Answers
Simply find the volume of each figure using their corresponding formulas and compare them! :D
CYLINDER: πr2h
CONE: πr2h ÷ 3
CYLINDER WORK:
Your radius is 2, which was a simple find! It wants it squared, so simply do 2x2 to get your squared radius of 4. Now that you know this, as well as your height, which is 3, let's plug it in!
π×4×3 (I would suggest putting this in your calculator)
=37.7
CONE WORK:
Your radius is 2 again, which was a simple find because its half your diameter, or 4! It wants it squared again, so simply do 2x2 to get your squared radius of 4. Now that you know this, as well as your height, which is 9, let's plug it in! The only difference is you have to divide your whole answer by three since it's different for a cone.
π×4× 9 ÷ 3 (I would suggest putting this in your calculator)
=37.7
Well, what a coincidence, they are the same! This proves that it does not depend on the height, it will only depend on the proportions of your shape, since the cylinder could have had a much larger scale of numbers, which would make it bigger not based on it's shape, but it's overall size.
Related Questions
Use a parameterization to find the flux ModifyingBelow Integral from nothing to nothing Integral from nothing to nothing With Upper S Bold Upper F times n d sigma of Bold Upper F equals z squared Bold i plus xj minus 4 z Bold k in the outward direction (normal away from the x-axis) across the surface cut from the parabolic cylinder zequals1minusysquared by the planes xequals0, xequals1, and zequals0.
Answers
Here is the correct interpretation of the question with the help of the text editor tool.
Use a parameterization to find the flux [tex]\int\limits \int\limits_s \ F. \ n \ d \sigma[/tex] of F = z²i + xj - 2zk in the outward direction
(normal away from the x-axis) across the surface cut from the parabolic cylinder z = 16 -y² by the planes x = 0 , x = 1, and z = 0 .
The flux is .
Answer:
[tex]-\frac{512}{3}[/tex]
Step-by-step explanation:
F(x,y,z) = (z² ,x , - 2z)
To find the flux across a surface : [tex]\int\limits \int\limits_s \ F. \ n \ dS = \int\limits \int\limits_D \ F. (r_u * r_v) \ dA[/tex]
The sphere z is given as = 16 -y², above x = 0 , x= 1, and z = 0
When z = 0 ⇒ 16 - y² = 0
⇒ y = ± 4
The parameterization is y=v⇒z= 16 -v² and x= u
⇒ r = (x,y, z) = ( u,v,16 - v²)
with 0 ≤ u ≤ 1 and -4 ≤ v ≤ 4
However the normal vector can now be determined as :
[tex]r_u = (1,0,0) , \ \ \ r_v = (0,1, - 2v)[/tex]
[tex]n = r_u*r_v = \left[\begin{array}{ccc}i&j&k\\1&0&0\\0&1&-2v\end{array}\right] = (0,2v,1)[/tex]
[tex]\int\limits \int\limits_s \ F. \ n \ dS = \int\limits \int\limits_D \ F. (r(u,v)) .(r_u*r_v)dA[/tex]
[tex]=\int\limits^1_0 \int\limits^4_{-4} [(16-v^2)^2 , u , -2 (16-v^2)](0,2v,1)dvdu[/tex]
[tex]=\int\limits^1_0 \int\limits^4_{-4} [2uv-2(16-v^2))dvdu[/tex]
[tex]=\int\limits^1_0 (uv^2 -32v+ \frac{2v^3}{3})^ ^4}__{-4}} du[/tex]
[tex]=\int\limits^1_0 (u(16-16)-32(8)+\frac{2}{3}(128))du[/tex]
[tex]= \int\limits^1_0 (-\frac{512}{3})du[/tex]
[tex]= - \frac{512}{3}(u)^ ^1}__0[/tex]
= [tex]-\frac{512}{3}[/tex]
The flux of a vector field across a surface is calculated by computing the surface integral of the vector field in the direction normal to the surface. This involves parametrizing the surface and taking antiderivatives based on the defined area. The direction of the flux is crucial as it determines the sign of the flux.
Explanation:To find the flux of the vector field upper Case Bold F across a surface, we need to compute the surface integral of upper Case Bold F in the given direction. For the given problem, the surface is defined by the parabolic cylinder z = 1 - y^2 and the planes x = 0, x = 1, z = 0. We parametrize this surface using two parameters x and y, with x ranging from 0 to 1, and y ranging from -1 to 1.
