Please look at the image

Answer:

[tex]\boxed{\pink{\tt I = \dfrac{1}{3}sin(3x) - 3cos(x) + C}}[/tex]

Step-by-step explanation:

We need to integrate the given expression. Let I be the answer .

[tex]\implies\displaystyle\sf I = \int (cos(3x) + 3sin(x) )dx \\\\\implies\displaystyle I = \int cos(3x) + \int sin(x)\ dx [/tex]

[tex]\implies\displaystyle\sf I = \int cos\ u \dfrac{1}{3}du + \int 3sin \ x \ dx \\\\\implies\displaystyle \sf I = \int \dfrac{cos\ u}{3} du + \int 3sin\ x \ dx \\\\\implies\displaystyle\sf I = \dfrac{1}{3}\int \dfrac{cos(u)}{3} + \int 3sin(x) dx \\\\\implies\displaystyle\sf I = \dfrac{1}{3} sin(u) + C +\int 3sin(x) dx \\\\\implies\displaystyle \sf I = \dfrac{1}{3}sin(u) + C + 3\int sin(x) \ dx \\\\\implies\displaystyle\sf I = \dfrac{1}{3}sin(u) + C + 3(-cos(x)+C) \\\\\implies \underset{\blue{\sf Required\ Answer }}{\underbrace{\boxed{\boxed{\displaystyle\red{\sf I = \dfrac{1}{3}sin(3x) - 3cos(x) + C }}}}}[/tex]

Answer:

The rate at which the tip of his shadow is moving down is [tex]\frac{24}{15} ft/sec[/tex]

Step-by-step explanation:

Given - A flood lamp is installed on the ground 200 feet from a vertical wall. A six-foot-tall man is walking towards the wall at the rate of 30 feet per second.

To find - How fast is the tip of his shadow moving down the wall when he is 50 feet from the wall ?

Proof -

From the given information, the figure becomes

Triangle ABC and Triangle DBE are similar triangle

AC/DE = BC/BE

⇒h/6 = 200/(200-x)

⇒h = 1200/(200 -x)

Now,

Differentiate h with respect to t, we get

[tex]\frac{dh}{dt} = 1200(-\frac{1}{(200-x)^{2} } )(-1)\frac{dx}{dt}[/tex]

⇒[tex]\frac{dh}{dt} = (\frac{1200}{(200-x)^{2} } )\frac{dx}{dt}[/tex]

Now,

If the rate of the tip is moving down the wall

At x = 50 feet, dx/dt = 30 feet per second

So,

⇒[tex]\frac{dh}{dt} = (\frac{1200}{(200-50)^{2} } )(30)[/tex]

⇒[tex]\frac{dh}{dt} = \frac{1200}{(150)^{2} } (30)[/tex]

⇒[tex]\frac{dh}{dt} = \frac{1200}{(150)(150) } (30)[/tex]

⇒[tex]\frac{dh}{dt} = \frac{24}{15 }[/tex]

So, we get

The rate at which the tip of his shadow is moving down is [tex]\frac{24}{15} ft/sec[/tex]

Answer:

790000

Step-by-step explanation:

Answer:

790,000

Step-by-step explanation:

Answer:

0.8k +14

Step-by-step explanation:

See the steps below:)

Answer:

we have

-3+4i

let magnitude be |z|

|z|=[tex] \sqrt{( - 3) {}^{2} + 4 {}^{2} } [/tex]

|z|=5 unit

Answer:

The magnitude of -3 +4i is 5

Step-by-step explanation:

Answer:

49

Step-by-step explanation:

the number would simply be

14÷2=7

7²=49

Answer:

15 plates

Step-by-step explanation:

450 divided by 30 = 15, meaning 30 x 15 would be 450 mg. This also means that if the weight of some plates was 450 mg, there would be 15 plates.

Answer:

15

Step-by-step explanation:

Your units are a little confused.

The mass (total ) is 450 mg

1 plate weighs 30 mg

1 plate / 30 mg  =  x plates / 450 mg             Cross multiply

1 * 450 = 30x                                                   Divide by 30

450 / 30 = x

x = 15

There are 15 gold plates.

Answer:

Elimination

x = 2

y = -2

Step-by-step explanation:

Elimination

2x + 4y = -4

2x - y = 6

Subtract the second equation from the first

5y = -10

Divide both sides by 5

y = -2

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

Substitute for y = -2 in the second equation

2x - -2 = 6

2x + 2 = 6

subtract 2 from both sides

2x = 4

Divide both sides by 2

x = 2

Answer:

Of(x) = 2(x + 5)(x + 5)(x + 5)(x - 12) or Choice 2

Step-by-step explanation:

The last two answers get eliminated because their leading coefficients aren't 2. The first option is wrong because if you plug in -5 and +12 into x the function won't equal 0. So the correct answer is the Second answer: Of(x) = 2(x + 5)(x + 5)(x + 5)(x - 12)

Answer:

The polynomial function that has a leading coefficient of 2, a root of 5 with a multiplicity of 3, and a root of 12 with a multiplicity of 1 is choice 2.

Step-by-step explanation:

A leading coefficient of 2 means that the number multiplying all the binomial would be 2, so you know it is not choices 3 and 4. A root of -5 with a multiplicity of 3 means that when you replace x with -5, three binomials will result in 0, which helps eliminate the first choice. A root of 12 with a multiplicity of 1 means that when you replace x with 12, you will have a binomial that results in 0. Using all of this information, you'll get that the polynomial that has a leading coefficient of 2, a root of -5 with a multiplicity of 3, and a root of 12 with a multiplicity of 1 is [tex]f(x)=2(x+5)(x+5)(x+5)(x-12)[/tex].

