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kenny6666 [7]
3 years ago
7

Two people start from the same point. One walks east at 4 mi/h and the other walks northeast at 8 mi/h. How fast is the distance

between the people changing after 15 minutes?
Mathematics
1 answer:
kvasek [131]3 years ago
4 0

Answer:

5.89 mi/h

Step-by-step explanation:

This problem can be solved by using different methods. I will use vectors since it's the simplest way in which we can solve it. This can be solved by using related rates of change though.

First, we start by drawing a diagram with the velocity vectors.

A= velocity of the first person

B= velocity of the second person

C= velocity in which they are moving away from each other.

Since there is no acceleration in the problem, we can suppose we are talking about constant speeds, so the velocity at which they are moving away from each other will always remain constant. (It doesn't matter what time it is, the velocity will always be the same)

Having said this we can solve this problem by using the components, by using law of cosines or graphically. I will use law of cosines. The idea is to find the length of side c.

Law of cosines:

C^{2}=A^{2}+B^{2}-2ABcos \gamma

so we can solve the formula for C so we get:

C=\sqrt{A^{2}+B^{2}-2ABcos \gamma}

and now we can substitute the values we know:

C=\sqrt{(4)^{2}+(8)^{2}-2(4)(8)cos 45^{o}}

C=\sqrt{16+64-32\sqrt{2}}

C=\sqrt{80-32\sqrt{2}} mph

if we want an exact answer, then that will be the exact answer, which approximates to:

C=5.89 mph

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The base of the triangle decreases by 30% and the height increases by 20%.
sergeinik [125]

Answer:

Area decreases by 16%

Step-by-step explanation:

Use formula for the area of the triangle

A=\dfrac{1}{2}\cdot \text{Base}\cdot \text{Height}

<u>Initial triangle:</u>

The base is 18 cm

The height is 5 cm

The area is

A_{initial}=\dfrac{1}{2}\cdot 18\cdot 5=45\ cm^2

<u>New triangle:</u>

The base is (1-0.3)\cdot 18=0.7\cdot 18=12.6\ cm

The height is (1+0.2)\cdot 5=1.2\cdot 5=6\ cm

The area is

A_{new}=\dfrac{1}{2}\cdot 12.6\cdot 6=37.8\ cm^2

Area decreases by

100\%-\dfrac{37.8}{45}\cdot 100\%=100\%-84\%=16\%

5 0
3 years ago
A right triangle has legs measuring 18 in. and 26 in. What is the length of the hypotenuse? Round to the nearest tenth. A) 18.8
Evgen [1.6K]

Answer:

a

Step-by-step explanation:

3 0
3 years ago
X + 2y = –6<br> 3x + 8y = –20
Kay [80]
What do you want to calculate?

CALCULATE IT!
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Problem:
Solve
x
+
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−
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3
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+
8
y
=
−
20
Steps:
I will solve your system by substitution.
(You can also solve this system by elimination.)
x
+
2
y
=
−
6
;
3
x
+
8
y
=
−
20
Step: Solve
x
+
2
y
=
−
6
for x:
x
+
2
y
+
−
2
y
=
−
6
+
−
2
y
(Add -2y to both sides)
x
=
−
2
y
−
6
Step: Substitute
−
2
y
−
6
for
x
in
3
x
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−
20
:
3
x
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8
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3
(
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y
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6
)
+
8
y
=
−
20
2
y
−
18
=
−
20
(Simplify both sides of the equation)
2
y
−
18
+
18
=
−
20
+
18
(Add 18 to both sides)
2
y
=
−
2
2
y
2
=
−
2
2
(Divide both sides by 2)
y
=
−
1
Step: Substitute
−
1
for
y
in
x
=
−
2
y
−
6
:
x
=
−
2
y
−
6
x
=
(
−
2
)
(
−
1
)
−
6
x
=
−
4
(Simplify both sides of the equation)
Answer:
x
=
−
4
and
y
=
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1
3 0
3 years ago
The height of a right rectangular prism is 3 units greater than the length of the base. The edge length of the square base is x
jok3333 [9.3K]

Answer:

B. x^3 + 3x^2

Step-by-step explanation:

Volume of a rectangular prism=width * length * height

V=w*l*h

h=3 greater than the length of the base

h=x+3

Length of the base=x

Width=x

Substituting values into the formula

V=w*l*h

=(x)*(x)*(x+3)

Multiplying

=(x^2)(x+3)

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Option B is the correct answer

5 0
3 years ago
Can you help me please I don't understand. ​
Dimas [21]

B. A and b parrel never touch

C. 44

D.136

E.44

Hope this helps a little

8 0
3 years ago
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