someone please help me work this out??

we know that θ is in the I Quadrant, namely that cosine as well as sine are both positive, well, we know that

[tex]cos(\theta )=\cfrac{\stackrel{adjacent}{2}}{\underset{hypotenuse}{\sqrt{19}}}\qquad\qquad \textit{let's get the \underline{opposite side}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2-a^2}=b \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ \pm\sqrt{(\sqrt{19})^2-2^2}=b\implies \pm\sqrt{19-4}=b\implies \pm\sqrt{15}=b\implies \stackrel{I~Quadrant}{+\sqrt{15}=b} \\\\[-0.35em] ~\dotfill[/tex]

[tex]tan(\theta)=\cfrac{\stackrel{opposite}{\sqrt{15}}}{\underset{adjacent}{2}}~\hspace{10em} tan(2\theta)=\cfrac{2tan(\theta)}{1-tan^2(\theta)} \\\\[-0.35em] ~\dotfill\\\\ tan(2\theta)=\cfrac{2\cdot \frac{\sqrt{15}}{2}}{1-\left( \frac{\sqrt{15}}{2} \right)^2}\implies tan(2\theta)=\cfrac{\sqrt{15}}{1-\frac{15}{4}}\implies tan(2\theta)=\cfrac{\sqrt{15}}{~~\frac{4-15}{4}~~} \\\\\\ tan(2\theta)=\cfrac{\sqrt{15}}{~~ \frac{-11}{4}~~}\implies tan(2\theta)=-\cfrac{4\sqrt{15}}{11}[/tex]

The inflow rate of water is given by the function of the volume of the

tank derived from the shape of the tank.

Response:

The given parameter are;

Shape of the tank = Conical

Rate at which water is leaking out of the tank = 7,000 cm³/min

Height of the tank = 6 m

Diameter of the tank = 4 m

Solution:

We have;

[tex]\dfrac{D}{h} = \mathbf{\dfrac{2 \cdot r}{h}}[/tex]

[tex]r = \mathbf{\dfrac{D}{2 \cdot h}}[/tex]

Which gives;

[tex]r= \mathbf{\dfrac{h}{3}}[/tex]

[tex]V = \dfrac{1}{3} \cdot \pi \cdot r^2 \cdot h = \dfrac{1}{3} \cdot \pi \cdot \left(\dfrac{h}{3} \right)^2 \cdot h = \mathbf{ \pi \cdot \dfrac{h}{27} ^3}[/tex]

Which gives;

[tex]\dfrac{dV}{dh} = \mathbf{\pi \cdot \dfrac{h}{9} ^2}[/tex]

By using chain rule of differentiation, we have;

[tex]\dfrac{dV}{dt} = \mathbf{\dfrac{dV}{dh} \times \dfrac{dh}{dt}}[/tex]

Which gives;

[tex]\dfrac{dV}{dt} = \mathbf{\pi \cdot \dfrac{h}{9} ^2\times 20}[/tex]

[tex]\dfrac{dV}{dt} = \pi \cdot \dfrac{200}{9} ^2\times 20 \approx 279,252.68[/tex]

[tex]\dfrac{dV}{dt} = \mathbf{Inflow \ rate - Outflow \ rate}[/tex]

Therefore;

[tex]Inflow \ rate = \mathbf{\dfrac{dV}{dt} + Outflow \ rate}[/tex]

Which gives;

Inflow rate ≈ 279,252.68 + 7000 = 286,252.68 ≈ 286,253

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Answer:

Step-by-step explanation:

For the given data the height of the tree will be 12.86.

A triangle is a three-sided polygon having three edges and three vertices in terms of geometry. The sum of the inner angles of the triangle is 180°.

Given that, Andrés is 1.65 meters tall, this is obvious. He determines the length of a tree's shadow at 2 p.m. to be 40.15 meters. The tip of his shadow touches the tip of the tree's shadow while he stands 35 meters away from the tree.

Since the triangle ABC and ADF are similar, their ratio will be the same.

Suppose the height of the tree to the nearest hundredth of a meter will be x.

5.15/40.15=1.65/x

5.15x=1.65× 40.15

5.15x=66.2475

x=66.24/5.15

x=12.86

Thus, the height of the tree will be 12.86.

