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2 years ago

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two friends went rowing on the river. they traveled with current for 3 hours. the way back took them 4 hours and 48 minutes. fin

d the speed of the rivers current if they can row in still water at the speed of 6.5 mph

1 answer:

N76 [4]2 years ago

4 0

Answer:

1.5 mph

Step-by-step explanation:

The speed in the still water = 6.5 mph.

The speed of the current = x mph.

1. Two friends traveled with current for 3 hours. The speed with the current is 6.5 + x mph, so they traveled $3(x+6.5)$ miles.

2. Two friends traveled against the current for 4 hours and 48 minutes that is $4\dfrac{4}{5}=4.8$ hours. The speed against the current is 6.5 - x mph, so they traveled $4.8(6.5-x)$ miles.

They traveled the same distance with the current and against the current, hence,

$3(x+6.5)=4.8(6.5-x)$

Solve this equation:

$3x+19.5=31.2-4.8x\\ \\3x+4.8x=31.2-19.5\\ \\7.8x=11.7\\ \\x=1.5\ mph$

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John is skiing on a mountain with an altitude of 1200 feet. The angle of depression is 21 About how far does

Agata [3.3K]

Answer:

John ski down the mountain is 1285.37 feet.

Step-by-step explanation:

Given : John is skiing on a mountain with an altitude of 1200 feet. The angle of depression is 21.

To find : About how far does John ski down the mountain ?

Solution :

We draw a rough image of the question for easier understanding.

Refer the attached figure below.

According to question,

Let AB be the height of mountain i.e. AB=1200 feet

The angle of depression is 21 i.e. $\theta=21^\circ$

We have to find how far does John ski down the mountain i.e. AC = ?

Using trigonometric,

$\cos\theta = \frac{AB}{AC}$

$\cos(21)= \frac{1200}{AC}$

$AC=\frac{1200}{\cos(21)}$

$AC=1285.37$

Therefore, John ski down the mountain is 1285.37 feet.

7 0

2 years ago

Find the equation of the plane through the point (2,5,7) that is parallel to the line r=(3i+2j−2k)+t(i+2j+9k) and perpendicular

insens350 [35]

The plane we want to find has general equation

$a(x-2)+b(y-5)+c(z-7)=0$

with $a,b,c$ not equal to 0, and has normal vector

$\vec n=a\,\vec\imath+b\,\vec\jmath+c\,\vec k$

$\vec n$ is perpendicular to both the normal vector of the other plane, which is $4\,\vec\imath+5\,\vec\jmath+6\,\vec k$ , as well as the tangent vector to the line $\vec r(t)$ , which is $\vec\imath+2\,\vec\jmath+9\,\vec k$ .

This means the dot product of $\vec n$ with either vector is 0, giving us

$\begin{cases}4a+5b+6c=0\\a+2b+9c=0\end{cases}$

Suppose we fix $c=1$ . Then the system reduces to

$\begin{cases}4a+5b=-6\\a+2b=-9\end{cases}$

and we get

$(4a+5b)-4(a+2b)=-6-4(-9)\implies-3b=30\implies b=-10$

$a+2(-10)=-9\implies a=11$

Then one equation for the plane could be

$\boxed{11(x-2)-10(y-5)+(z-7)=0}$

or in standard form,

$\boxed{11x-10y+z=-21}$

The solution is unique up to non-zero scalar multiplication, which is to say that any equation $(11x-10y+z)k=-21k$ would be a valid answer. For example, suppose we instead let $c=2$ ; then we would have found $a=22$ and $b=-20$ , but clearly dividing both sides of the equation

$22(x-2)-20(y-5)+2(z-7)=0$

by 2 gives the same equation as before.

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2 years ago

Classify the following polynomials. combine any like terms first

Vaselesa [24]

Answer:

Monomial

Trinomial

Monomial

Trinomial

Binomial

Step-by-step explanation:

Monomial = 1 unique term

Binomial = 2 unique terms

Trinomial = 3 unique terms

In the first one, the -x^2 and the +x^2 cancel out, and since 2x and 4x are like terms, you can combine them, leaving you with 6x, a Monomial.

In the second one, after combining +3-2 you have 3 separate terms that cannot be combined, making it a Trinomial

In the third one, all of the variables cancel each other out, leaving you with one term, 3, making it a Monomial

In the fourth one, after combining like temrs, you are left with:

x^3 + 3x^2 + 7x

Making it a Trinomial

In the last one, the 6x and -6x cancel out, leaving you with two terms, making it a Binomial.

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2 years ago

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Based on the table, how many boys who prefer soccer would you

Citrus2011 [14]

Answer:

Option B) 100

Step-by-step explanation:

we know that

For a total number of 80 students , the number of boys that prefer soccer is equal to 10 (based on the table)

so

using proportion

Find out the number of boys that prefer soccer for a total number of 800 students

$\frac{80}{10}=\frac{800}{x}\\\\x=800(10)/80\\\\x=100$

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2 years ago

Alicia can choose 2 of her 5 best friends to go with her to the amusement park. Her best friends are Connie, Dale, Eric, Finley,

dlinn [17]

Answer:

2

Step-by-step explanation:

5/2= 2.5 ((or 2 1/2) (or 250%) any you prefer) But you can't get half a person to come in the amusement park so we round it down (2.5 → 2)

So the answer is 2

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2 years ago