The two numbers so that the exact answer is between 6×7381 are 28,000 and 48,000.
Given:
To find two numbers the exact answer is between 6×7381.
7,381 is between the numbers 7,000 and 8,000.
Rounding the number 7,381 down to 7000 and multiplying 6 by it.
6 × 7,000 is 28,000
Rounding the number 7,381 up to 8000 and multiplying 6 by it.
6 × 8,000 is 48,000
The two numbers so that the exact answer is between 6×7381 are 28,000 and 48,000 respectively.
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Question 8 of 15
Triangle ABC with vertices A(-1, 2), B(-1, -2), and C(-4,-2) is dilated by a scale factor of 2 to form triangle A'B'C'.
у
A
C
4321
-4-3-2-10 이 1234
1
OHN 3 +
B
+2+
-3+
Submit Test
-4-
What is the length, in units, of side A'B'?
units
2223 Math Grade 8 IA1
X
The formula that most accurately captures the dilatation that Triangle ABC underwent to produce A'B'C will be:
(x, y) → (1/2x, 1/2y)
Detailed explanation?
A triangle's vertices are given.
A(-2, -4) (-2, -4)
B(2, -4) (2, -4)
C(-8, -4) (-8, -4)
The vertices of an image triangle should be after the dilatation
A' (-1, -2) (-1, -2)
B '(1, -2) (1, -2)
C' (-4, -2) (-4, -2)
If we look attentively, we can see that the vertices of the image triangle, A'B'C', make up half of the original triangle ABC.
For example, (x, y) (1/2x, 1/2y)
verification
A(-2, -4) → A'(-2/2, -4/2) = A'(-1, -2) (-1, -2)
B(2, -4) → B'(2/2, -4/2) = B'(1, -2) (1, -2)
C(-8, -4) → C'(-8/2, -4/2) = C'(-4, -2) (-4, -2)
As a result, it is confirmed, and we come to the conclusion that the rule that best captures the dilatation that Triangle ABC underwent to form A'B'C' will be:
(x, y) → (1/2x, 1/2y)
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The amount of air in a Suba diving tank with a capacity of 2400 liters is decreasing at a rate of 48
For given details the function is f(t) = 2400 - 48t
a) the amount of air in the tank is a function of the number of minutes it contain the air.
b) Domain of the function: [0, 50] and the domain is continuous one.
c) Graph of the function is attached below.
Function:
The function also know as expression, rule, or law that defines a relationship between one variable and another variable.
Given,
The amount of air in a scuba diving tank with a capacity of 2400 liters is decreasing at a constant rate of 48 liters per minute.
Here we need to find the following:
a) Whether the amount of air in the tank a function of the number of minutes?
b) Domain of the function
c) Graph of the function
Through the given question we know that,
The total amount of air in the tank = 2400 liters
Discharge unit per minute = 48 liters
Let us consider f(t) be the amount of air in a scuba diving tank.
where t represents the time in minutes.
Through the given information we get a function,
f(t) = 2400 - 48t
While using the given function, we can observe that the amount of air in the tank a function of the number of minutes.
Now, we need to find the domain of the function f(t)
Let us consider f(t) = 0
2400 - 48t = 0
2400 = 48t
t = 2400 / 48
t = 50
Therefore, t takes values in from the interval [0, 50]
We know that time is continuous to the function.
so, the domain is also continuous.
Now we have to plot the graph of the function..
Therefore, for given situation the function is f(t) = 2400 - 48t is attached below.
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P (A) =0.17, P (A and B) =0.06, FIND P (B)
Answer:
P(B) = 0,35
Step-by-step explanation:
P(B) = P(A and B) divided by P(A)
What do all rectangles have that some parallelograms do not have?
A. Opposite angles that are congruent
B. Diagonals that are congruent
C. Opposite sides that are congruent
D. Diagonals that bisect each other
Answer:
B. Diagonals that are congruent
Complete the table for the arithmetic sequence.
Airthemetic Sequence : arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.