We then compute the surface integral by taking the antiderivative of the defined area with the boundaries of surface as the integral's bounds. This process might involve computation of multiple integrals if the surface is composed of multiple parts.
Note that the direction of the flux, which is normal away from the x-axis, is important for the calculation, as it determines the sign of the flux. The flux is positive if the angle between the vector field and the outward normal to the surface is less than 90 degrees, and negative otherwise.
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Using modern methods, the first step in solving the quadratic equation x2 + 7x = 8 would be to put it in standard form by
Answers
Answer:subtracting 8 from both sides
Step-by-step explanation:
Answer:
The answer is C, subtracting 8 from both sides
Step-by-step explanation:
The second answer is A, -8
assuming youre on edg
When you send mail via the post office, you have an 80% chance that it is
delivered to the correct location. (Use this information to answer questions #3 &
#4 below.)
Your answer
Answers
1. On Monday, about 86 letters were delivered incorrectly out of 430.
2. On Tuesday, approximately 625 letters were delivered in total.
1. For Monday:
Given an 80% chance of delivering correctly, the expected number of letters delivered incorrectly is 20% of 430:
[tex]\[ 0.20 \times 430 = 86 \text{ letters} \][/tex]
2. For Tuesday:
If 500 letters were delivered correctly, it means 100% - 80% = 20% were delivered incorrectly. So, the total number of letters delivered is:
[tex]\[ \frac{100}{80} \times 500 = 625 \text{ letters} \][/tex]
Complete Question:
Latoya made $306 for 17 hours of work.
At the same rate, how many hours would she have to work to make $ 162?
hours
Answers
Answer:
9 hours of work
Step-by-step explanation:
306/17 = 18 per hour
so 162/18 = 9
Answer:
9 hours
Step-by-step explanation:
We can make a proportion and solve
She makes $306 for 17 hours of work,and she makes $162 for x hours of work
306/17=162/x
Cross multiply
306*x=17*162
306x=2754
Now we need to solve for x, by getting x by itself. x is being multiplied by 306; to undo this, divide both sides by 306
306x/306=2754/306
x=9
So, she needs to work 9 hours to make $162
7/4y=-(2x-7) slope intercept form
Answers
Answer:
y = -8/7x +4
Step-by-step explanation:
7/4y=-(2x-7)
Distribute the minus sign
7/4y=-2x+7
Multiply each side by 4/7
4/7*7/4y=4/7*-2x+7*4/7
y = -8/7x +4
Answer:
y = -8/7x + 4
Step-by-step explanation:
1) First remove the parentheses
7/4 y = -2x + 7
2) Then multiply by 4 to get rid of the denominator
7y = -8x +28
3) Now divide by 7 on both sides, this way you'll isolate the y variable on the left side
y = -8/7x +4
ask me questions if u have any
Which ratio is equivalent to 3:3?
Answers
The ratio 3:3 signifies equality between two quantities and an equivalent ratio can be found by scaling both parts by the same number. Dividing both parts by 3 gives us the simplest form, which is 1:1.
Explanation:A ratio compares two quantities and can be written in various forms such as fractions, with a colon, or with the word "to". The ratio 3:3 is an expression comparing two equal quantities. To find an equivalent ratio, we can simplify or scale the ratio by multiplying or dividing the numerator and denominator (the two parts of the ratio) by the same number.
In this case, dividing both parts of the ratio 3:3 by 3 gives us an equivalent ratio of 1:1, which also represents equality between two quantities. Multiplying both parts by a common number will also produce an equivalent ratio. For example, multiplying 3:3 by 2 gives us 6:6, which is still equivalent. It's essential to maintain the equality of the two parts when finding an equivalent ratio.
Ratios can be applied to various situations, including unit conversions, scale factors, proportions, and comparisons in scientific experiments, such as the ratio of amplitudes in a double-slit experiment in Physics.
A box contains some shapes, out of which 3 are triangles, 5 are squares and 2 circles. If a shape is selected randomly from the box, what is the probability of selecting a triangle or circle? Question 10 options: a) 1/2 b) 1/4 c) 7/10 d) 4/5
Answers
Answer:
a) 1/2
Step-by-step explanation:
All we have to do is simply find the probability of selecting a triangle, find the probability of selecting a circle and then add them together.
