Trigonometric Equations

Solve the equation over the interval [0°, 360°)

cos(theta) = -1/2

The launching of the hot air balloon is from the ocean beach is an illustration of a projectile motion

The function is given as:

[tex]p(x) =-\frac{2}{2500}x^2 + 0.7x[/tex]

Differentiate

[tex]p'(x) =-\frac{4}{2500}x + 0.7[/tex]

Set to 0

[tex]-\frac{4}{2500}x + 0.7 = 0[/tex]

Subtract 0.7 from both sides

[tex]-\frac{4}{2500}x =- 0.7[/tex]

Multiply through by -2500/4

[tex]x =437.5[/tex]

Hence, the horizontal distance which a maximum height is attained is 437.5 meters

In (a), we have:

[tex]x =437.5[/tex]

Substitute [tex]x =437.5[/tex] in p(x)

[tex]p(437.5) =-\frac{2}{2500} * 437.5^2 + 0.7 * 437.5[/tex]

Evaluate

[tex]p(437.5) =153.125[/tex]

Hence, the maximum height above the sea level is 153.125 metres

In (b), the maximum height above the sea level is 153.125 metres

The ratio of the height on land and sea is given as:

Land : Sea = 2 m : 20 m

For the maximum height, we have:

Land : 153.125 m= 2 m : 20 m

Express as fraction

Land / 153.125 m = 2 /20

Multiply both sides by 153.125

Land = 15.3125

Approximate

Land = 15.3

Hence, the maximum height above the ground level is 15.3 meters

We have:

[tex]p(x) =-\frac{2}{2500}x^2 + 0.7x[/tex]

Substitute 50 for P(x)

[tex]-\frac{2}{2500}x^2 + 0.7x = 50[/tex]

Using a graphing calculator, we have:

x = 78.465 and 796.535

Hence, the horizontal distances where the balloon 50 m above the ground are 78.465 and 796.535 meters

Read more about projectile motion at:

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Answer:

128 because formula is bh

Step-by-step explanation:

Answer:

6 3 5 6 8 8

Step-by-step explanation:

number is farthest apart from others

Answer:

The correct answer is 90

Step-by-step explanation:

90 is the biggest number in the number set so therefore it is an outlier.

Have an amazing day!!

Please rate and mark brainliest!!

Answer:

Amount Robert will pay back = $434.04

Step-by-step explanation:

Formula for interest is;

I = (P * R * T)/100

We are given;

P = $390

Rate = 18%

Time; T = 229 days = 229/365

Thus;

I = (390 * 18 * (229/365))/100

I = $44.04

Thus, total amount Mario will pay back = $390 + $44.04 = $434.04

Answer:

that would be the circumference of  the circle

= 2 pi  r

= 2 * pi * 2

=  6.28 feet   to 2 DP's.

Step-by-step explanation:

Answer:

6 ft

Step-by-step explanation:

Convert the unit of length. Round the answer to one decimal place if necessary. 180 cm ≈ _____ ft

[tex]Ft=\frac{cm}{30.48}\\\\Ft=\frac{180}{30.48}\\\\Ft=5.90551181\\\\Ft\approx 6[/tex]

180 cm ≈ 6 ft

Hope this helps!

Answer:

10 large bags and 11 small bags because 10*9=90 and 156-90=66 and 6*11=66 so 90+66=156

Still stuck? Get 1-on-1 help from an expert tutor now.

Step-by-step explanation:

EZ

Answer:

Four and three arithmetic numbers of this equation are then

Step-by-step explanation:

[tex]x = 3 = x = 4 > - 4 > < - 3 = x = 4[/tex]

And the numbers are equal

[tex]x = 4 \\ y = 3 \\ x \times y = 12 = 12 > 4 > 3 = xy = 0 = \\ xy = - 12[/tex]

Answer:

Step-by-step explanation:

numbers are {3.46,3.47,3.48,3.49,3.50,3.51,3.52,3.53,3.54,3.55,3.56,3.57,3.58,3.59}

Answer:

3/5

Step-by-step explanation:

3/5=6/10

3/5=60/100

Answer:

6

Step-by-step explanation:

Divide the amount of eggs by the amount of people this gives you the amount of eggs needed for one person then times by 9

(4÷6) x9

Answer:

is this from flvs?