It express as :
[tex]a_n=a_1+(n-1)d[/tex]In the given question the 88 term is ( 25)
Substitute the value in the expression of n terms
[tex]\begin{gathered} a_n=a_1+(n-1)d \\ \text{for : n =25, a}_n=88,a_1=(-8) \\ a_n=a_1+(n-1)d \\ 88=(-8)+(25-1)d \\ 88=-8+24d \\ 88+8\text{ =24d} \\ 24d=96 \\ d=\frac{96}{24} \\ d=4 \end{gathered}[/tex]In the given Airthmetic sequence the constant difference, d = 4
Now for the position of term 8
[tex]\begin{gathered} a_n=a_1+(n-1)d \\ \text{for a}_n=8,a_1=(-8),\text{ d =4} \\ 8=-8+(n-1)4 \\ 16=4(n-1) \\ 4=n-1 \\ n=5 \end{gathered}[/tex]for n= 5 terms is 8
Now for the term of position 8:
[tex]\begin{gathered} a_n=a_1+(n-1)d \\ \text{for n=8, a}_1=(-8),d=4 \\ a_n=-8+(8-1)4 \\ a_n=-8+7\times4 \\ a_n=20 \end{gathered}[/tex]So, the term with position 8 is 20
Now for the position of term 36 :
[tex]\begin{gathered} a_n=a_1+(n-1)d \\ \text{for :a}_n=36,a_1=(-8),\text{ d = 4} \\ 36=-8+(n-1)4 \\ 36+8=4(n-1) \\ 44=4(n-1) \\ n-1=\frac{44}{4} \\ n-1=11 \\ n=10 \end{gathered}[/tex]Thus, for n = 10, an = 36
Now, for the term of position 19
[tex]\begin{gathered} a_n=a_1+(n-1)d \\ \text{for n=19, d=4, a}_1=(-8) \\ a_n=-8+(19-1)4 \\ a_n=-8+(18)4 \\ _{}a_n=-8+72 \\ a_n=64 \end{gathered}[/tex]Thus at n = 19 the term i 64
Elizabeth drew a right triangle and labeled the sides as follows: leg lengths = 5 inches and 8 inches, hypotenuse = 14 inches. Can the side lengths form a right triangle? Explain your reasoning. I need a good explaination
X_X
The side length of the triangle Elizabeth drew cannot form a right triangle.
How to find the sides of a right triangle?A right triangle is a triangle that has one of its angle as 90 degrees.
The sides of a right triangles are hypotenuse side, adjacent side and the opposite side. This is base on the angle position.
Right triangle obeys Pythagoras's theorem.
a² + b² = c²
where
a and b are the legs of the right trianglec is the hypotenuse side of the right triangle.Therefore, let's test if the labelled side of the triangle Elizabeth drew is a right triangle. We will use Pythagoras theorem to confirm it
5² + 8² = 14²
25 + 64 = 196
Therefore,
89 ≠ 196
Therefore, the side length cannot form a right triangle
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Jumbo shrimp are defined as those that require 10 to 15 shrimp to make a pound. Suppose that the number of jumbo shrimp in a 1-pound bag
averages u 12.5 with a standard deviation of a 1.5 and forms a normal distribution. Using the Distributions tool, find the probability of random
picking a sample of n = 25 1-pound bags that average more than M = 13 shrimp per bag.
Standard Deviation - 1.0
The probability of randomly picking a sample of n 25 1-pound bags that average more than M - 13 shrimp per bag is p =
Answer:
0.0475
Step-by-step explanation:
find the exact perimeter of hexagon ABCDEF plotted below
The perimeter of the hexagon ABCDEF is 36.01.
Given,
The hexagon ABCDEF
We have given the points:
A(-6, 2), B(1, 5), C(6, 5), D(6, -1), E(1, -3), F(-6, -3)
We have to find the perimeter of hexagon.