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#SPJ2

Answer:

the answer is graph 1

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

Answer:

i guess the answer is 64x^5

Step-by-step explanation:

(4x^2)^3

=64x^5

Answer:

4 hours

Step-by-step explanation:

the cost of movie is $48

means they have $32 left with them

parking charge is $8 (32/8= 4)

means they can spend 4 hours in Emeryville

Answer:

yellow box

Step-by-step explanation:

if you follow the graph. it is a difference of 6 between each 2 points

so you don't have to solve with the formula

6/2 = 3 so 3 is your X

and you get larger as you go towards 0 so it is positive

and so add 6 to 10 because (-2,10) and you follow the 6 y for every 2 you go

so (0,16)

y = 3x + 16

#1

Interest be I

[tex]\\ \rm\hookrightarrow I=PRT/100[/tex]

[tex]\\ \rm\hookrightarrow I=9573(4)(2)/100=76584/100=765.84\$[/tex]

#2

[tex]\\ \rm\hookrightarrow I=9573(4)(4)/100=153168/100=1531.68\$[/tex]

Answer:

a) $765.84

b) $1,531.68

Step-by-step explanation:

Simple interest formula:  SI = PRT

where P = principal amount of loan, R = annual rate of Interest in decimal format, and T = Time.

Given:

a) when T = 2:  

SI = 9573 x 0.04 x 2 = 765.84

b) when T = 4:  

SI = 9573 x 0.04 x 4 =  1531.68

The domain of a function is the set of input values the function can take

The domain is all set of real numbers

The expression is given as:

[tex]\frac{x^2 - x - 12}{x - 4}[/tex]

Factorize the numerator of the expression

[tex]\frac{(x - 4)(x + 3)}{x - 4}[/tex]

Simplify: Cancel out the common terms

[tex]x + 3[/tex]

The above expression can take any value of x.

Hence, the domain is all set of real numbers

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Answer:

Jessica scored 20 points, Letitia scored 40 points, and Sally scored 48 points.

Step-by-step explanation:

Let x represent the points Jessica score then...

Letitia scored 2x points (twice as many as Jessica) and Sally scored 2x+8 (8 more than Letitia) points.

We can use this information to set up an equation:

x+2x+2x+8=108

Combine like terms

5x+8=108

Subtract 8 from both sides

5x=100

Divide both sides by 5

x=20 (Jessica)

2x=2(20)=40 (Letitia)

2x+8=2(20)+8=48 (Sally)

Jessica scored 20 points, Letitia scored 40 points, and Sally scored 48 points.

Answer:

8cm

Step-by-step explanation:

The area of a shape is the amount of space it can occupy.

The length of BE is 8 units

The question is incomplete.

So, I will give a general solution

Assume that the length BE is 2/5 of length FH.

Then the length BE would be:

BE = 2/5 * FH

Substitute 20 for FH

BE = 2/5 * 20

Evaluate the product

BE = 8

Using the assumed value, the length of BE is 8 units

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Answer:

Explained below

Step-by-step explanation:

4(x + 2) = - 4

Let's solve:

4(x + 2) = - 4

4(x) + 4(2) = - 4

4x + 8 = - 4

    - 8     - 8

4x = -12

/4     /4

x = -3

Hope this helps!

Answer:

Linear Regression: y = 0x + 2.67

Quadratic Regression: y = 1x^2 + 0x - 4

Step-by-step explanation:

USE STATS CALCULATOR

[tex] \leadsto f( \rm x) = - (x - 3)(x - 5)[/tex]

[tex] \\ \\ [/tex]

[tex] \leadsto f( \rm x) = - ( {x}^{2} - 5x - 3x + 15) \\ [/tex]

[tex] \\ \\ [/tex]

[tex] \leadsto f( \rm x) = - ( {x}^{2} - 8x + 15) \\ [/tex]

[tex] \\ \\ [/tex]

[tex] \leadsto f( \rm x) = - {x}^{2} + 8x - 15 \\ [/tex]

Answer:

3rd option is correct

Step-by-step explanation:

hope this helps you :)

The equation of the parabola whose focus is at (3, 0) and the directrix is at x = –3 is y=6x²+6x.

y = a(x-h)² + k

where,

(h, k) are the coordinates of the vertex of the parabola in form (x, y);

a defines how narrower is the parabola, and the "-" or "+" that the parabola will open up or down.

