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lyudmila [28]
3 years ago
5

A square has the sides length 2k-1 units. An equilateral triangle has the sides of the length k+2 units. the square and the tria

ngle have the same perimeter. what is the value of k?
I got k=3 I think I got wrong can someone please correct me???
Mathematics
1 answer:
AlladinOne [14]3 years ago
8 0
I think that you assumed that:
2k - 1 = k + 2

However we can't do this, because a square has 4 sides whilst a triangle only has 3 sides. 
This means that we can say
4(2k - 1) = 3(k + 2) 

We multiply by 4 due to 4 sides of the square, and by 3 due to the 4 sides of the triangle.

Lets expand the brackets, and solve it:

4(2k - 1) = 3(k + 2)
8k -4 = 3k + 6
5k -4 = 6    ( subtract both sides by 3x to collect the x values)
5k = 10      (add both sides by 4 to get the x's alone)
k = 2           (divide both sides by 5 to get what just x is)

So k = 2 units
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The mean is when you add up all of the numbers and divide by the number of numbers. For example, 1,3,5,7,10,13,14
You add all of them. 1+3+5+7+10+13+14 equals 53. Then divide 53 by 7 because there are seven digits.

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EXAMPLE 5 If f(x, y, z) = x sin(yz), (a) find the gradient of f and (b) find the directional derivative of f at (1, 2, 0) in the
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Answer:

<h2>a) f =  sin(yz)i + xzcos(yz)j + xycos(yz)k</h2><h2>b) -2</h2>

Step-by-step explanation:

Given f(x, y, z) = x sin(yz), the formula for calculating the gradient of the function is expressed as ∇f(x, y, z) = fx(x, y, z)i+ fy(x, y, z)j+fz(x, y, z)k where;

fx, fy and fz are the differential of the functions with respect to x, y and z respectively.

a) ∇f(x, y, z) = sin(yz)i + xzcos(yz)j + xycos(yz)k

The gradient of f =  sin(yz)i + xzcos(yz)j + xycos(yz)k

b) Directional derivative of f at (1,2,0) in the direction of v = i + 4j − k is expressed as ∇f(1, 2, 0)*v

∇f(1, 2, 0) = sin(2(0))i +1*0cos(2*0)j + 1*2cos(2*0)k

∇f(1, 2, 0) = sin0i +0cos(0)j + 2cos(0)k

∇f(1, 2, 0) = 0i +0j + 2k

Given v = i + 4j − k

∇f(1, 2, 0)*v (note that this is the dot product of the two vectors)

∇f(1, 2, 0)*v =  (0i +0j + 2k)*(i + 4j − k )

Given i.i = j.j = k.k =1 and i.j=j.i=j.k=k.j=i.k = 0

∇f(1, 2, 0)*v = 0(i.i)+4*0(j.j)+2(-1)k.k

∇f(1, 2, 0)*v = 0(1)+0(1)-2(1)

∇f(1, 2, 0)*v =0+0-2

∇f(1, 2, 0)*v= -2

 

Hence, the directional derivative of f at (1, 2, 0) in the direction of v = i + 4j − k is -2

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Mrs. Nguyen used 1.48 meters of netting to make 4 identical mini hockey goals. How much netting did she use per goal?
snow_tiger [21]

0.37 meters  of netting

<h3>Further explanation</h3>

<u>Given:</u>

Mrs. Nguyen used 1.48 meters of netting to make 4 identical mini hockey goals.  

<u>Question:</u>

How much netting did she use per goal?

<u>The Process:</u>

We will solve the problem of conversion or in other words the ratio or proportion.

Option A: the conversion

Mrs. Nguyen used 1.48 meters of netting to make 4 identical mini hockey goals.  

Then for every 1 goal, she needs 0.37 meters of netting.

Because \boxed{ \ 1 \ goal \times \frac{1.48 \ meters}{4 \ goals} = 0.37 \ meters \ of \ netting.}

Option B: the ratio (or proportion)

In the ratio, we process as follows:

\boxed{ \ 4 \ goals : 1.48 \ meters \ of \ netting \ }

Both are divided by 4.

\boxed{ \ 1 \ goals : 0.37 \ meters \ of \ netting \ }

Thus, she uses 0.37 meters of netting per goal.

Alternative problem

How much netting did she use for 8 goals?

\boxed{ \ 8 \ goal \times \frac{1.48 \ meters}{4 \ goals} = \ ? \ } meters of netting.

We cross out eight and four because they can be divided.

\boxed{ \ 2 \times 1.48 \ meters = 2.96 \ meters \ of \ netting. \ }

She uses 2.96 meters of netting to make 8 identical mini hockey goals.

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Keywords: Mrs. Nguyen, 1.48 meters of netting, to make 4 identical mini hockey goals, how much netting, she uses per goal, conversion, the ratio, proportion

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3 years ago
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