Perimeter of hexagon = AB + BC + CD + DE + EF + FA
Now,
Distance formula is as [tex]\sqrt{(x_{2}-x_{1} )^{2} +(y_{2} -y_{1} )^{2} }[/tex]
So,
Distance of AB,A(-6, 2), B(1, 5) : x₁ = 1, x₂ = -6, y₁ = 2, y₂ = 5
[tex]\sqrt{(x_{2}-x_{1} )^{2} +(y_{2} -y_{1} )^{2} }[/tex]
= [tex]\sqrt{(1-(-6))^{2} +(5-2)^{2} }[/tex]
=[tex]\sqrt{7^{2} +3^{2} }[/tex]
= [tex]\sqrt{49+9}[/tex]
= √58
= 7.62
Distance of BC,B(1, 5), C(6, 5) : x₁ = 1, x₂ = 6, y₁ = 5, y₂ = 5
[tex]\sqrt{(x_{2}-x_{1} )^{2} +(y_{2} -y_{1} )^{2} }[/tex]
= [tex]\sqrt{(6-1)^{2}+(5-5)^{2} }[/tex]
= √5²
= 5
Distance of CD,C(6, 5), D(6, -1) : x₁ = 6, x₂ = 6, y₁ = 5, y₂ = -1
[tex]\sqrt{(x_{2}-x_{1} )^{2} +(y_{2} -y_{1} )^{2} }[/tex]
= [tex]\sqrt{(6-6)^{2}+(-1-5)^{2} }[/tex]
= √-6²
= 6
Distance of DE,D(6, -1), E(1, -3) : x₁ = 6, x₂ = 1, y₁ = -1, y₂ = -3
[tex]\sqrt{(x_{2}-x_{1} )^{2} +(y_{2} -y_{1} )^{2} }[/tex]
= [tex]\sqrt{(1-6)^{2}+(-3-(- 1))^{2} }[/tex]
= [tex]\sqrt{(-5)^{2} +(-3+1)^{2} }[/tex]
= [tex]\sqrt{25 + 4}[/tex]
= √29
= 5.39
Distance of EF,E(1, -3), F(-6, -3) : x₁ = 1, x₂ = -6, y₁ = -3, y₂ = -3
[tex]\sqrt{(x_{2}-x_{1} )^{2} +(y_{2} -y_{1} )^{2} }[/tex]
= [tex]\sqrt{(-6-1)^{2}+(-3-(-3))^{2} }[/tex]
= √-7²
= 7
Distance of FA,F(-6, -3), A(-6, 2) : x₁ = -6, x₂ = -6, y₁ = -3, y₂ = 2
[tex]\sqrt{(x_{2}-x_{1} )^{2} +(y_{2} -y_{1} )^{2} }[/tex]
= [tex]\sqrt{(-6-(-6))^{2} +(-3-(2))^{2} }[/tex]
= √-5²
= 5
So, we have
AB = 7.62
BC = 5
CD = 6
DE = 5.39
EF = 7
FA = 5
Now,
Perimeter of hexagon = AB + BC + CD + DE + EF + FA
Perimeter of hexagon= 7.62 + 5 + 6 + 5.39 + 7 + 5
Perimeter of hexagon = 36.01
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In a far away galaxy are two planets named Eenie and Meenie. Planet Eenie has
population of approximately 72,980,001, and Planet Meenie has a population o
approximately 54,908. About how many times greater is the population of Plan
Eenie than the population of Planet Meenie?
► 0:00/0:50
1.4 x 103
7.14 x 10-4
1.4 x 104
7 11 v 103
-
⠀
Population of Planet Eenie is 1.4 × [tex]10^{3}[/tex] times greater than the population of Planet Meenie.
Two planets named Eenie and Meenie.
Population of Planet Eenie = 72,980,001
Population of Planet Meenie = 54,908
We need to find how many times greater is the population of Planet
Eenie than the population of Planet Meenie. So, we need to follow the steps written below:
( Population of Planet Eenie / Population of Planet Meenie )
= ( 72,980,001 / 54,908 )
= 1329.1323
= 1.33 × [tex]10^{3}[/tex]
This calculated value is near option 2 i.e., 1.4 × [tex]10^{3}[/tex]. So, 1.4 × [tex]10^{3}[/tex] is the correct option.
