 3x - 9 + 4 =

= 2x² + 9x + 13

The best investment of the company is in southeast contract. The probability of profit of this contract is maximum 50% and of loss is minimum 20%.

Probability of an event is the ratio of number of favorable outcome to the total number of outcome of that event.

A company has an opportunity to bid on three contracts. Probability of profit and loss by all three contract is listed in the table below.

Contract profit,   (P)* of profit, (P)* to break even loss, (P)* of loss

The company which will give the maximum profit probability and minimum loss probability will be the best investment.

In the above table, the southeast contract has the maximum probability of profit, which is 50% among all the contracts. Similarly, it has the lowest probability of loss, which is 20%.

Thus, the best investment of the company is in southeast contract. The probability of profit of this contract is maximum 50% and of loss is minimum 20%.

Learn more about the probability here;

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Answer:

It's A. Southeast

Step-by-step explanation:

Answer:

30 degrees

Step-by-step explanation:

because if its 60 at the bottom and 30 on the left it only makes sense that it would be 30 on the right.

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Answer: AAS

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

a/b=c/d

ad=bc

3/x=x/13

3*13=x*x

√39=√x2

6.244997998398=x

Answer:

See below ↓

Step-by-step explanation:

We need to prove :

⇒ cos⁻¹ [tex]\frac{12}{13}[/tex] + sin⁻¹ [tex]\frac{3}{5}[/tex] = tan⁻¹ [tex]\frac{56}{65}[/tex]

Let's simplify the LHS.

Convert the inverse cos and sin functions into inverse tan functions

Identity

Using this identity, we can simplify our earlier equation!

⇒ tan⁻¹ [(5/12 + 3/4)/(1 - (5/12 x 3/4))]

⇒ tan⁻¹ [(20 + 36) / (48 - 15)

⇒ tan⁻¹ (56/65)

⇒ RHS

⇒ Proved ∴√

[tex]\text{L.H.S}\\\\=\cos^{-1} \dfrac{12}{13} + \sin^{-1} \dfrac 35\\\\=\sin^{-1} \dfrac 5{13} + \sin^{-1} \dfrac 35\\\\[/tex]

[tex]=\sin^{-1}\left[\dfrac 5{13}\sqrt{1- \left(\dfrac 35 \right)^2} + \dfrac 35\sqrt{1-\left(\dfrac 5{13} \right)^2} \right]\\\\=\sin^{-1} \left(\dfrac 5{13} \sqrt{1-\dfrac 9{25} }+\dfrac 35 \sqrt{1-\dfrac{25}{169}} \right)\\\\=\sin^{-1} \left(\dfrac 5{13} \sqrt{\dfrac{16}{25}}+\dfrac 35 \sqrt{\dfrac{144}{169}} \right)\\\\=\sin^{-1} \left(\dfrac{5}{13} \cdot \dfrac 45 + \dfrac 35 \cdot \dfrac{12}{13} \right)\\[/tex]

[tex]=\sin^{-1} \left(\dfrac 4{13} +\dfrac{36}{65}\right)\\\\=\sin^{-1} \left(\dfrac{20}{65} + \dfrac{36}{65} \right)\\\\=\sin^{-1} \left(\dfrac{20+36}{65} \right)\\\\=\sin^{-1} \left(\dfrac{56}{65} \right)\\\\=\text{R.H.S}[/tex]

Check the picture below.

[tex]\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2-b^2}=a \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ \sqrt{19.5^2-18^2}=r\implies \sqrt{56.25}=r \\\\[-0.35em] ~\dotfill[/tex]

[tex]\textit{lateral area of a cone}\\\\ LA=\pi r\sqrt{r^2+h^2}~~ \begin{cases} r=radius\\ h=height\\ \stackrel{slant~height}{\sqrt{r^2+h^2}}\\[-0.5em] \hrulefill\\ r=\sqrt{56.25} \end{cases}\implies \begin{array}{llll} LA=\pi \sqrt{56.25}\stackrel{slant~height}{(19.5)} \\\\\\ LA\approx 459.46~cm^2 \end{array}[/tex]

Answer:

[tex]\displaystyle y' = - \frac{e^{x^2 + 7} \sqrt{\csc 5x} \Bigg[ \bigg[ 5 \cot (5x) - 4x \bigg] \sin (3x + 4) - 6 \cos (3x + 4) \Bigg] }{2}[/tex]

General Formulas and Concepts:

Calculus

Differentiation

Derivative Property [Multiplied Constant]:
[tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]

Derivative Property [Addition/Subtraction]:
[tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]

Derivative Rule [Basic Power Rule]:

Derivative Rule [Product Rule]:
[tex]\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)[/tex]

Derivative Rule [Chain Rule]:
[tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]

Step-by-step explanation:

Step 1: Define

Identify.

[tex]\displaystyle y = e^{x^2 + 7} \sin (3x + 4) \sqrt{\csc (5x)}[/tex]

Step 2: Differentiate

∴ we have found the derivative of the function.

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Learn more about differentiation: https://brainly.com/question/26836290
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Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

To find the derivative of the function [tex]\displaystyle\sf\:y=e^{x^{2}+7}\sin(3x+4)\sqrt{\csc(5x)}}[/tex] with respect to [tex]\displaystyle\sf x[/tex], we'll use the chain rule and product rule.

Let's break down the function into its individual parts:

[tex]\displaystyle\sf u= e^{x^{2}+7}[/tex]

[tex]\displaystyle\sf v= \sin(3x+4)[/tex]

[tex]\displaystyle\sf w= \sqrt{\csc(5x)}}[/tex]

Now, let's differentiate each part separately:

Using the chain rule, the derivative of [tex]\displaystyle\sf u= e^{x^{2}+7}[/tex] is:

[tex]\displaystyle\sf \dfrac{du}{dx}= (2x)e^{x^{2}+7}[/tex]

Using the chain rule, the derivative of [tex]\displaystyle\sf v= \sin(3x+4)[/tex] is:

[tex]\displaystyle\sf \dfrac{dv}{dx}= 3\cos(3x+4)[/tex]

To differentiate [tex]\displaystyle\sf w= \sqrt{\csc(5x)}}[/tex], we can rewrite it as [tex]\displaystyle\sf w= (\csc(5x))^{1/2}[/tex]. Using the chain rule, the derivative of [tex]\displaystyle\sf w[/tex] is:

[tex]\displaystyle\sf \dfrac{dw}{dx}= \dfrac{1}{2}(\csc(5x))^{-1/2}(-\cot(5x))(5)[/tex]

Simplifying the derivative [tex]\displaystyle\sf \dfrac{dw}{dx}[/tex]:

[tex]\displaystyle\sf \dfrac{dw}{dx}= -\dfrac{5\cot(5x)}{2\sqrt{\csc(5x)}}[/tex]

Now, using the product rule, the derivative of [tex]\displaystyle\sf y[/tex] with respect to [tex]\displaystyle\sf x[/tex] can be calculated as follows:

[tex]\displaystyle\sf \dfrac{dy}{dx}= \dfrac{du}{dx} \cdot v \cdot w + u \cdot \dfrac{dv}{dx} \cdot w + u \cdot v \cdot \dfrac{dw}{dx}[/tex]

Substituting the values of [tex]\displaystyle\sf \dfrac{du}{dx}[/tex], [tex]\displaystyle\sf \dfrac{dv}{dx}[/tex], and [tex]\displaystyle\sf \dfrac{dw}{dx}[/tex]:

[tex]\displaystyle\sf \dfrac{dy}{dx}= \left((2x)e^{x^{2}+7}\right) \cdot \sin(3x+4) \cdot \sqrt{\csc(5x)} + e^{x^{2}+7} \cdot \left(3\cos(3x+4)\right) \cdot \sqrt{\csc(5x)} - e^{x^{2}+7} \cdot \sin(3x+4) \cdot \dfrac{5\cot(5x)}{2\sqrt{\csc(5x)}}[/tex]

Simplifying further:

[tex]\displaystyle\sf \dfrac{dy}{dx}= \left(2xe^{x^{2}+7}\right) \sin(3x+4) \sqrt{\csc(5x)} + 3e^{x^{2}+7}\cos(3x+4) \sqrt{\csc(5x)} - \dfrac{5e^{x^{2}+7} \sin(3x+4) \cot(5x)}{2\sqrt{\csc(5x)}}[/tex]

