Answer:
81/100
Step-by-step explanation:
Answer:
81/100
Step-by-step explanation:
Q13. A stone is dropped from a height of 5 km. The distance it falls through varies directly with the
square of the time taken to fall through that distance. If it falls 64 min 4 seconds. find the distance the
stone covers in the 5th second?
A. 36 m
B. 58 m
C. 72 m
D. 100 m
Answer:
The stone covers 36 m in the 5th second. Correct choice: A.
Step-by-step explanation:
Proportions
Two variables are said to be proportional if one of them can be calculated by multiplying the other by a constant of proportionality. If y and x are those variables, then:
y=k.x
There are other similar proportions where the relation is not linear. For example, if y is proportional to the square of x, then:
[tex]y=k.x^2[/tex]
According to the conditions of the question, the distance traveled by a stone dropped from a height of 5 Km varies directly with the square of the time taken to fall through that distance. If d is the distance and t is the time, then;
[tex]d=k.t^2[/tex]
To find the value of k, we use the given condition: The stone falls d=66 meters in t=4 seconds. Substituting:
[tex]64=k.4^2=16k[/tex]
Solving:
[tex]k=64/16=4[/tex]
Substitute the value of k into the equation to get the complete model.
[tex]d=4.t^2[/tex]
Now we calculate the distance when t=5 seconds:
[tex]d=4\cdot 5^2=4\cdot 25=100[/tex]
The stone has covered 100 m in 5 seconds. But we need to find the distance covered in the 5th second, that specific interval between 4 sec and 5 sec.
Since we already know the distance for t=4 sec (64 m), and the distance for t=5 sec (100 m), then:
distance in the 5th second = 100 m - 64 m = 36 m
The stone covers 36 m in the 5th second. Option A.
How many kilograms of potatoes will each person get if 5 people share 1/3 of a kilogram of potatoes equally?
Answer:
1/15 kg
Step-by-step explanation:
Divide by 5 can be written as multiply by 1/5
1/3 * 1/5 = 1/15
in exercises 15-20 find the vector component of u along a and the vecomponent of u orthogonal to a u=(2,1,1,2) a=(4,-4,2,-2)
Answer:
The component of [tex]\vec u[/tex] orthogonal to [tex]\vec a[/tex] is [tex]\vec u_{\perp\,\vec a} = \left(\frac{9}{5},\frac{6}{5},\frac{9}{10},\frac{21}{10}\right)[/tex].
Step-by-step explanation:
Let [tex]\vec u[/tex] and [tex]\vec a[/tex], from Linear Algebra we get that component of [tex]\vec u[/tex] parallel to [tex]\vec a[/tex] by using this formula:
[tex]\vec u_{\parallel \,\vec a} = \frac{\vec u \bullet\vec a}{\|\vec a\|^{2}} \cdot \vec a[/tex] (Eq. 1)
Where [tex]\|\vec a\|[/tex] is the norm of [tex]\vec a[/tex], which is equal to [tex]\|\vec a\| = \sqrt{\vec a\bullet \vec a}[/tex]. (Eq. 2)
If we know that [tex]\vec u =(2,1,1,2)[/tex] and [tex]\vec a=(4,-4,2,-2)[/tex], then we get that vector component of [tex]\vec u[/tex] parallel to [tex]\vec a[/tex] is:
[tex]\vec u_{\parallel\,\vec a} = \left[\frac{(2)\cdot (4)+(1)\cdot (-4)+(1)\cdot (2)+(2)\cdot (-2)}{4^{2}+(-4)^{2}+2^{2}+(-2)^{2}} \right]\cdot (4,-4,2,-2)[/tex]
[tex]\vec u_{\parallel\,\vec a} =\frac{1}{20}\cdot (4,-4,2,-2)[/tex]
[tex]\vec u_{\parallel\,\vec a} =\left(\frac{1}{5},-\frac{1}{5},\frac{1}{10},-\frac{1}{10} \right)[/tex]
Lastly, we find the vector component of [tex]\vec u[/tex] orthogonal to [tex]\vec a[/tex] by applying this vector sum identity:
[tex]\vec u_{\perp\,\vec a} = \vec u - \vec u_{\parallel\,\vec a}[/tex] (Eq. 3)
If we get that [tex]\vec u =(2,1,1,2)[/tex] and [tex]\vec u_{\parallel\,\vec a} =\left(\frac{1}{5},-\frac{1}{5},\frac{1}{10},-\frac{1}{10} \right)[/tex], the vector component of [tex]\vec u[/tex] is:
[tex]\vec u_{\perp\,\vec a} = (2,1,1,2)-\left(\frac{1}{5},-\frac{1}{5},\frac{1}{10},-\frac{1}{10} \right)[/tex]
[tex]\vec u_{\perp\,\vec a} = \left(\frac{9}{5},\frac{6}{5},\frac{9}{10},\frac{21}{10}\right)[/tex]
The component of [tex]\vec u[/tex] orthogonal to [tex]\vec a[/tex] is [tex]\vec u_{\perp\,\vec a} = \left(\frac{9}{5},\frac{6}{5},\frac{9}{10},\frac{21}{10}\right)[/tex].