There are a total of 10 shapes in the box.
There are 3 triangles, so, the probability of picking a triangle is:
3/10
There are 2 circles, so, the probability of selecting a circle is:
2/10
Adding them together yields:
3/10 + 2/10 = 5/10 = 1/2
The probability of selecting a triangle or circle is 1/2.
A random sample of 100 people from region A and a random sample of 100 people from region B were surveyed about their grocery-shopping habits. From the region A sample, 16 percent of the people indicated that they shop for groceries online. From the region B sample, 24 percent of the people indicated that they shop for groceries online. At the significance level of α=0.05, do the data provide convincing statistical evidence that there is a difference between the two regions for the population proportions of people who shop online for groceries? Complete the appropriate inference procedure to support your answer.
Answers
Answer:
Step-by-step explanation:
This is a test of 2 population proportions. Let a and b be the subscript for people from region A and region B. The population proportions would be pa and pb
pa - pb = difference in the proportion of people from region A and region B.
The null hypothesis is
H0 : pa = pb
pa - pb = 0
The alternative hypothesis is
H1 : pa ≠ pb
pa - pb ≠ 0
it is a two-tailed test
Sample proportion = x/n
Where
x represents number of success
n represents number of samples
For region A,
xa = 16
na = 100
pa = 16/100 = 0.16
For region B,
xb = 24
nb = 100
pb = 24/100 = 0.24
The pooled proportion, pc is
pc = (xa + xb)/(na + nb)
pc = (16 + 24)/(100 + 100) = 0.2
1 - pc = 1 - 0.2 = 0.8
z = (pa - pb)/√pc(1 - pc)(1/na + 1/nb)
z = (0.16 - 0.24)/√(0.2)(0.8)(1/100 + 1/100) = - 0.08/√0.0002891223
z = - 1.41
Since it is a 2 tailed test, we would find the p value by doubling the area to the left of the z score to include the area to right.
Area to the left from the normal distribution table is
0.07927
P value = 0.07927 × 2 = 0.16
Since 0.05 < 0.16, we would accept the null hypothesis
Therefore, the data does not provide convincing statistical evidence that there is a difference between the two regions for the population proportions of people who shop online for groceries.
Final answer:
To determine if the differences in grocery shopping habits between two regions are statistically significant, a two-proportion z-test is conducted. We first state the null and alternative hypotheses, calculate the test statistic, find the p-value, and make a decision based on the significance level of 0.05.
Explanation:
To evaluate if there is a significant difference between the population proportions of people who shop online for groceries in two regions, we need to conduct a two-proportion z-test. The steps are as follows:
State the null and alternative hypotheses. The null hypothesis (H₀) is that there is no difference in the proportions of people who shop online for groceries in the two regions (p₁ = p₂). The alternative hypothesis (Ha) is that there is a difference (p₁ ≠ p₂).Calculate the test statistic using the formula for the two-proportion z-test. To compute this, we first find the pooled proportion, which combines the successes and total sample sizes from both regions.The p-value is then determined based on the calculated z-score. This p-value represents the probability of observing a test statistic as extreme as, or more extreme than, the observed result, under the assumption that the null hypothesis is true.Decide to reject or not reject the null hypothesis by comparing the p-value to the significance level (α = 0.05). If the p-value is less than α, we reject the null hypothesis, indicating sufficient evidence to say there is a significant difference in the proportions.In this scenario, with 16% of 100 people from Region A and 24% of 100 people from Region B indicating they shop for groceries online, a two-proportion z-test will reveal if the observed difference is statistically significant at the 0.05 level.
A point is chosen at random in the larger circle. What percent of the time will the point be in the shaded region? Round to the nearest tenth of a percent. Please help me!!
Answers
Answer:
Check the explanation
Step-by-step explanation:
Kindly check the attached image for the step by step explanation of the answer to the question
In the function y = 5x, what is the value of x?
Answers
The value of x in the given question is: x = y/5
How to change the subject of the formula?
We are given that the function for getting y is:
y = 5x
Now, to make x the subject of the formula, we will use division property of equality to divide both sides by 5 to get:
y/5 = 5x/5
x = y/5
Thus, the value of x in the given question is:
x = y/5
Please help me guys!!!!!!!!
Answers
Answer:
-64
Step-by-step explanation:
Answer:
[tex]-64=64cos(\pi )+64i/ sin(\pi )[/tex]
Step-by-step explanation:
For a complex number a + bi, polar form is given by [tex]r(cos(0)+ i sin(0))[/tex], where [tex]r = \sqrt{a^2+b^2}[/tex] and [tex]a = atan(\frac{b}{a} )[/tex]
In this case, we have [tex]a = -64[/tex] and [tex]b=0[/tex]
Therefore, [tex]r = \sqrt{(-64)^2+(0)^2} =64[/tex]
Also, [tex]0 = atan(\frac{0}{-64} )+\pi =\pi[/tex]
Which means that, [tex]-64=64cos(\pi )+64i/ sin(\pi )[/tex]!!!
I'm happy i finally got it!
there are 300 student and teachers at a sports event.Grade k to 2 is students: 137 Grade 3 to 5 students: 145 Teachers: ? what is the percentage of teachers at the sports event.
Answers
Answer:
6%
Percentage of teachers = 6%
Step-by-step explanation:
Given;
Number of grade k-2 students = 137
Number of grade 3-5 students = 145
Total = 300
Number of teachers = 300 - (137+145) = 18
Percentage of teachers = (number of teachers÷total)× 100%
%T = (18/300) × 100
%T = 6%
What’s the answer ??????
Answers
Answer:
The best estimate is 100 per month
Step-by-step explanation:
Take 618 and divide by 6 to get the exact amount
We want an estimate
Round 618 to 600
600/6 = 100
Answer:
A
Step-by-step explanation:
It is $100
pleaseeee helppppp me I'm dumbbbb
Answers
Answer:
-12
(someone check)
Answer: -12
Step-by-step explanation:
|-16|=16, (-2)^2=4, 4^2=16
So, (16÷4) -16 = -12
PLEASE HELP!!!!!! WILL MARK CORRECT ANSWER BRAINLIEST!!!!!!!!!!!!!!
Solve a triangle with b =7, c =10, and a=51 degrees. Round to the nearest tenth.
Answers
Answer:
a=7.8
<C=84.8°
<B=44.19
Step-by-step explanation:
Answer:
Step-by-step explanation:
What it means to "solve for a triangle" is to basically find ALL the missing parts, which in this case, are the lengths.
You are given the angles of the triangle, which we can use to help find the lengths.
By using sin, cos, and tan we can find the missing lengths
** quick side note, an easy way to remember how to use sin, cos, tan is SOH CAH TOA. In other words "for sine, multiply the opposite and hypotenuse, for cosine, multiply adjacent and hyp., and for tan, multiply opposite and adj.
start w/ solving for an angle (it doesn't matter which one but ill do A)
Bc you aren't given any side lengths, you have it a little easier by having to only use one method of SOH CAH TOA to solve. The method is sine
Using your calculator, type in sin(degree) or sin(51), and you should get
= 0.777145 OR 0.8
** make sure your calculator is is DEGREES not RADIANS
Now do this for the rest of the angles:
sin(7)= 0.1
sin(10)= 0.2
You have all the lengths (0.8, 0.1, 0.2) add them together to find the perimeter and if you want to find the area use Bh/2. But to find the area you must have a height, which you don't have
To find the height use formula: sqrt/( S(S-A)(S-B)(S-C)
A, B, C are the sides you've found using sine, and S is 1/2( A+B+C) or fast math is 0.55.
Plug in the values and solve :)
MEC makes a big family tent in the shape of a symmetrical triangular prism. The floor of the tent is 5 m long and 2.5 m wide. The peak of the tent is 1.9 m off the ground. The diagonal sides of the tent are 2.3 m long.
a) Draw a picture of the tent with dimensions
b) Polyurethane is a sheet material that is fairly waterproof and lightweight. It is sold in sheets of any area you desire. How much polyurethane was needed to make the tent? (remember: The bottom of the tent needs material to keep your sleeping bag dry)
c) How much space is there inside the tent? Predict how many people that might fit!?
* SHOW how you would you calculate that
d) MEC also sells an extra-waterproof fly made of polyester (every time I’ve camped it has snowed or rained…). The fly only covers the top and ends of the tent. How much polyester material is needed to make the fly?