As it is given that the focus of the parabola is at F(3,0) and its directrix is the line x=−3, therefore, we can write that

x=-3

x+3=0

Now, Let A(x,y) be any point in the plane of the directrix and focus, and MA be the perpendicular distance from A to the directrix, therefore, A lies on parabola if FA=MA,

[tex]FA=MA\\\\\sqrt{(x-3)^2 +(y-0)^2}=\dfrac{|x+3|}{1}\\\\{(x-3)^2 +(y-0)^2}={(x+3)^2}\\\\-6x^2+y=6x\\\\y=6x^2+6x[/tex]

Hence, the equation of the parabola whose focus is at (3, 0) and the directrix is at x = –3 is y=6x²+6x.

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The price is $27.00

Step-by-step explanation:

First you find 40% of 60 which is 24.

Next you subtract 24 from 60 (60-24) which equals 36.

Then you find 25% of the discounted price (36) which is 9.

Finally you subtract 9 from 36 (36-9) which is 27.

Conclusion:

So therefore the answer is $27.00.

I don't care if I get brainlyist just glad I could help :)

Answer: 0 = 0 and/or Infinitely Many Solutions

Step-by-step explanation:

When solving this equation we want to find x then substitute the answer we find for x to see if both sides are equal to the same number.

So once we find x replace x with that number: x = 8

Rewrite equation: [tex]-24+3(8)=16-2(8)[/tex]

So we solve          [tex]-24+24=16-16\\0=0[/tex]      

Since both sides are equal the answer would be Infinitely Many Solutions

Answer:

C. [tex]tan(B) =2[/tex]

Step-by-step explanation:

Here we can see tan(B) has a opposite side of 2 and adjacent of 1.

[tex]tan(B) = \frac{opposite}{adjacent}[/tex]

[tex]tan(B) = \frac{2}{1}[/tex]

[tex]tan(B) =2[/tex]

Answer:

[tex]\textsf{tan(B)}=2[/tex]

Step-by-step explanation:

The trig ratio for tan is tan(x) = O/A

where x is the angle,

O = side OPPOSITE to the angle, and

A = side ADJACENT to the angle

For angle B:

O = 2

A = 1

Therefore, [tex]\textsf{tan(B)}=\frac{2}{1}=2[/tex]

The first school sends 3 times as many German students as French students, so if they send 21 German students, they must also be sending 21/3 = 7 French students. The first school then sends a total of 21 + 7 = 28 students.

The other 3 schools send the same number of students. There are 4 schools, so the total number of students is 4 × 28 = 112.

Answer:

Step-by-step explanation:

Given equation:

Solve:

Answer: 40 percent

Step-by-step explanation:

To get percentage you divide the part by the whole, so you do 20 divided by 50, which is 40 percent.

Answer:

50.24 units^2

Step-by-step explanation:

A=(3.14)(4)^2

Answer:

$232.57

Step-by-step explanation:

1 year = 12 months

⇒ 5 years = 5 x 12 = 60 months

APR credit score of 700 or higher = 13.25%

(using the APR calculator) total payment over term of loan = $10,296.56

APR credit score of 699 or lower = 14.25%

(using the APR calculator) total payment over term of loan = $10,529.13

Savings = $10,529.13 - $10,296.56 = 232.57

Answer:

B.) 2 3/4 + (-4 1/4) = -1 2/4

Step-by-step explanation:

blue line: forward with positive +[tex]2\frac{3}{4}[/tex]

red line: backward with negative -[tex]4\frac{1}{4}[/tex]

so the number line follows: [tex]2\frac{3}{4}[/tex] + -[tex]4\frac{1}{4}[/tex] = -1 2/4

Step-by-step explanation:

Mark the end of arrows

So add them

[tex]\\ \tt\hookrightarrow 2\dfrac{3}{4}+(-4\dfrac{1}{4})=-1\dfrac{2}{4}[/tex]

Answer:

8x+10y=160

Step-by-step explanation:

x could equal 20 and y can be 0 or x can be 0 and y is 16.

it's was helpful to you

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