Answer:

The standard error is [tex]s = \sqrt{\frac{\pi_1(1-\pi_1)}{n_1}+\frac{\pi_2(1-\pi_2)}{n_2}}[/tex], in which [tex]p_1,p_2[/tex] are the proportions and [tex]n_1,n_2[/tex] are the sample sizes.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

The standard error is:

[tex]s = \sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

For the difference of proportions:

For proportion 1, the standard error is:

[tex]s_1 = \sqrt{\frac{\pi_1(1-\pi_1)}{n_1}}[/tex]

For proportion 2, the standard error is:

[tex]s_2 = \sqrt{\frac{\pi_2(1-\pi_2)}{n_2}}[/tex]

For the difference:

The standard error is the square root of the sum of the squares of each separate standard error. So

[tex]s = \sqrt{(\sqrt{\frac{\pi_1(1-\pi_1)}{n_1}})+(\sqrt{\frac{\pi_2(1-\pi_2)}{n_2}})^2} = \sqrt{\frac{\pi_1(1-\pi_1)}{n_1}+\frac{\pi_2(1-\pi_2)}{n_2}}[/tex]

The standard error is [tex]s = \sqrt{\frac{\pi_1(1-\pi_1)}{n_1}+\frac{\pi_2(1-\pi_2)}{n_2}}[/tex], in which [tex]p_1,p_2[/tex] are the proportions and [tex]n_1,n_2[/tex] are the sample sizes.

Answer:

700

Hope this helps!!

Answer:

700

Step-by-step explanation:

Answer:

3 gallons or 3.032

Step-by-step explanation:

find the total surface area (758)

divide by 250 or subtract 250 till it is under that number

Answer:

1/16

Explanation:

You have a 1/4 chance both times but in probability you multiply when in a sequence of events. 1/4*1/4= 1/16

If G is the incenter of ∆ABC, then GD = GF = GE.

Given, GD is 3x + 5 and GF is 6x - 4.

According to the above statement,

GD = GF

or, 3x + 5 = 6x - 4

or, 5 + 4 = 6x - 3x

or, 9 = 3x

or, 9/3 = x

or, 3 = x

The value of x is 3.

By putting the value of x in GD or GF, we get

GD = 3(3) + 5 = 9 + 5 = 14

GF = 6(3) - 4 = 18 - 4 = 14

Therefore, GE = 14.

Answer:

C. [tex]D_\frac{1}{7} (P)=P'(\frac{1}{4},-\frac{5}{14} )[/tex]

Step-by-step explanation:

[tex]\frac{7}{4}*\frac{1}{7}=\frac{7}{28} =\frac{1}{4}[/tex]

[tex]-\frac{5}{2} *\frac{1}{7} =-\frac{5}{14}[/tex]

Answer:

That would be (8,0) my good sir ( ma'am )

Step-by-step explanation:

Have a nice day

Answer: 270°

Step-by-step explanation:

A full rotation is 360° so to find out the clockwise equivalent of a 90° counterclockwise rotation, deduct the counterclockwise rotation from 360°:

= 360 - 90

= 270°

If you rotated 90° counterclockwise, you would get to the same point as if you rotated 270° clockwise.

[tex]{\boxed{\mathcal{\red{h\:=\:9.5}}}}[/tex] ✅

[tex]h + \frac{1}{2} = 10 \\ ⇢ h + 0.5 = 10 \\ ⇢ h \: = 10 - 0.5 \\ ⇢ h = 9.5[/tex]

[tex]\circ \: \: { \underline{ \boxed{ \sf{ \color{green}{Happy\:learning.}}}}}∘[/tex]

Answer:

If cookies are for $1 and brownies are for $2, let number of cookies = x and number of brownies = y

∴ $1*(x*1) + $2*(y*1) = $13

Step-by-step explanation:

1) You can buy 4 brownies for $2 each = 2*4 = $8

The rest you can buy cookies = 5 cookies = $5

$8+$5=$13

2) You can buy 5 brownies and 3 cookies = $10+$3 = $13

3) You can buy 3 brownies and 7 cookies = $6+$7=$13

Equation: -

If cookies are for $1 and brownies are for $2, let number of cookies = x and number of brownies = y

∴ $1*(x*1) + $2*(y*1) = $13

Answer:

2x= 38.5

Step-by-step explanation:

I'm not sure where u got 12x but 2 x = 38.5:

2x + 5 =82

subtract 5 for 82

2x = 77

77 divided by 2 is 38.5

x = 38.5

hope this helps :)

Answer:

72 in²

Step-by-step explanation:

lateral area: the surface area of a 3D figure, but excluding the area of any bases

the lateral area of this prism is the sum of the three rectangular sides.

calculate the third side of the triangle first because it's also the side of one of the rectangle:

√(5² - 4²) = 3

4 × 6 + 5 × 6 + 3 × 6 = 72

Step-by-step explanation:

7equitacion h< y ⚽ de los siguientes dominios

Answer:

C and F

Step-by-step explanation:

Answer:

A, F

Step-by-step explanation:

ratio of sides in a 30-60-90 triangle is  1 : [tex]\sqrt{3}[/tex] : 2

Answer:

3x-1

Step-by-step explanation:

3x^2+2x-5=3x-1 x1-25

Answer:

(1/4)×4=1/16

Step-by-step explanation:

Blue is 1 out of the 4 colours, it rolls for 4 times

Answer:

b

Step-by-step explanation:

Step-by-step explanation:

school c so B would be correct

Answer:

678.24 cubic centimeters

Step-by-step explanation: