Answer: 200cm long
Step-by-step explanation:
Let the length of the rod be x
red = 1/4 of the rod , which means 1/4 of x
orange = 2/5 of x
The remainder = x - ([tex]\frac{x}{4}[/tex] +[tex]\frac{2x}{5}[/tex])
= x - ([tex]\frac{13x}{20}[/tex])
= [tex]\frac{7x}{20}[/tex]
yellow = 2/7 of the remainder , that is
yellow = 2/7 of [tex]\frac{7x}{20}[/tex]
yellow = [tex]\frac{x}{10}[/tex]
and it was given that the yellow section was 20cm long , that is
[tex]\frac{x}{10}[/tex] = 20cm
x = 20 x10
x = 200
Therefore the rod was 200cm long
To determine the length of a rod based on fractions of it being painted different colors, with the yellow section known to be 20cm, we set up a proportion based on the fractions of the rod painted and use this to solve for the total length of the rod, which is 200cm.
Explanation:The subject of this question is Mathematics, and it is typically encountered at the Middle School level. To find the length of the entire rod when 1/4 is painted red, 2/5 is painted orange, and 2/7 of the remainder is painted yellow with the yellow section being 20cm, we need to set up an equation and solve for the total length of the rod.
First, we determine the fraction of the rod that remains after painting 1/4 red and 2/5 orange:
Calculate the total fraction painted already (red and orange combined): (1/4) + (2/5).Subtract that from 1 to find the remaining fraction.Of that remaining fraction, 2/7 is painted yellow.Since 2/7 of the remainder is 20cm, we can set up the proportion (2/7 of remainder) = 20cm to find the remainder.Once we find the remainder, we use it to calculate the full length of the rod.Let's start the calculations:
1. (1/4) + (2/5) = 5/20 + 8/20 = 13/20.
2. The remaining fraction = 1 - 13/20 = 7/20.
3. Let x be the total length of the rod. Since 2/7 of the remainder is 20cm, we can write the equation (2/7) * (7/20) * x = 20cm.
4. Simplify and solve for x:
(2/7) * (7/20) * x = 20cm,
(1/10) * x = 20cm,
x = 20cm * 10,
x = 200cm.
Therefore, the total length of the rod is 200cm.
On a coordinate plane, a straight red line with a positive slope, labeled g of x, crosses the x-axis at (negative 3, 0) and the y-axis at (0, 3). A straight blue line with a positive slope, labeled f of x, crosses the y-axis at (0, negative 3) and the x-axis at (1, 0). Both lines intersect at (3, 6). Which statement is true regarding the functions on the graph? f(6) = g(3) f(3) = g(3) f(3) = g(6) f(6) = g(6)
Answer:
f(3) = g(3)
Step-by-step explanation:
we know that
When solve a system of linear equations by graphing, the solution of the system is the intersection point both lines
The intersection point is common point for bot lines
In this problem
we have the system of equations
f(x)
g(x)
The intersection point is (3,6)
That means that the solution for the system is the point (3,6)
so
For x=3
The value of f(3)=6 and the value of g(3)=3
therefore
f(3)=g(3)
Verify the statements
Find the equation of the blue line f(x)
(0,-3) and (1,0)
the slope is
[tex]m=(0+3)/(1-0)=3[/tex]
The equation in slope intercept form is equal to
[tex]f(x)=3x-3[/tex]
Find the equation of the red line g(x)
(-3,0) and (0,3)
the slope is
[tex]m=(3-0)/(0+3)=1[/tex]
The equation in slope intercept form is equal to
[tex]g(x)=x+3[/tex]
case 1) f(6) = g(3)
The statement is false
Because
For x=6 -----> [tex]f(6)=3(6)-3=15[/tex]
For x=3 ----> [tex]g(3)=3+3=6[/tex]
therefore
[tex]f(6) \neq g(3)[/tex]
case 2) f(3) = g(3)
The statement is true
Because
For x=3 -----> [tex]f(3)=3(3)-3=6[/tex]
For x=3 ----> [tex]g(3)=3+3=6[/tex]
therefore
[tex]f(3)=g(3)[/tex]
case 3) f(3) = g(6)
The statement is false
Because
For x=3 -----> [tex]f(3)=3(3)-3=6[/tex]
For x=6 ----> [tex]g(6)=6+3=9[/tex]
therefore
[tex]f(3) \neq g(6)[/tex]
case 4) f(6) = g(6)
The statement is false
Because
For x=6 -----> [tex]f(6)=3(6)-3=15[/tex]
For x=6 ----> [tex]g(6)=6+3=9[/tex]
therefore
[tex]f(6) \neq g(6)[/tex]
Answer:
f(3)=g(3)
Step-by-step explanation:
Edge 2021
given A=LW solve for W
Answer:
[tex]\large\boxed{W=\dfrac{A}{L}}[/tex]
Step-by-step explanation:
[tex]A=LW\qquad\text{divide both sides by}\ L\neq0\\\\\dfrac{A}{L}=\dfrac{LW}{L}\\\\\dfrac{A}{L}=W[/tex]
6. Mark wants to mail postcards to eight of his friends while he is on vacation. If postcards cost $1.25 each and stamps for the cards cost $0.40 each, how much will it cost
Mark to mail the eight postcards?