Answers
Answer:
15,236 sq in
Step-by-step explanation:
First, you have to split the net into three rectangles and two triangles
step 1
triangular base area
1/2 bh = 1/2 (44 in)(64 in)
= 1/2 (2,816 sq in)
= 1,408 sq in.
2 x 1,408 sq in = 2,816 sq in.
step 2
end rectangle area
lw = (68 in)(69 in)
= 4,692 sq in
2 x 4,692 sq in = 9,384 sq in
Now find the area of the middle rectangle
lw - (69 in) (44 in) = 3,039 sq in.
then add all the areas together
2,816 + 9,384 + 3,036 = 15,236 sq in
Hope this helps :)
Paul, who is standing 150 feet above the water on a balcony of a cruise ship,
sees two boats located due north. The angles of depression from Paul
to the boats are 33
and 22°
Find the distance between the two boats to the nearest tenth of a foot.
Answers
Answer:140.3
Step-by-step explanation:
Answer:
140.3
Step-by-step explanation:
Triangle A B C is shown. Angle A B C is a right angle. The length of hypotenuse A C is 9, the length of B C is 2, and the length of A B is 8.77. Law of cosines: a2 = b2 + c2 – 2bccos(A) What is the measure of AngleC to the nearest whole degree? 70° 77° 80° 85°
Answers
Answer:
answer is B 77
Step-by-step explanation:
got it right on edg 2020-2021
The nearest whole degree is 77
What are trigonometric functions?In mathematics, trigonometric functions are real functions that relate an angle of a right-angled triangle to ratios of two side lengths. The six trigonometric functions are Sine, Cosine, Tangent, Secant, Cosecant, and Cotangent.
Given here: ABC is a right angle triangle AC=9, BC=2 and AB=8.77
The formula for law of cosines is given by a²=b²+c²-2bcosA
81=4+76.9129-2×2cos A
0.0871=-4Cos A
cos A=-0.21775
A=77.43208
Hence, The nearest whole degree is 77
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2.3 + r = 7.1
solve for r
Answers
Answer:
2.3+r=7.1
move all terms to the left:
2.3+r-(7.1)=0
add all the numbers together, and all the variables
r-4.8=0
move all terms containing r to the left, all other terms to the right
r=4.8 is the answer
Answer:
r = 4.8
Step-by-step explanation:
2.3 + r = 7.1
r + 2.3 = 7.1
r = 7.1 - 2.3
r = 4.8
6. Frozen fruit bars cost $3.95 for 5 bars.
Find how many you can buy with $12. Show your work.
Answers
Final answer:
By dividing the total cost of 5 fruit bars by 5, we get the cost per bar, which is $0.79. Then, dividing $12 by $0.79 per bar, we find that you can buy 15 bars with $12.
Explanation:
To determine how many frozen fruit bars can be purchased with $12 when 5 bars cost $3.95, we first need to calculate the cost per bar. We do this by dividing the total cost of 5 bars ($3.95) by the number of bars (5), giving us:
Cost per bar = $3.95 ÷ 5 = $0.79 per bar.
Next, we divide the total amount of money available ($12) by the cost per bar to find out how many bars can be bought:
Number of bars = $12 ÷ $0.79 per bar
When we do the calculation, we get:
Number of bars = 15.19 bars
Since we can't buy a fraction of a bar, we round down to the nearest whole number:
Number of bars that can be bought = 15 bars
Therefore, with $12, you can buy 15 frozen fruit bars.
Point O is the center of this circle. What is m
A.) 56
B.) 62
C.) 72
D.) 76
Answers
Answer: its b. i suck at explaining so sorry lol but its b
Please help me now plz
I will mark you brainliest
Answers
Answer:
x= 12 units.
Step-by-step explanation:
To solve this equation, we can find each half of the base using the Pythagorean theorem. We will use 'x' as denoting each HALF of the base:
45= 3²+x²
Subtracting from both sides will give us:
36= x²
x=6.
However, the base in this problem is '2x' because 'x' is HALF of the base.
2(6)= 12 units.
Use the earnings statement below to calculate the total percentage of income for taxes. To the nearest one percent, the percentage of gross income going to taxes and FICA is: 44% 31% 69% 11%
Answers
Answer: 31%
Step-by-step explanation: We need to find the amount deducted from the check which is $101.15. Keep in mind that this is the amount DEDUCTED, so if we add it to the net pay we will get the full amount which is $330.