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4 over 15 divided by 10 over 13
4/15 = 3.75
10/13 = 1.3
you have to divide it from its higher number or you'll get something like this: 0.7692307692307692 but if it helps it = 0.00205128205
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Divide and solve: r^2/r^12
Given:
[tex]\frac{r^2}{r^{12}}[/tex]Let's solve using law of indices below:
[tex]\frac{a^m}{a^n}=a^m\ast a^{-n}=a^{m-n}[/tex]Using the same method, we have:
[tex]\frac{r^2}{r^{12}}=r^2\ast r^{-12\text{ }}=r^{2-12}=r^{-10}[/tex]ANSWER:
[tex]r^{-10}[/tex]solve the inequality and describe the graph of the solution.[tex]4x - 5 \geqslant 7[/tex]
The given expression is :
[tex]4x-5\ge7[/tex]To simplify the expression for x :
Add 5 on both side :
[tex]\begin{gathered} 4x-5+5\ge7+5 \\ 4x\ge12 \end{gathered}[/tex]
Divide the expression by 4 on both side :
[tex]\begin{gathered} 4x\ge12 \\ \frac{4x}{4}\ge\frac{12}{4} \\ x\ge3 \end{gathered}[/tex]Thus : x ≥ 3
The graph is :
Since x is greater than or equal to 3
So, it is closed on 3
Answer :
The graph has a closed circle on 3 and is shaded to the right of the origin
the area of rectangular pool
Answer:
multiply length times width.
Step-by-step explanation:
A. 3/5B.4/5C.3/4D.4/3
The tangent relation is given by the length of the opposite side to the angle over the length of the adjacent side to the angle.
So we have:
[tex]\begin{gathered} \tan (\beta)=\frac{AC}{BC} \\ \tan (\beta)=\frac{3}{4} \end{gathered}[/tex]Therefore the correct option is C.
How do i solve this problem?
The function exists a Power function. The power of function is 3 and the constant variation is - 1/3
What is meant by Power function?Any function where y = x n, where n is any real constant integer, is referred to be a power function. In reality, many of our parent functions, including linear and quadratic functions, are power functions. A few other power functions are y = x³, y = 1/x, and y = x squared.
A parameter function used in statistical testing that represents the likelihood of rejecting the null hypothesis for a given value of the parameter, assuming that value is true.
Therefore, the power of function is 3 and the constant variation is - 1/3.
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A theatre has 30 rows of seats there are 22 seats in the first row 26 in the second row 30 in the third row etc how many people will the theatre hold
Using the arithmetic progression, If a theatre has 30 rows of seats there are 22 seats in the first row,26 in the second row, 30 in the third row, then the total number of people that the theatre hold is 2400
The total number of rows = 30
Number of seats in the first row = 22
Number of seats in the second row = 26
Number of seats in the third row = 30
Common difference= Second term - first term
= 26-22
= 4
The given sequence is in arithmetic progression
Sum of n terms = [tex]\frac{n}{2}[2a+(n-1)d][/tex]
Substitute the values in the equation
= [tex]\frac{30}{2}[2(22)+(30-1)4][/tex]
= 15[44+29×4]
= 15[44+116]
= 15×160
= 2400
Hence, using the arithmetic progression, if a theatre has 30 rows of seats and there are 22 seats in the first row,26 in the second row, 30 in the third row, then the total number of people that the theatre hold is 2400
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Name the property, if any, that is illustrated below
The given expression xy = yx represents the cumulative property of multiplication.
What is cumulative property?If altering the operands' order has no effect on the outcome, the binary operation is commutative in mathematics. Numerous binary operations share this essential characteristic, and numerous mathematical arguments rely on it.
The given expression is xy = yx.
The expression xy = yx is representing the cumulative property of multiplication. According to this property, the value of the expression will remain the same after the order is changed.
