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3 years ago

HELPP PPLEASEEE!!!

Mathematics

2 answers:

olga2289 [7]3 years ago

5 0

Answer:

See below in bold.

Step-by-step explanation:

Ship's vector:

Horizontal component = 30 cos 30 = 25.98.

Vertical component = 30 sin(-30) = -15.

So it is <25.98, -15).

The current's vector:

Horizontal component = 5 sin 20 = 1.71.

Vertical component = 5 cos 20 = 4.7.

So it is <1.71, 4.7>.

astraxan [27]3 years ago

3 0

Answer:

Step-by-step explanation:

Resultant R of the two vectors is

$R^2=a^2+b^2+2abcos\theta$

$R^2=30^2+5^2+2\left ( 30\right )\left ( 5\right )cos\theta$

Where $\theta$ is the angle between Two vectors which is 100^{\circ}[/tex]

$R^2=900+25+2\times 30\times 5\times cos100$

$R^2=925-52.094$

R=29.544 miles per hour

and it makes an angle $\phi$ with 30 miles/hr vector

$tan\phi =\frac{5}{30}$

$\phi =tan^{-1}\frac{1}{6}$

$\phi =9.462^{\circ}$

i.e.it makes an angle of 20.538 South of east with horizontal

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1 Point

I am Lyosha [343]

Option C

The ratio for the volumes of two similar cylinders is 8 : 27

<h3><u>Solution:</u></h3>

Let there are two cylinder of heights "h" and "H"

Also radius to be "r" and "R"

$\text { Volume of a cylinder }=\pi r^{2} h$

Where π = 3.14 , r is the radius and h is the height

Now the ratio of their heights and radii is 2:3 .i.e

$\frac{\mathrm{r}}{R}=\frac{\mathrm{h}}{H}=\frac{2}{3}$

<em><u>Ratio for the volumes of two cylinders</u></em>

$\frac{\text {Volume of cylinder } 1}{\text {Volume of cylinder } 2}=\frac{\pi r^{2} h}{\pi R^{2} H}$

Cancelling the common terms, we get

$\frac{\text {Volume of cylinder } 1}{\text {Volume of cylinder } 2}=\left(\frac{\mathrm{r}}{R}\right)^{2} \times\left(\frac{\mathrm{h}}{\mathrm{H}}\right)$

Substituting we get,

$\frac{\text {Volume of cylinder } 1}{\text {Volume of cylinder } 2}=\left(\frac{2}{3}\right)^{2} \times\left(\frac{2}{3}\right)$

$\frac{\text {Volume of cylinder } 1}{\text {Volume of cylinder } 2}=\frac{2 \times 2 \times 2}{3 \times 3 \times 3}$

$\frac{\text {Volume of cylinder } 1}{\text {Volume of cylinder } 2}=\frac{8}{27}$

Hence, the ratio of volume of two cylinders is 8 : 27

7 0

3 years ago

An employee receives a weekly salary of $340 and a 6% commission on all sales.

Alina [70]

340+.06(sales)
340+.06(660)

$379.60

5 0

3 years ago

The MagicSoft software company has a proposal to the city council of Alva, Florida, to relocate there. The proposal claims that

EleoNora [17]

Answer:

The correct estimate of the amount generated to the local economy is $3,333,333. $\bar3$

Step-by-step explanation:

The amount the expected to be generated for the local economy = $3.3 million

The amount of salaries that will generate $3.3 million = $1 million

The percentage of the amount of the salaries and the subsequent earnings expected to be spent on the local community = 70%

Therefore, we have;

For a first amount of 1 million into the economy, the next amount to into the economy is 70/100 × 1 million = 700,000, then we have 70/100 × 700,000 and so on, which is a geometric sequence, with first term, a = $1 million, the common ratio, r = 70/100 = 0.7, the number of terms = Infinity = ∞

The sum of a geometric sequence to infinity is given as follows;

$\sum\limits_{k = 0}^{\infty }a \cdot r^k = S_{\infty} = \dfrac{a}{1 - r}$