$10.40
$10.32
$12.00
$13.20
Answer:
$13.20
Step-by-step explanation:
so add the prices up 1.25+0.40 should be
$1.65 now multiply it by the 8 postcards he will send
so 1.65•8= $13.20
891 g, 7,800 mg, 0.5 kg order least to greatest
Answer:
0.5 891 7,800
Step-by-step explanation:
is because least always go first
To order from least to greatest, convert all measurements to grams: 7,800 mg becomes 7.8 g, and 0.5 kg becomes 500 g. The order is 7.8 g, 500 g, and 891 g.
To order the weights 891 g, 7,800 mg, and 0.5 kg from least to greatest, we first convert them all to the same unit. Given that there are 1,000 mg in a gram (g) and 1,000 g in a kilogram (kg), we can convert as follows:
7,800 mg is converted to grams by dividing by 1,000, which gives us 7.8 g.0.5 kg is converted to grams by multiplying by 1,000, which gives us 500 g.Now that we have all the weights in grams, we can easily compare them:
7.8 g891 g500 gOrdering these from least to greatest, we get: 7.8 g < 500 g < 891 g.
|x|, if x=10; .3; 0; −2.7; −9
Answer:
if x = 10, then
x
=
;
if x = .3, then
x
=
;
if x = 0, then
x
=
;
if x = −2.7, then
x
=
;
if x = −9, then
x
=
Answer:
For [tex]\left | x \right |[/tex] we will have positive values only.
[tex]\left | -2.7 |\right =2.7[/tex]
[tex]\left | -9 |\right =9[/tex]
Rest are positive so will give positive values out of the modulus function.
Step-by-step explanation:
The absolute value of any number is its positive value only.
As for example [tex](-2.7)[/tex] and [tex](2.7)[/tex] both are having equal distance from [tex]0[/tex] in a number line, one on the left other on the right side of the number line but are equidistant from [tex]0[/tex].
So absolute value of a number is its distance on number line from reference point [tex]0[/tex].
One by one we will work with all of our question.
[tex]\left | 10 |\right =10[/tex]
[tex]\left | 0.3 |\right =0.3[/tex]
[tex]\left | 0 |\right =0[/tex]
[tex]\left | -2.7 |\right =2.7[/tex]
[tex]\left | -9 |\right =9[/tex]
So we have to take the positive number out of the modulus function that is also called absolute value.
solve
4(t+1/4) = 3 plz
Answer:
t = 1/2
Step-by-step explanation:
4(t+1/4)=3
First, distribute:
4(t)+4(1/4)=3
4t+1=3
Then isolate the variable:
4t+1-1=3-1
4t=2
4t/4=2/4
t=2/4
t=1/2
The equation is solved first by distributing the 4, then by subtracting 1 from both sides to isolate the variable term, and finally by dividing both sides by 4 to solve for 't', which gives the solution t = 0.5.
Explanation:To solve the equation 4(t+1/4) = 3, we start by distributing the 4 inside the parentheses, so we get 4t + 1 = 3.
Then, we subtract 1 from both sides of the equation to isolate the variable term, and this gives us 4t = 2.
Finally, to solve for 't', we divide both sides of the equation by 4, and we find that t = 0.5.
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Complete the two-column proof using the answers in the bank.
Answer:
The proof is written below.