Now we can do some math.
101.5 x 100 / 300 = 30.6515152% or 31%
The percentage of gross income going to taxes and FICA will be 38.75%.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
To the nearest one percent, the percentage of gross income going to taxes and FICA is: 44% 31% 69% 11%
P = [(0.44 + 0.31 + 0.69 + 0.11) / 4] x 100
P = (1.55 / 4) x 100
P = 0.3875 x 100
P = 38.75%
The percentage of gross income going to taxes and FICA will be 38.75%.
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The radius of a circle is 3.8 feet find the diameter
Answers
Answer:
7.6 feet
Step-by-step explanation:
The radius of a circle is halfway through. The diameter is the full way through. So what you do is multiply the radius by two. In this case, it's 3.8*2.
Answer:
7.6 ft
Step-by-step explanation:
The diameter of a circle is 2 times the length of the radius.
The formula to find the diameter is
d=2r
d= diameter
r= radius
Since the radius of this circle is 3.8, when multiplied by its self, it is 7.6 feet.
I hope this helped! :)
Divide 6.35 ÷ 1.57. Round the quotient to the nearest hundredth.
Answers
Answer:
4.45
Step-by-step explanation:
Answer:
4.04
Step-by-step explanation:
6.35/ 1.57= 4.044585987261146
round to nearest hundredth is where the 4 is located at so its 4.04
NEED HELP ASAP!!!! WILL GIVE BRAINLIEST!!
Answers
Answer:
1st one the other 2 are linear
Answer:
the first one
Step-by-step explanation:
the other two are linear.
Solve the equation by completing the square. 0=x^2-14x+46
Answers
Answer:
x = 7+√(3), 7-√(3)
Step-by-step explanation:
x^2 - 14x + ___ = -46 + ___
x^2 - 14x + 49 = -46 + 49
(x-7)^2 = 3
√(3) = x-7
x = 7+√(3), 7-√(3)
The value of x is x = 7+√(3), 7-√(3)
What is completing the square method.?Completing the square means writing a quadratic in the form of a squared bracket and adding a constant if necessary.
Given:
x² - 14x ++46 = 0
x² - 14x ++46 + 7²- 7² = 0
x² - 14x + 7² +46 - 49 = 0
(x- 7)² - 3=0
(x- 7)² = 3
x = 7+√(3), 7-√(3)
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Help. help and I gonna give prainliest
Answers
Answer: $585
Step-by-step explanation:
Find the area of the trapezoid (Area: 117 sq ft)
Multiply the area by 5 because each square feet is $5
And vola your answer!
help me please will give brainlest
Answers
Answer:
Data Set 2, seventh graders:
Center: The median value is 54. (Count to the middle: it's the tenth value.) The set is bimodal, with modes at 53 and 55. (The mode is the number that occurs most frequently.)
Shape: The set looks to be fairly symmetrical, though data lies closer to the right than the left.
Spread: The range is 60-50 = 10, so it's less spread out than the sixth graders.
A gopher has dug holes in opposite corners of a rectangular yard. One length of the yard is 8 meters and the distance between the gopher's holes is 10 meters. How wide is the yard?
Answers
The width of the yard is 6 meters, calculated using the Pythagorean theorem with one side as 8 meters and the other side as the unknown width.
We can use the Pythagorean theorem to solve this problem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In this case, the two sides of the triangle represent the length and width of the yard, and the hypotenuse represents the distance between the gopher's holes.
Let's denote the width of the yard as (w). According to the problem:
Length of the yard (L) = 8 meters
Distance between the gopher's holes (h) = 10 meters
Width of the yard ((w)) = ?
We can set up the following equation using the Pythagorean theorem:
[tex]\[ w^2 + 8^2 = 10^2 \][/tex]
[tex]\[ w^2 + 64 = 100 \][/tex]
[tex]\[ w^2 = 100 - 64 \][/tex]
[tex]\[ w^2 = 36 \][/tex]
[tex]\[ w = \sqrt{36} \][/tex]
[tex]\[ w = 6 \, \text{meters} \][/tex]
Therefore, the width of the yard is 6 meters.