what is the rate of change for the liner relationship modeled in the table?
i'm sorry wheres the picture?
last year, emilia went bowling several times and earned an average score of 100 points. this year, after taking a class at school, her average is now 98% higher. what is her current average?
Mark reeds 42 pages of a book every 3/4 of an hour write an equation that models the relationship between Z, the number of hours mark reads, NY, the number of pages of the book He reads
Answer:
The equation that models the relationship between Z and N is N = 56 Z
Step-by-step explanation:
The form of the linear equation is y = m x + b, where
m is the rate ⇒ slopeb is the initial amount ⇒ y-intercept∵ Mark reads 42 pages of a book every [tex]\frac{3}{4}[/tex] of an hour
→ Find his rate per hour by dividing the number of pages by its time
∴ His rate of reading = 42 ÷ [tex]\frac{3}{4}[/tex] = 42 × [tex]\frac{4}{3}[/tex] = 56 pages per hour
∵ His rate = 56 pages/hour
∴ m = 56
∵ Z represents the number of hours Mark reads
→ That means replace x in the form of the equation above with Z
∵ N represents the number of pages of the book he reads
→ That means replace y in the form of the equation above with N
∴ N = 56 Z + b
∵ There is no initial amount of reading
∴ b = 0
∴ N = 56 Z
The equation that models the relationship between Z and N is N = 56 Z
show that: (1-sin x)/(cos x)=(sec x - tan x)
This is the step-by-step explanation
The length of a rectangle is three times the width of the rectangle. The area of the rectangle is 48cm2. Draw the rectangle on the centimetre grid.
Answer:
The width is 4 cm
The length is 12 cm.
Step-by-step explanation:
Area of a rectangle
Given a rectangle of width W and length L, its area is calculated as follows:
[tex]A=W\cdot L[/tex]
The area of the given rectangle is 48 cm^2, and the length is three times the width, thus:
L = 3W
Substituting into the formula of the area:
[tex]W\cdot L=48[/tex]
[tex]W\cdot 3W=48[/tex]
Simplifying:
[tex]3W^2=48[/tex]
Solving:
[tex]W^2=48/3=16[/tex]
[tex]W=\sqrt{16}=4[/tex]
The width is 4 cm. Find the length:
L=3W=3*4= 12
The length is 12 cm.
The image attached shows the rectangle on the centimeter grid
sub to astronaut gaming i have 27 or 28 subs if you need help finding i will help
More on Linear Equations & Linear Systems: Question 1
How many solutions does the system of equations below
have?
y - 2x + 2
y-r-1
Select one:
none
infinitely many
O o o o
one
two
Answer:
21
Step-by-step explanation:
A system of equations is shown:
2x = -y + 6
--4x + 3y = 8
What is the solution to this system of equations?
0 (-1,-4)
O (1.4)
(4, 1)
(-4,-1)
[tex]\large\underline{\bf \red{Step \:by\: Step \:Explanation:}}[/tex]
Given two equations are :
2x = - y + 6.-4 x + 3y = 8 .We may write them as ,
2x + y - 6 = 0 .................(i) 4x - 3y + 8 = 0 ...............(ii)Multiplying equⁿ (i) by 2 :
⇒ 2(2x + y - 6 ) = 0.