Step-by-step explanation:
Given:
[tex]DF \cong EF\\FG\ \textrm {bisects}\ \angle DFE[/tex]
Prove :
[tex]\triangle DFG \cong \triangle EFG[/tex]
Proof:
[tex]DF \cong EF \ \textrm{Given}\\FG\ \textrm{bisects}\ \angle DFE\ \textrm{Given}\\[/tex]
[tex]\angle 1 \cong \angle 2[/tex] Definition of angle bisector
[tex]\overline{FG} \cong \overline{FG}\ \textrm{Reflexive Property}\\\triangle DFG \cong \triangle EFG\ \textrm {SAS Congruence}[/tex]
2.5 x 13.7
4.9 + 1.6
Write down your full calculator displ
Answer:
2.5 x 13.7 = 34.25
4.9 + 1.6 = 6.5
Step-by-step explanation:
Here we are multiplying 2 decimals we can just write it as
[tex]25 * 10^{-1} * 137 * 10^{-1}[/tex]
= [tex]25*137*10^{-2}[/tex]
= [tex]3425 *10^{-2}[/tex]
= 34.25
Here we are just performing simple addition
4.9 + 1.6
= [tex]49 *10^{-1} +16*10^{-1}[/tex]
= [tex](49+16)*10^{-1}[/tex]
=[tex]65 * 10^{-1}[/tex]
= 6.5
explain how a number can be a power of 10
Answer:
A power of 10 is the number 10 multiplied by itself by the number of times indicated by the exponent.When the exponent is greater than o it is followed by zeros
An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
The value of the number with a power 10 is a multiplication of that number 10 times.
1024 can be a number with power 10
i.e [tex]2^{10}[/tex]
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
A number with power 10.
This means,
The value of the number with a power 10 is a multiplication of that number 10 times.
i.e
[tex]2^{10}[/tex] = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2
[tex]2^{10}[/tex] = 2³ x 2³ x 2³ x 2 = 8 x 8 x 8 x 2 = 1024
Similarly,
1024 can be a number with power 10
Thus,
The value of the number with a power 10 is a multiplication of that number 10 times.
1024 can be a number with power 10
i.e [tex]2^{10}[/tex]
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When the y-intercepts of a line is 0, the relationship is....
Answer:
I am going to assume you mean the relationship between x and y.
If the y-intercept is 0, that means the point is on the origin.
So x and y are equal to each other. they are both zero
the bells obtain a 20-year, $90,000 conventional mortgage at a 8.5% rate on a house selling for $130,000. their monthly mortgage payment, including principal and interest, is $781.20. They also pay 3 points at closing.
a) determine the total amount the bells will pay for their house.
b) how much of the cost will be interest (including the 3 points)?
c) how much of the first payment on the mortgage is applied to the principal?
a) The total amount the Bells will pay for their house is $187,488. b) The interest paid, including the 3 points, is $97,488. c) The exact amount applied to the principal in the first payment is unknown without additional information.
Explanation:a) To determine the total amount the Bells will pay for their house, we need to calculate the total amount paid over 20 years. The monthly mortgage payment is $781.20, so the annual payment would be $781.20 x 12 = $9374.40. Therefore, over 20 years, the Bells will pay $9374.40 x 20 = $187,488.
b) The interest paid over the 20-year mortgage period can be calculated by subtracting the total mortgage amount from the total amount paid. The total mortgage amount is $90,000, so the interest paid is $187,488 - $90,000 = $97,488, including the 3 points.
c) The first payment on the mortgage is typically applied mostly to the interest. However, to determine the exact amount applied to the principal, we need more information about the breakdown of the monthly mortgage payment between interest and principal.
write the set in set builder notation {2,4,6,8,10,12}
Answer:
{x∈Z+ | x is an even, 2≤x≤12}
Step-by-step explanation:
∈ = elememt of
Z+ = +ve integer
even = even no.
≤ = smaller than or equal to
The set builder notation is {x : x = 2n where n ∈ N and n < 6}.
What is a set?A set is a group or collection of objects or numbers, considered as an entity unto itself.
Now the given set is,
Let S = {2,4,6,8,10,12}
Now, Set-builder notation describe a set by saying what properties its members have.
It uses curly brackets called "braces".
The first part after the first curly bracket tells you what set of numbers x belongs to.
The ∈ symbol means "is an element of".