Therefore, the derivative of [tex]\displaystyle\sf y[/tex] with respect to [tex]\displaystyle\sf x[/tex] is:

[tex]\displaystyle\sf y' = -2e^{x^{2}+7}\csc(5x)[5\cot(5x)-4x]\sin(3x+4) - 3e^{x^{2}+7}\sqrt{\csc(5x)}\cos(3x+4) - \dfrac{5e^{x^{2}+7}\sin(3x+4)\cot(5x)}{2\sqrt{\csc(5x)}}[/tex]

Simplifying further, we have:

[tex]\displaystyle\sf y' = -2e^{x^{2}+7}\csc(5x)[5\cot(5x)-4x \sin(3x+4) - 6e^{x^{2}+7}\cos(3x+4)\sqrt{\csc(5x)}[/tex]

Therefore, the derivative of [tex]\displaystyle\sf y[/tex] with respect to [tex]\displaystyle\sf x[/tex] is:

[tex]\displaystyle\sf y' = -2e^{x^{2}+7}\csc(5x)[5\cot(5x)-4x]\sin(3x+4) - 6e^{x^{2}+7}\cos(3x+4)\sqrt{\csc(5x)}[/tex]

[tex]\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}[/tex]

♥️ [tex]\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}[/tex]

Answer:

5.1 cm

Step-by-step explanation:

The equation for the circumference of a circle is 2πr or πd.

So, we can plug in 16 and 3.14 to get 16 = 3.14×diameter.

Divide both sides by 3.14 to get approximately 5.1 cm.

Hope that helps! :)

Answer: 81

Step-by-step explanation:

90% is the same as 0.9

We can multiply .9 by 90 to see how many students are enrolled in health

0.9×90=81.0

Answer:

[tex]\huge\boxed{\sf 81\ students }[/tex]

Step-by-step explanation:

Total students = 90

Enrolled in health:

= 90 % of 90

[Key: "of" means "to multiply" and "%" means "out of hundred"]

[tex]\displaystyle = \frac{90}{100} \times 90\\\\= 9 \times 9\\\\= 81[/tex]

So, 81 students are enrolled in health.

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

Answer:

$3.50

Step-by-step explanation:

For this question, you just take the price paid and divide it by the number of gallons.  In this case, you get $3.50 per gallon.

Answer:

Step-by-step explanation:

hours              Cost

  0                   $15

   1                    $15 + 2.50 = $17.50

   2                    $15 + 2.50(2) = $15 + 5 = $20

   3                     $15 + 2.50(3)= $15 + 7.50 = $22.50

   4.                     $15 + 2.50(4)= $15 + 10 = $25

Answer:

slope = 7

Step-by-step explanation:

Slope-intercept form of a linear equation:  y = mx + b

(where m is the slope, and b is the y-intercept)

Therefore, for the equation: y = 7x + 9/16

Answer:

A&C

Step-by-step explanation:

It would be A because it has 750 mL and C because it has 250mL and 750+250=1000

Also can you mark brainlyist you dont have to

Answer:

22 tickets

Step-by-step explanation:

4/6 is 2/3
2/3 of 32 is 21 .3
Can't sell 0.3 of a ticket, so round up.
22 tickets

Answer:

60 feet

Step-by-step explanation:

The easiest way to do this is to go answer by answer with the triangle area formula :)

Formula: A=hb/2

H = height

B: base

Now lets solve this :)

Choice 1: 50 feet

50 x 20 = 1000

1000/2 = 500

Choice 2: 40 feet

Since 40 feet is smaller than the 50, we know this will not be correct :)

Choice 3: 120 feet

120 x 20 = 2400

2400/2 = 1200

Choice 4: 60 feet

60 x 20 = 1200

1200/2 = 600

The correct answer is 4, 60 feet :)

Have an amazing day!!

Please rate and mark brainliest!!