⇒ 4x + 2y - 12 = 0 .....................(iii) .
Subtract equⁿ (ii) from equⁿ (iii) :-
⇒ 4x + 2y - 12 = 0
ㅤ- 4x + 3y - 8 = 0 [ Sign changes ]
__________________
⇒ 5y - 20 = 0.ㅤㅤㅤㅤㅤ
⇒ 5y = 20.
⇒ y = 20/5.
⇒ y = 4
Put this value in (i) to obtain x .
⇒ 2x + y - 6 = 0.
⇒ 2x +4 - 6 = 0.
⇒ 2x - 2 = 0.
⇒2x = 2 .
⇒ x = 2/2.
⇒ x = 1 .
Hence the value of x is 1 & y is 4.
[tex]\boxed{\purple{\bf\pink{\dag}\:Hence\:the\: correct\: option\:is\:[b]\:(1,4)}}[/tex]
A lot contains 12 items, and 4 are defective. If three items are drawn at random from the lot, what is the probability they are not
defective?
Answer:
ur nan
Step-by-step explanation:
Use a factor rainbow to determine if 729 is a perfect square. Explain your reasoning.
Answer:
729 is a perfect square
Step-by-step explanation:
because 27 * 27 = 729
An airplane pilot over the Pacific sights a ship wreck at an angle of depression of 5°. At this time, the horizontal distance from the airplane to the wreck is 4629 meters. What is the height of the plane to the nearest meter?
405 m
Answer:
The height of the plane is 405 meters
Step-by-step explanation:
Trigonometric Ratios
The situation can be represented as shown in the image below. The ground, the height H, and the direct distance to the plane to the shipwreck form a right triangle, where the trigonometric ratios stand.
Since the known distance is adjacent to the angle, and the required height is opposite to the given angle, we use the tangent ratio, defined as:
[tex]\displaystyle \tan\ x=\frac{\text{opposite leg}}{\text{adjacent leg}}[/tex]
[tex]\displaystyle \tan 5^\circ=\frac{H}{4629}[/tex]
We need to find H, so we solve for H:
[tex]H=4629\cdot\tan5^\circ[/tex]
H=405 m
The height of the plane is 405 meters
I need to solve for n.
Enter the equivalent distance in km in the box.
1 km = 1000 m
1 m = 100 cm
35,000 cm =
km
Answer:
0.350 km
Step-by-step explanation:
Hi there !
35000 cm = 35000/100 m = 350 m
350 m = 350/1000 km = 0.350 km
Good luck !
Hi guys I’m bored can someone talk to me please? :)
Answer:
sure
Step-by-step explanation:
Answer:
hello
Step-by-step explanation:
Two angles form a linear pair. The measure of one angle is 6 less then the measure of the other angle. Find the measure of each angle
Answer: one angle would be 50 degrees while the other would be 130 degrees.
Step-by-step explanation:
Text a friend and write a clear set of instructions on how to find a ratios amount
Answer:
Hi ___
A ratio is created from two numbers it can also be a fraction.
To find a ratio you have to have 2 numbers
You can take these 2 numbers and divide them so they are a unit ratio
For example 3:6 can be reduced to 1:3
Step-by-step explanation:
Hope this helps please give brainliest
Hey now please just anser if itnus a try i will still give 5 stars. THE Question is what is the most easy way to SOLVE THE NINES TABLE IK THIS BUT I WANT to see who else knows sorry fir the big ketters i did not means to put that
Answer:
Tbh, I think the easiest way is to count on your fingers. I still do it, however I can now do my chart tables to 17x17 by using fingers. People may tease, however, it is a good way to make sure you do not mess up as much as memorizing. You should memorize, and count on your fingers at the same time to solve extremely fast.
Step-by-step explanation:
9x4
You can pretend that your thumb equals nine, and count 9 plus 9 plus 9 plus 9, with each other finger, such as your ring finger, pointer, middle, and pinky , which equals 36. 5x9, you have five fingers on each hand, so each finger can equal nine (I don't care if people say that your thumb isn't a finger, just take it and move on lol).