Step-by-step explanation:

The exponential function with a growth factor has a rate greater than 1

The percentage growth rate is 276%

The growth factor (b) is given as:

b = 3.76

The growth factor (b) is greater than 1.

So, the percentage growth rate (r) is calculated as:

r = b - 1

Substitute known values

r = 3.76 - 1

Evaluate the difference

r = 2.76

Express as percentage

r = 276%

Hence, the percentage growth rate is 276%

Read more about exponential functions at:

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Answer:

176cm

400 times

Step-by-step explanation:

Answer:

(0,5)

Step-by-step explanation:

I'm really not sure but I'm pretty positive that this is the answer if not than my bad

Answer:

570 ft²

Step-by-step explanation:

Basically, you find the area of Juan and Matthew's gardens then add them up.  

First let's find the area of Juan's garden.

Area is equal to length times width ([tex]a = lw[/tex])

So you do 16 * 12 which equals 192.

Now let's find the area of Matthew's garden.

So you do 18 * 21 which equals 378.

Then you add up both areas.

192 + 378 = 570

Answer:

En la Imagen adjunta

Step-by-step explanation:

Toca Para Abrir Imagen

Espero haberte ayudado si es así dame Corona

Answer:

One Solution

Step-by-step explanation:

Given:

6 + x/5 = x/5 - 5 - 3x/10

To Find:

How many solutions?

Solve:

[tex]6+\frac{x}{5}=\frac{x}{5}-5-\frac{3x}{10}[/tex]

[tex]\mathrm{Subtract\:}\frac{x}{5}\mathrm{\:from\:both\:sides}[/tex]

[tex]6+\frac{x}{5}-\frac{x}{5}=\frac{x}{5}-5-\frac{3x}{10}-\frac{x}{5}[/tex]

[tex]\mathrm{Simplify}[/tex]

[tex]6=-5-\frac{3x}{10}[/tex]

[tex]\mathrm{Add\:}5\mathrm{\:to\:both\:sides}[/tex]

[tex]-5-\frac{3x}{10}+5=6+5[/tex]

[tex]\mathrm{Simplify}[/tex]

[tex]-\frac{3x}{10}=11[/tex]

[tex]\mathrm{Multiply\:both\:sides\:by\:}10[/tex]

[tex]10\left(-\frac{3x}{10}\right)=11\cdot \:10[/tex]

[tex]\mathrm{Simplify}[/tex]

[tex]-3x=110[/tex]

[tex]\mathrm{Divide\:both\:sides\:by\:}-3[/tex]

[tex]\frac{-3x}{-3}=\frac{110}{-3}[/tex]

[tex]\mathrm{Simplify}[/tex]

[tex]x=-\frac{110}{3}\;or\;\left(\mathrm{In \;Decimal\;form}:\quad x=-36.66666\dots \right)[/tex]

~lenvy~

The number of times that the clock was skipping every 30 minutes from Friday noon to Monday 6 pm is; 3 seconds

We know that from time conversion;

1 day = 24 hours

1 hour = 60 minutes = 2 × (30 minutes)

1 day = 24 hours × 2 × (30 minutes)

1 day = 48 × (30 minutes)

Thus, there are 48 times of 30-minutes in a day. However on Friday, we start counting at noon, which is half of the day.

Thus, on Monday, the mark is only up to 6 pm, which is three-fourths of the day. Thus;

Friday = 48 × (3/4)  = 24

Saturday = 48

Sunday = 48

Monday = 48 × (3/4)  = 36

Total times = 24 + 48 + 48 + 36 = 156

Thus, it means that there was 156 times of  30-minutes that have passed during the time period.

x = 468 seconds ÷ 156

x = 3 seconds  

Therefore, the clock was skipping 3 seconds every 30 minutes from Friday noon to Monday 6 pm.

Read more about Least common multiple at; https://brainly.com/question/10749076

Answer:

the answer b

Step-by-step explanation:

te answer b because I guessed

Answer

Parallelogram: A quadrilateral with 2 pairs of parallel sides. Rectangle: A parallelogram with 4 right angles.

Answer:

Suppose that we want to find the probability that when six consumers are randomly selected, actually three of them are comfortable with delivery by drones.

Step-by-step explanation:   hopes this helps you!

x = 6

Step-by-step explanation:

[tex]\sf3(x - 2) = 12 \\ \sf3x - 6 = 12 \\\sf3x = 12 + 6 \\ \sf3x = 18 \\ \sf \: x = \frac{18}{3} \\ \sf \: x = 6[/tex]

Answer: (negative solution): x=-2, (positive solution): x=6

Solve for x by simplifying both sides of the equation, then isolating the variable.

x=−2

hope this is what your looking for

Answer:

x = -2

Step-by-step explanation:

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

[tex]\mathrm{Add\:}4\mathrm{\:to\:both\:sides}[/tex]

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

[tex]Simplify[/tex]

[tex]x=-\frac{1}{2}+\frac{3}{4}x[/tex]

[tex]\mathrm{Subtract\:}\frac{3}{4}x\mathrm{\:from\:both\:sides}[/tex]

[tex]x-\frac{3}{4}x=-\frac{1}{2}+\frac{3}{4}x-\frac{3}{4}x[/tex]

[tex]\frac{1}{4}x=-\frac{1}{2}[/tex]

[tex]\mathrm{Multiply\:both\:sides\:by\:}4[/tex]

[tex]4\cdot \frac{1}{4}x=4\left(-\frac{1}{2}\right)[/tex]

[tex]x=-2[/tex]

~lenvy~

Answer:

A. shifted 3 units left and 2 units up

Answer:

shifted 3 units left and 2 units up

Hello!

To solve this exercise, we must use the formula below:

[tex]\mathrm{C=2\cdot\pi\cdot r}[/tex]

Knowing these values, let's replace them in the formula to obtain r:

[tex]\mathrm{62.8=2\cdot\ 3.14\cdot r}\\\mathrm{62.8=6.28r}\\\mathrm{6.28r=62.8}\\\\\mathrm{r=\dfrac{62.8}{6.28}}\\\\\boxed{\mathrm{r=10}}[/tex]

So, the radius of this circle is 10cm.

Hope this helps!

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

The volume of the cylinder is 218.4 cubic centimeter

The given parameters are:

Circumference (C) = 14 cm

Height (h) = 10.1 cm

Start by calculating the radius (r) using:

[tex]C = 2\pi r[/tex]

So, we have:

[tex]2\pi r = 14[/tex]

Make r the subject

[tex]r =\frac 7\pi[/tex]

The volume of the cylinder is then calculated as:

[tex]V =\pi r^2h[/tex]

This gives

[tex]V =\pi * (\frac{7}{\pi})^2 * 14[/tex]

Evaluate

[tex]V =218.4[/tex]

Hence, the volume of the cylinder is 218.4 cubic centimeter

Read more about volumes at:

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Answer:

Sticks of butter : 2

Number of cookies : 40

Step-by-step explanation:

Given that :You need 3 sticks of butter for every 24 giant cookies you bake.

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

Sticks of butter                    Number of cookies

 3                                           24

 x                                             16

5                                                 y

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

Let the unknown be x and y..

Since you need 3 sticks of butter for every 24 giant cookies you back

Then 24/3 = 8

Since the number of cookies is 16 then 16/8 = 2

Thus x = 2

Next for y.

Since you need 3 sticks of butter for every 24 giant cookies you back

Then 5 * 8 = 40

Thus, y = 40

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

Completed table below:

Sticks of butter                    Number of cookies

 3                                           24

 2                                             16

5                                                 40

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

~lenvy~

Answer:

See below ↓

Step-by-step explanation:

Given

Base rate

16 cookies

5 butter sticks

Answer:

4x + 9 ≥ 0

Step-by-step explanation:

The inside of the square root, the radicand, cannot be negative.

It can only be zero or positive.

Zero or positive is also described as being greater than or equal to 0.

Set the radicand to be greater than or equal to zero.

4x + 9 ≥ 0

Answer:

4x+9>=0

Step-by-step explanation:

The domain of a square root is that it can’t be less than 0. So we have the equation 4x+9>=0.

Answer:

[tex]x=8[/tex]

Step-by-step explanation:

For an equation in the form of [tex]y=a(x-h)^2+k[/tex], the axis of symmetry is where [tex]x=h[/tex]. In this case, the axis of symmetry is the line [tex]x=8[/tex]

Step-by-step explanation:

please mark me as brainlest

Answer:

Step-by-step explanation:

1 2/3 -(-1/2)

=5/3+1/2

[tex]=\frac{10+1}{6} \\=\frac{11}{6} \\=1\frac{5}{6}[/tex]