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Triss [41]
3 years ago
10

Vector u has a magnitude of 5 units, and vector v has a magnitude of 4 units. Which of these values are possible for the magnitu

de of u + v?
I believe there are more than one answers:

A: 1 Unit
B: 9 units
C: 11 Units
D: 13 Units
Mathematics
2 answers:
almond37 [142]3 years ago
4 0

Answer:

I would say B-C

Step-by-step explanation:

Alekssandra [29.7K]3 years ago
3 0

Answer:

Option A and B are the correct answer.

Step-by-step explanation:

We have vector u has a magnitude of 5 units, and vector v has a magnitude of 4 units.

We need to find possible magnitude of u +v.

Consider u and v are in same direction, it will give maximum magnitude possible.

         u + v = 5 + 4 = 9, so 9 is the maximum magnitude.

Consider u and v are in opposite direction, it will give minimum magnitude possible.

         u + v = 5 - 4 = 1, so 1 is the minimum magnitude.

So magnitude of u + v lies in between 1 and 9.

Here option A, B lies in between A and B

Option A and B are the correct answer.

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The height of a cylindrical tank is 9.5 feet. The diameter of this tank 1.5 feet longer than the height. The tank was holding wa
dimulka [17.4K]

Answer:

The remaining water on the tank has a volume of approximately 773.841 feet³

Step-by-step explanation:

To solve this problem we first need to calculate the volume of the tank at full capacity, since it is a cylinder we can use the appropriate formula shown below:

volume = pi*r²*h

Where r is half the diameter. Since the diameter of this tank is 1.5 feet longer than the height and the height is 9.5 feet, then the diameter is equal to 11 feet, so the radius must be r = 11/2 = 5.5 feet. We can now use the formula:

volume = pi*(5.5)²*9.5 = 902.815 feet³

Since someone consumed 1/7 of the water, the remainder must be 6/7 of the total volume. So we have:

remainder volume = (6/7)*volume = (6/7)*902.815 = 773.841 feet³

5 0
3 years ago
Read 2 more answers
A carpentry shop currently sells 66000 decoy ducks per year at a cost of 16 dollars each. In the previous year when they raised
Rus_ich [418]

Answer:

19 dollars

Step-by-step explanation:

<h2>Buckle up! This is a good one!</h2>

First we have to find the line that goes trough the two points. And it has the form :

y=mx+b

<em>m is often called the slope.</em>

Given the two points (66000, 16) and (51000, 21) we find m with this formula:

m=\frac{y_{2} -y_{1} }{x_{2} -x_{1} }\\m=\frac{21-16}{51000-66000} \\m=-\frac{5}{15000} \\m=-\frac{1}{3000}

We pick the point (51000,21) and plug it into the equation of the line and we find b:

y= mx + b\\21=(-\frac{1}{3000} )(51000)+b\\21=-17+b\\21+17=b=38

<h3>And we have got our line equation</h3>

y= -\frac{1}{3000}x + 38\\

<u>Where x represents the quantity and y represents the price.</u>

<u />

<h2>The revenue</h2>

The revenue is price times quantity, since price is y and quantity is x, we get

y=-\frac{1}{3000} x+38\\y*x=x*(-\frac{1}{3000} x+38)\\yx=-\frac{1}{3000} x^2+38x\\R(x)=-\frac{1}{3000} x^2+38x

<h3>to maximize the revenue, we get the first derivative:</h3>

R(x)=-\frac{1}{3000} x^2+38x\\R'(x)=-(2)\frac{1}{3000} x+38\\R'(x)=-\frac{2}{3000} x+38\\\\R'(x)=-\frac{1}{1500} x+38\\\\

<h3>and we make R'(x)=0:</h3>

R'(x)=-\frac{1}{1500} x+38=0\\38=\frac{1}{1500} x\\38*1500=x=57000

So the quantity that maximizes revenue is 57000,

<h3>let's find out the price by plugging it into the equation:</h3>

y= -\frac{1}{3000}x + 38\\y= -\frac{1}{3000}(57000) + 38\\y= -19 + 38\\y=19

<h2>And there you go! 19 dollars is the price the carpentry shop should charge per decoy duck.</h2>
7 0
3 years ago
419.10 419.099 greater than equal too or less than
Veronika [31]
419.10>419.099 419.10 is greater than 419.009
4 0
3 years ago
the cost of having one shirt laundered is 6 dollars. each additional shirt costs 4 dollars. write the explicit and recursive for
Katarina [22]

Answer:

<h3>explicit formula- a(n)=6+4(n-1)</h3><h3>recursive formula- a(n)=a(n)-1 +4; a(1)=6</h3>

Step-by-step explanation:

4 0
3 years ago
Which is longer 6 feet or 70 inches
Alja [10]
6 feet.
Hope I helped!
~ Zoe
6 0
3 years ago
Read 2 more answers
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