Step-by-step explanation:

please mark me as brainlest

Answer:

a)  5, -3, -4, 0

b)  Curve B

Step-by-step explanation:

Given equation:

[tex]y=x^2-4x[/tex]

Inputting the values of x into the equation to find the missing values of y:

[tex]x=-1 \implies y=(-1)^2-4(-1)=5[/tex]

[tex]x=1 \implies y=(1)^2-4(1)=-3[/tex]

[tex]x=2 \implies y=(2)^2-4(2)=-4[/tex]

[tex]x=4 \implies y=(4)^2-4(4)=0[/tex]

[tex]\large\begin{array}{| c | c | c | c | c | c | c | c |}\cline{1-8} x & -1 & 0 & 1 & 2 & 3 & 4 & 5\\\cline{1-8} y & 5 & 0 & -3 & -4 & -3 & 0& 5\\\cline{1-8}\end{array}[/tex]

According to the table:

Therefore, Curve B matches the graph of [tex]y=x^2-4x[/tex]

Answer:

nasa pic yung answer

Step-by-step explanation:

hope its help

correct me if im wrong

Answer:

x=-3 x=-3

Step-by-step explanation:

You have the equation x^2+6x+9=0. So we are tying to find two terms that add to 6 but multiply to 9. Those numbers are 3 and 3. So now we have x^2+3x+3x+9=0. Then factor it to get (x+3) and (x+3) then to isolate x do x+3=0, x=-3 (move 3 to the other side to get x=-3).

Answer:

48 ounce bag of granola per month.

T = 48x

Where 'x' represents the months.

Replace x with 12, because we want to know how many ounces she eats each year.

T = 48x

T = 48(12)

T = 576 ounces, she eats each year.

Thus, the best estimate for Sam to quote as expected profits in the next year in his new business plan is $66,933.60.

Net profit is the amount of a business earn after deducting all the expenditure over it.

Sam has been running his swimming pool cleaning business now for five years. He is considering enlarging his service area to a 100 mile radius, which would require two new offices in different parts of town.

He would like to take out a business loan to cover the cost of expansion. The profits for Sam's business over the last 5 years are outlined in the table below.

Using the regression graph, the quadratic equation we get for this data as,

[tex]y=192.4493x^2+3318.1733x+39998.214[/tex]

For the 6 year value,

[tex]y=192.4493(6)^2+3318.1733(6)+39998.214\\y\approx 66835.43[/tex]

This value is much near to the option b which is $66,933.60.

Thus, the best estimate for Sam to quote as expected profits in the next year in his new business plan is $66,933.60.

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Step-by-step explanation:

X + Y = 90

Y = 24

X = 6x

X + 24 = 90

X = 66

x = X/6 = 66/6 = 11

Answer: 36533

Step-by-step explanation:

- 5 + 5x = - 1 + 6x

- 5 + 5 + 5x = - 1 + 5 + 6x

5x = 4 + 6x

5x - 6x = 6x - 6x + 4

- x = 4

x = - 4

Answer:

The answer is that x = -4.

Step-by-step explanation:

You first take away the parenthesis so it would look like this: -5+5x=-1+6x

Then, you add 5 to both sides of the problem: -5+5x+5=-1+6x+5

Then, you simplify it down: 5x=6x+4

You then subtract 6x from each side: 5x-6x=6x+4-6x

Then simplify again: -x=4

Then, divide both sides by -1: -x/-1 = 4/-1

Then simplify to get x = -4.

Answer:

I believe the correct answer is f^-1 (x) = x - 3/2

Answer:

105³

Step-by-step explanation:

3x5=15

15x7=105

105 is your answer.

Answer: If you want you can put 480 seconds or 8 minutes.

480 seconds = 8 minutes

Step-by-step explanation:

8 inches multiply by 60 feet

The volume of the figure is the amount of space in the figure

The volume of the figure is 10488 cubic inches

The figure is a composite figure, and it contains:

The volume (V1) of the rectangular prism is:

V1 = Length * Width * Height

V1 = 18 in * 23 in * 16 in

V1 = 6624 cubic inches

The volume (V2) of the triangular prism is:

V2 = 0.5 * Base * Width * Height

V2 = 0.5 * 23 in * 16 in * 21 in

V2 = 3864 cubic inches

Add the volumes of both figures

V =  V1 + V2

V = 6624 cubic inches + 3864 cubic inches

V = 10488 cubic inches

Hence, the volume of the figure is 10488 cubic inches

Read more about volumes at:

https://brainly.com/question/1972490

Answer:

The answer is D: 10488

Step-by-step explanation:

Answer:

See below ↓

Step-by-step explanation:

Information we need

Solving