Let x = 5 and y = 10. Now verify the cumulative property of multiplication.
xy = yx
5 x 10 = 10 x 5
50 = 50
Therefore, the given expression xy = yx represents the cumulative property of multiplication.
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Molly is making peanut butter cookies to make a batch of cookies. She needs 3/4 cups of peanut butter 1.5 cups of sugar and 1 egg if Molly is 3 cups of peanut butter, 9 cups of sugar and 5 eggs how many batches can she make
Para resolver una operación matemática ¿por qué es importante
primero conocer los signos y los números?
Answer:
para hacer la repuesta xd
Discrete Math19. Rolling the Dice An experiment was conducted in whichtwo fair dice were thrown 100 times. The sum of the pipsshowing on the dice was then recorded. The following fre-quency histogram gives the resultsSum of Two Dice252015Frequency1032 3 4 5 6 7Value of Dice9 10 11 12(a) What was the most frequent outcome of the experi-ment?(b) What was the least frequent?(c) How many times did we observe a 7?(d) Determine the percentage of time a 7 was observed,(e) Describe the shape of the distribution
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
frequency histogram
Step 02:
discrete math:
sum of two dice:
we must analyze the graph to find the solution.
most frequent outcome:
value of dice = 8
frequency = 20
least frequent outcome:
value of dice = 2
frequency ≅ 2
how many times (7):
15 times (frequency)
percentage of times (7):
percentage (7) = (15 / 100) * 100%
percentage (7) = 15%
shape of distribution:
non-symmetric, bimodal
That is the full solution.
A flower bed is in the shape of a triangle with one side twice the length of the shortest side and the third side is 21 feet
more than the length of the shortest side. Find the dimensions if the perimeter is 121 feet.
What is the length of the shortest side?
The length of the shortest side is
Answer: 25 ft
Step-by-step explanation:
Let the shortest side be s. Then, the other two sides are 2s and s+21.
[tex]s+2s+s+21=121\\\\4s+21=121\\\\4s=100\\\\s=25[/tex]
use the rectangle diagram at the right.Write and solve an inequality to find the value of x for which the perimeter of the rectangle is less than 120.
The perimeter is the sum of all the sides of a geometric figure, so
[tex]\begin{gathered} (x+4)+x+(x+4)+x<120 \\ x+4+x+x+4+x<120 \\ 4x+8<120 \end{gathered}[/tex]To resolve this inequality you can first subtract 8 from both sides
[tex]\begin{gathered} 4x+8-8<120-8 \\ 4x<112 \end{gathered}[/tex]Then you divide by 4 on both sides of the inequality
[tex]\begin{gathered} \frac{4x}{4}<\frac{112}{4} \\ x<28 \end{gathered}[/tex]Therefore, for the perimeter of the rectangle to be less than 120, its shortest side must measure less than 28.
When a number is decreased by 20% of itself, the result is 336. What is the number?
The number which is decreased by 20% and result is 336 then number is 420
According to the question, given that
when a number is decreased by 20 % of itself, it became 336
then, the number is :
x - (x ×[tex]\frac{20}{100}[/tex] )= 336
x - [tex]\frac{x}{5}[/tex] = 336
[tex]\frac{5x - x}{5}[/tex] = 336
[tex]\frac{4x}{5}[/tex] = 336
x = [tex]\frac{336 *5}{4}[/tex]
x = 84 * 5
x = 420
Therefore, we get the number is 420
PERCENT INCREASE =(new amount−original amount)/original amount
Some people append 100% at the end of this calculation to stress that it should be stated as a percent since it represents an increase in percentage.
So, as an alternative, here is the formula:
PERCENT INCREASE = (new amount−original amount)/original amount*100%
PERCENT DECREASE=(original amount−new amount)original amount
OR
PERCENT DECREASE=(original amount−new amount)original amount*100%
Both formulas have the following pattern:
PERCENT INCREASE/DECREASE=change in amount /original amount
OR
PERCENT INCREASE/DECREASE=change in amount/ original amount*100%
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Find the savings plan balance after 3 years with an APR of 7% and monthly payments of $100.
The savings plan balance (future value) after 3 years with a 7% APR and monthly payments of $100 is $3,993.01.
What is the future value?The future value is the present value or cash flows compounded at an interest rate for a period.
The future value can be computed using an online finance calculator.
N (# of periods) = 36 months
I/Y (Interest per year) = 7%
PV (Present Value) = $0
PMT (Periodic Payment) = $100
Results:
FV = $3,993.01
Sum of all periodic payments = $3,600 ($100 x 36)
Total Interest = $393.01
Thus, at the end of 3 years, the saving plan balance grew to a future value of $3,993.01.
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In evaluating the expression 8+ 9/4 (-2) jenny found the volume to be 25/2. She thinks that the number is too great, but is not sure what she did wrong. Evaluate the expression
After evaluting the expression 8+ 9/4 (-2) we get 8 1/4.and result in decimals: 8.25
Given expression -
8+ 9/4 (-2) = ?
Combine the whole numbers and fractions together:
(8 – 2) + (9/4 - 0)
The whole numbers part is:
8 – 2 = 6
For the fractions part:
(9/4 - 0)
The Least Common Multiple (LCM) of 4 and 1 is 4. Multiply the numerator and denominator of each fraction by whatever value will result in the denominator of each fraction being equal to the LCM:
9/4 - 0 = 9/4 - 0/4
Now that the fractions have like denominators, subtract the numerators:
9 - 0/4 = 9/4
9 ÷ 4 = 2R1, therefore
9/4 = 2 1/4
Put the whole number and fraction together:
6 +2(1/4) 1
8 1/4.
Hence , the result of the expression 8+ 9/4 (-2) = 8 1/4.
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Cos(x)=-11/28, sin(x/2)
By using a trigonometric identity, we will see that the value of sin(x/2) is:sin(x/2) = ±√39/√56 = ± 0.834
How to find the value of sin(x/2)?Here we need to use the identity: (sin(x/2))^2 = (1 - cos(x))/2
So, we know that:
cos(x) = -11/28
Then:
(1 - cos(x)) = 1 + 11/28 = 28/28 + 11/28 = 39/28
Replacing the identity that we get:
(sin(x/2))^2 = (1 - cos(x))/2 ]= (39/28)/2 = (39/56)
Now we can apply the square root in both sides, so we will get:
sin(x/2) = ±√(39/56)= ±√39/√56 = ± 0.834
So, the value of sin(x/2) can be either 0.834 or -0.834.
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The ratio of boys to girls in Fiona's class is
1 to 3. There are 24 students in the class.
How many of the students are girls?
Answer:
Step-by-step explanation:
Given,
The ratio of boys to girls in Fiona's class is 1:3
The total student in the class is 24
To find,
how many students are girls
Solution,
It is clear that the total number of boys and girls is 24
i.e., boys + girls=24 ------ (equation 1)
Let the ratio be in the terms of x
Consider boys ratio as x
And the girl's ratio as 3x
Now as per the equation 1,
x + 3x= 24
4x= 24
x= 6
Hence, Boys (x)= 6
And Girls (3x)= 3× (6)= 18
You can verify it by adding 6+18= 24
What can be concluded about the line represented in the table? Select 3 options.
x
y
–6
–7
2
–3
8
0
The slope is 2.
The slope is One-half.
The y-intercept is –4.
The y-intercept is 8.
The points (–2, –5) and (8, 0) are also on the line.
The points (–5, –2) and (1, 10) are also on the line.
Conclusions that can be made about the line in the table include:
The slope is One-half.The y-intercept is –4.The points (–2, –5) and (8, 0) are also on the line.How to find the slope of a line?The slope of a line is found by the formula:
= Change in y / Change in x
Two points from the table:
(-6, -7) (2, -3)
Slope is:
= (-3 - (-7)) / 2 - (-6))
= 4 / 8
= 1/2
The y-intercept is:
y = Slope (x) + y-intercept
-3 = 2(1/2) + y-intercept
y-intercept = -3 - 1
y-intercept = -4
Points on the line as shown on the table:
(-2, -5) and (8,0)
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From the window of a building, a ball is tossed from a height y0 above the ground with an initial velocity of 7.90 m/s and angle of 24.0° below the horizontal. It strikes the ground 5.00 s later. (a) If the base of the building is taken to be the origin of the coordinates, with upward the positive y-direction, what are the initial coordinates of the ball? (Use the following as necessary: y0. Assume SI units. Do not substitute numerical values; use variables only.) xi = yi = (b) With the positive x-direction chosen to be out the window, find the x- and y-components of the initial velocity. vi, x = m/s vi, y = m/s (c) Find the equations for the x- and y-components of the position as functions of time. (Use the following as necessary: y0 and t. Assume SI units.) x = m y = m (d) How far horizontally from the base of the building does the ball strike the ground? m (e) Find the height from which the ball was thrown. m (f) How long does it take the ball to reach a point 10.0 m below the level of launching? s
The description of the motion of the ball, which is a projectile are as follows;
(a) The window coordinates are; (0, 138.49)
(b) The x–component is 7.22 m)s
The y–component is -3.22 m/s
(c) The equations for displacement are;
x = 7.22•ty = 3.21•t + 4.91•t²(d) 16.07 m from the base
(e) Height of the ball location before it was thrown is 138.49 meters
(f) Time to reach 10.0 m. is 1.14 s
What is a projectile motion?Projectile motion is the motion of an object that is thrown or thrusted into the air such that the major force acting on an object is the force of gravity
(a) The parameters of the motion of the ball are;
Initial velocity of the ball = 7.8 m/s
Direction to which the ball is tossed = 24° below the horizontal
Time it takes the ball to strike the ground = 5.00 s
Location of the origin of the coordinates = The base of the building
[tex]h = v_{iy} \cdot t + 0.5 \cdot g \cdot t²[/tex]
Where;
h = The height of the window
[tex]u_{y}[/tex]
The initial vertical velocity = 7.8×sin(24°) ≈ 3.173 m/s
g = The acceleration due to gravity ≈ 9.81 m/s²
t = The time duration of the motion = 5.00 s
Therefore;
h = 3.173×5 + 0.5×9.81×5²≈ 138.49
The height of the window, h ≈ 138.49 meters
Given that the window shares the same x–coordinates with the base, which is 0, we have;
The coordinates of the window = (0, 138.49)(b) The x and y–component of the initial velocity are therefore;
v = 7.9 m/s × (cos(24°)•i - sin(24°)•j)
v = 7.22•i - 3.21•j
The x and y component of the velocity are therefore
x–component [tex] v_{ix} [/tex] = 7.22•i
y–component, [tex] v_{y} [/tex] = -3.21•j
Therefore;
The x–component is 7.22 m/s to the rightThe y–component is 3.21 m/s towards the ground(c) The equation of the x–component of the position is found as follows;
x = 7.9×cos(24°) × t = 7.22 •t
x = 7.22•ty = 7.9×sin(24°) × t+ 0.5× 9.81×t²
y = 3.21•t + 4.91•t²(d) The distance from the base of the building where the ball lands is given by the equation
d ≈ 3.21 × 5 ≈ 16.07
The ball lands 16.07 meters from the base of the building(e) The height from which the ball was thrown, h, is given by the y–coordinate in option (a) therefore;
h = 138.49 meters(f) When the distance traveled = 10 meters, we have;
[tex]h = v_{iy} \cdot t + 0.5 \cdot g \cdot t²[/tex]
Which gives;
10 = 3.21•t + 0.5×9.81×t²
Solving with a graphing calculator, gives;
t ≈ -1.79 or t = 1.14
The possible value for the time it takes to reach the point 10 meters is therefore;
t ≈ 1.14 sLearn more about projectile motion of an object here;
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