Now, x = 2n where n ∈ N
and n < 6
Therefore, the required set builder notation is,
S = {x : x = 2n where n ∈ N and n < 6}
Thus, the set builder notation is {x : x = 2n where n ∈ N and n < 6}
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I round to 900 I have twice as many hundreds as ones and all my digits are different but their sums are 18 can someone answer this and explain it to me plz
Answer:
The number of once is 9.1
The number of hundreds is 8.9
Step-by-step explanation:
Given as :
The total of digits having ones and hundreds = 900
The sum of digits = 18
Let The number of ones digit = O
And The number of hundreds digit = H
So, According to question
H + O = 18 .........1
100 × H + 1 × O = 900 ........2
Solving the equation
( 100 × H - H ) + ( O - O ) = 900 - 18
Or, 99 H + 0 = 882
Or , 99 H = 882
∴ H = [tex]\frac{882}{99}[/tex]
I.e H = 8.9
Put the value of H in eq 1
So, O = 18 - H
I.e O = 18 - 8.9
∴ O = 9.1
So, number of once = 9.1
number of hundreds = 8.9
Hence The number of once is 9.1 and The number of hundreds is 8.9
Answer
Final answer:
The number that fits the criteria of rounding to 900, having twice as many hundreds as ones, having all different digits, and the sum of its digits being 18, is 864.
Explanation:
The question involves finding a number that meets a set of criteria: it rounds to 900, has twice as many hundreds as ones, all its digits are different, and the sum of its digits equals 18. To solve the problem, we can break down the clues and use them to narrow down the possibilities.
Since the number rounds to 900, we know it must be in the range of 850 to 949. The clue that it has twice as many hundreds as ones implies that the number of hundreds is a digit that is double the digit in the ones place. And since all digits must be different, we are looking for a number that does not repeat any digit.
Given the criteria, let's assume the hundreds digit is '8' (since it's in the 800 series), and therefore the ones digit would be '4'. The only digit left to assign is the tens place, which cannot be the same as the other two and must ensure the sum of all three digits equals 18. The digit for the tens place should then be 18 - 8 - 4 = 6, making the number 864, which satisfies all conditions.
So, the number we are looking for is 864: it rounds to 900, has twice as many hundreds (8 hundreds) as ones (4 ones), all digits are different, and the sum of the digits (8+6+4) equals 18.
-2(x + 8) = -2(7 + 2x)
Answer:
x = 1
Step-by-step explanation:
-2x - 16 = -14 - 4x
-2x + 4x = -14 + 16
2x = 2
x = 1
o to the repentant to ce actingon the surfaces or docts.
6. What are the units of friction
triction? Noaton, N = ham.s.
7. Review the questions in the lab manual.
ficient of static-boolean not
2.20 NS
22 Sino-206
8. A 220N box is set on 100 decline. What is the force of friction if the coefficient of static
docsit me
friction is 0.67? Does the object slide down, if so, with what acceleration? You may change
these numbers around for practice
box QƏN
fe Gm F ms
2200 casio
P= 220N CO510.6.67
F mga 0.67
9. A 400 N box is on a level floor. Instead of pushing it, you decide to drag it
ver Floor. Instead of pushing it, you decide to drag it by attaching a
rope at a 45°. You are able to muster 200 N of force pulling at that angle. With
does the box move? If not, how much force is required to get the box to move
with 300 and 600 with us = 0:4 and 0.6.
HON-0.3 =120N
SOX0.3/40 - dob
200-120- GON
VIII Momentum
120X0.
31H = 0.09
ce pulling at that angle. With a us of 0.3
quired to get the box to move? Try solving
Answer:s
Step-by-step explanation:
HELLLLLP WILL GIVE BRAINLIEST FIRST ANSWER
6(3x+2x)+(39-y)x2= what
Answer:− 1 x (small)2 y + 39 x(small) 2 + 30 x
Step-by-step explanation:
What is 14% of 21.55?
Simplify the equation 28 - 6n + 7(2n -8)-3n
Answer:
5n-28
Step-by-step explanation:
28-6n+7(2n-8)-3n
28-6n+14n-56-3n
28+8n-56-3n
28-56+8n-3n
-28+5n
5n-28
A 15- ounce box contains 0.425 kg of cereal. how many grams of cereal are in the box
425 g for the 15 ounce box of cereal?
24. Rectangle A is 16 feet wide and is 8 feet longer than Rectangle B which is 14 feet wide.
If the sum of both rectangles perimeters is 156 feet, what is the area of Rectangle A?
Answer:
The Area of rectangle A is 576 feet² .
Step-by-step explanation:
Given as :
The width of rectangle A = 16 feet
The Length of rectangle A = 8 feet + The length of rectangle B
The width of rectangle B = 14 feet
Let The length of rectangle B = L feet
So, The Length of rectangle A = 8 feet + L feet
The perimeter of rectangle A + The perimeter of rectangle B = 156 feet
So, 2 × ( Length A + width A ) + 2 × ( Length B + width B ) = 156 feet
Or, 2 × ( 8 + L + 16 ) + 2 × ( L + 14 ) = 156 feet
Or, 2 ×( 24 + L ) + 2 × ( L + 14 ) = 156 feet
Or, 48 + 2 L + 2 L + 28 = 156
Or, 76 L + 4 L = 156
So, 4 L = 156 - 76
Or, 4 L = 80
∴ L = [tex]\frac{80}{4}[/tex] = 20 feet
So , The Length of rectangle A = 8 feet + 28 feet = 36 feet
And The width of rectangle A = 16 feet
So, Area of rectangle A = Length of rectangle A × width of rectangle A
I.e Area of rectangle A = 36 × 16 = 576 feet²
Hence The Area of rectangle A is 576 feet² . Answer
It takes 2 5/6 spoons of chocolate syrup to make 4/6 of chocolate milk.how many spoons of syrup would it take to make 1 gallon of chocolate milk?
Answer:
17/4
Step-by-step explanation:
2 5/6=17/6
4/6=2/3
------------------
(17/6)/(2/3)=(17/6)(3/2)=51/12=17/4
93.75
x 0.99what's 93.95 * 0.99
Henry consistently makes seven out every ten free throws he shoots. At the same rate, how many free throws will he make after he shoots 90 of them?
Lynn is having a party. Pizzas cost $8.00 each. How many pizzas can she buy with $60.00
Answer: 7 pizzas
Step-by-step explanation:
Answer:
60/8 = 7.5 = 7 pizzas (round down to the nearest integer)
Step-by-step explanation:
You can only buy a whole pizza, not slices of it.
my new car radio was $179.95 plus 20 percent for installation. what did I end up paying?
Answer:
$215.94
Step-by-step explanation:
You do 20% × $179.95 to get $35.99
Since the 20% is being added to your bill, you add it to your base price
$179.95 + $35.99 = $215.94
Using the double number line shown, for the equation 5 x + 4 = 14 5x+4=14, what is the value of x?
Number line is the line in which the numbers are marked at the intervals to the show the inequality. The value of the x, is 2 which is shown on the number line by attached image below.
Given information-The equations given in the problem are,
[tex] 5 x + 4 = 14[/tex]
Number lineNumber line is the line in which the numbers are marked at the intervals to the show the inequality.
Here in the problem the given equation is,
[tex] 5 x + 4 = 14[/tex]
Solve it for the x,
[tex]\begin{aligned}\\ 5 x &= 14-4\\ 5x&=10\\ x&=\dfrac{10}{5} \\ x&=2\\ \end[/tex]
The value of the x is 2. It can be shown on the number line graph by making a circle on the number 2.
As the inequality is shown with the equal sign in the given equation. Therefore the direction would be nigher side. The graph for the given equation number line shown in the attached image.
Hence the value of the x, is 2 which is shown on the number line by attached image below.
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Final answer:
To solve the equation 5x + 4 = 14, subtract 4 from both sides, then divide by 5. This gives x = 2, which can be checked by substitution back into the equation and verifying it holds true.
Explanation:
To solve the equation 5x + 4 = 14, we need to isolate the variable x. First, we subtract 4 from both sides of the equation to get 5x = 10. Next, we divide both sides of the equation by 5 to find the value of x:
5x ÷ 5 = 10 ÷ 5
x = 2
This means that the value of x that satisfies the equation 5x + 4 = 14 is 2. We can check our answer by substituting 2 back into the original equation to see if it makes a true statement:
5(2) + 4 = 10 + 4 = 14
Since the left side of the equation equals the right side, x = 2 is indeed the solution.
-68 times the difference between a number and 11 is equal to the number one plus -94
Answer:
x=841/68
Step-by-step explanation:
-68(x-11)=1+(-94)
-68(x-11)=-93
-68x+748=-93
-68x=-93-748
-68x=-841
68x=841
x=841/68
Final answer:
To solve this problem, set up an equation by representing the unknown number as x. Distribute -68 to the terms inside the parentheses and solve for x by isolating it on one side of the equation.
Explanation:
To find the answer to this problem, we can set up an equation. Let's let the unknown number be represented by x. The difference between a number and 11 can be written as (x - 11). The problem states that -68 times this difference is equal to the number one plus -94, which can be written as -68(x - 11) = -94 + 1.
To solve this equation, we can distribute -68 to the terms inside the parentheses: -68x + 748 = -93. Then, we can subtract 748 from both sides to get -68x = -841. Finally, we divide both sides by -68 to find that x = 12.38.
Therefore, the solution to this problem is x = 12.38.
Suppose you have a $60,000 loan with an annual percentage rate of 8% for 25 years.
What would be the effect of paying the required monthly rate and an additional $100 each month on the cost of the two loan?
.
Paying an extra $100 each month on a $60,000 loan with an 8% APR over 25 years will reduce the loan term and total interest paid. To calculate the effect, compute the total cost of the loan with and without the extra payments and subtract these two sums.
Explanation:The subject at hand pertains to understanding the impact of additional payments on a loan, which falls under the domain of financial mathematics. Let's dissect the impact of paying an extra $100 per month on a $60,000 loan with an 8% annual interest rate over 25 years.
Firstly, we need to calculate the monthly payment for a 25-year loan of $60,000 at 8% interest. This can be calculated by using a loan calculator or the loan payment formula. Then, calculate the total cost of the loan by multiplying this monthly payment by the number of months in the loan term (25 years x 12 months).
You then do a similar calculation, but this time add an extra $100 to the monthly payment. The extra repayment will reduce the loan term and decrease the total interest paid. To see the effect, compare the total cost of the loan with and without the extra $100.
Therefore, the difference between these two sums will give you the saved amount due to the additional $100 monthly payment. This saving is the effect of making additional payments on the loan.
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Making additional monthly payments can shorten the loan term and save money on interest payments.
Explanation:To calculate the effect of making additional monthly payments on the cost of the loan, we can compare the total interest paid and the duration of the loan with and without the additional payments. Without any additional payments, the monthly payment for a $60,000 loan with an 8% APR and a 25-year term would be $459.18. With an additional $100 each month, the monthly payment would increase to $559.18.
By making the additional $100 payments, the loan would be paid off faster, reducing the term from 25 years to approximately 17 years and saving the borrower 8 years of monthly payments. Additionally, the total interest paid over the course of the loan would also be significantly reduced compared to just paying the required monthly payments.
In summary, making extra monthly payments of $100 can shorten the loan term and save the borrower money on interest payments.
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if h=-16t ²+160t represents the height of a rocket in T seconds after it was fired when will the rocket hit the ground?
Answer:
The time after which the rocket hit the ground is 5 seconds
Step-by-step explanation:
Given as :
The distance of the cover by rocket at the height h = - 16 t² + 160 t
Let the time after which rocket hit the ground = T seconds
Now, When the rocket hits the ground, then at that time, the velocity of the rocket becomes zero.
I.e velocity = [tex]\frac{\partial h}{\partial t}[/tex] = 0
Or, v = [tex]\frac{\partial h}{\partial t}[/tex] = 0
Now, v = [tex]\frac{\partial h}{\partial t}[/tex]
Or, v = [tex]\frac{\partial (-16t^{2}+160t)}{\partial t}[/tex]
or, v = - 32 t + 160
Now, ∵ velocity of rocket after reaching the ground becomes zero
So, v = - 32 t + 160 = 0
Or, 32 t = 160
Or, t = [tex]\frac{160}{32}[/tex]
∴ t = 5 sec
So, The time after which the rocket hit the ground = 5 sec
Hence The time after which the rocket hit the ground is 5 seconds answer
To find when the rocket will hit the ground using the quadratic equation h = -16t² + 160t, solve for t when h=0; the rocket will hit the ground after 10 seconds.
Explanation:To determine when the rocket will hit the ground given the equation h = -16t² + 160t, we need to find the value of t at which the height h is zero. The equation represents a quadratic equation, where t is the time in seconds after the rocket was fired, and h is the height of the rocket at any time t.
To solve for the time when the rocket hits the ground, we set h to zero and solve for t:
0 = -16t² + 160t0 = t(160 - 16t)Therefore, t = 0 or t = 10 secondsWe discard the t = 0 since it represents the initial time at launch. Thus, the rocket will hit the ground after 10 seconds.
During this entire period, while the rocket is ascending and descending, it is important to consider the horizontal motion if analyzing its trajectory in more detail, but for this problem, we are only concerned with the vertical motion.
Which number is larger? Justify your answer -4.03 or -4.3
Final answer:
To determine which negative number is greater between -4.03 and -4.3, compare their standard forms with the same exponent, concluding that -4.03 is larger due to its higher coefficient.
Explanation:
To determine which number is larger between -4.03 and -4.3, we can compare them in standard form:
-4.03 = -4.03 × 100
-4.3 = -4.3 × 100
Since both numbers have the same power of 10 (exponent), we compare the coefficient: -4.03 is larger than -4.3 because 0.03 is greater than 0. Therefore, -4.03 is larger than -4.3.