7n - 8n - 323
????????????
Answer:
−n−323
Step-by-step explanation:
I will give brainliest :D
Which equation matches this scenario?
A family buys 8 tickets to a show. They also pay a $5
parking fee. They spend $61 to see the show.
• 5x+8=61
• 61+8x=5
• 8+5x=61
• 8x+5=61
Answer: 8x + 5= 61
Step-by-step explanation: x represents the cost of one ticket for the show, 8 is the amount of tickets, 5 is the extra fee, 61 is the total.
Labor costs. Labor costs for a farmer are $55 per acre for corn and $45 per acre for soybeans. How many acres of each crop should the farmer plant if he wants to spend no more than $6,900 on labor?
Answer:
392984
Step-by-step explanation:
is this a equation or expression 4r+3=12
Answer:
Equation
Step-by-step explanation:
Because there is only one unknown term in it
I hope it helps
Thank U
Explain how you would solve -5/8 divided by 2/3 and what the solution is?
Answer:
-15/16
Step-by-step explanation:
-5/8 ÷ 2/3
Copy dot flip
-5/8 * 3/2
Multiply the numerators
-5*3 = -15
Multiply the denominators
8*2 =16
Put the numerator over the denominator
-15/16
A polling company reported that % of surveyed adults said that Complete parts (a) through (d) below.
a. What is the exact value that is 37% of 1018?
b. Could the result from part (a) be the actual number of adults who said that Why or why not?
1. No, the result from part (a) could not be the actual number of adults who said that because that is a very rare opinion.
2. No, the result from part (a) could not be the actual number of adults who said that because a count of people must result in a whole number.
3. Yes, the result from part (a) could be the actual number of adults who said that because the polling numbers are accurate.
4. Yes, the result from part (a) could be the actual number of adults who said that because the results are statistically significant.
c. What could be the actual number of adults who said that The actual number of adults with this opinion could be 296. (Type an integer or a decimal.)
d. Among the 1018 respondents, 415 said that cellular phones are not at all harmful. What percentage of respondents said that cellular phones are not at all harmful?
Answer:
a) 376.66
b) Option 2: No, the result from part (a) could not be the actual number of adults who said that rising gas prices are "quite annoying" because a count of people must result in a whole.
c) 377
d) 40.77%
Step-by-step explanation:
a) 37% of 1018 is;
37/100 × 1018 = 376.66
b) Thus, the result in a above is not a whole number. Thus;
No, the result from part (a) could not be the actual number of adults who said that rising gas prices are "quite annoying" because a count of people must result in a whole.
c) from a above a, we got a value of 376.66.
Now the actual number would be preferably an integer. Thus, actual number is approximately 377.
d) percentage of respondents said that cellular phones are not at all harmful = 415/1018 × 100% = 40.77%
If f(x)=x^2 and g(x) =3x-1 find [g • f](x)
Answer:
3x²-1
Step-by-step explanation:
f(x) = x²
g(x) = 3x-1
[g·f](x)
g(f(x))
3(x²)-1
6 TH grade math
On a hot day, Myra poured 4 1/8 buckets of water into a plastic wading pool. A few minutes later she added another 3 5/8 buckets. How much water did Myra pour into the pool?
Answer:
7 3/4
Step-by-step explanation:
4 1/8 + 3 5/8
Add the whole numbers, 4 + 3 = 7.
Add the fractions, 1/8 + 5/8 = 6/8.
You get 7 6/8. Simplify 6/8 to get 3/4.
Your answer is 7 3/4.
The neighborhood swimming pool drains at a rate of 99 gallons every 3 hours. At this rate, how many gallons are
emptied each hour?
Helllllpppppp meeee
Answer:
33mph
Step-by-step explanation:
because if u divide 99 by 3 that is the answer
please help!!!!!!!!!!!!!!
Answer:
A
Step-by-step explanation:
By solving (x+6)(x-9), we get x^2 - 3x - 54. By looking at our y-intercept, we can see that only option A has the correct intercept.
Answer:
A
Step-by-step explanation: