A. The functions are classified as follows:
House 1: Exponential.House 2: Linear.B. The functions are defined as follows:
House 1: f(x) = 294580(1.03)^x.House 2: f(x) = 295000 + 9000x.C. The value of each house after 25 years is given as follows:
House 1: $617,785.House 2: $520,000.There is a significant difference in the value of either house after 25 years, as exponential functions increase faster than linear functions, especially for larger input values.
How to classify the functions?A function is classified as exponential if when the input variable is changed by one, the output variable is multiplied by a constant.
Hence the house 1 has the value function as an exponential function, as:
312,519.92/303,417.40 = 303,417.40/294580 = 1.03
The function is defined as follows:
f(x) = 294580(1.03)^x.
And the value of the home after 25 years is given as follows:
f(25) = 294580(1.03)^25 = $6176,785.
A function is classified as linear if when the input variable is changed by one, the output variable is increased/decreased by a constant.
Hence the value of the house 2 is linear, as the rate of change each year is of $9,000.
The function is defined as follows:
f(x) = 295000 + 9000x.
The value after 25 years is given as follows:
f(25) = 295000 + 9000(25) = $520,000.
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What is the discount on a 1,725 couch marked 15% off?
We can find the discount by taking the product between the price of the couch and the decimal form of the percentage, the discount on the couch is equal to $258.75
What is the discount on the couch?We know that for a couch whose price is $1,725, we apply a discount of the 15%.
Then we just need to find the 15% of $1,725, to do so, we need tu multiply the number by the decimal form of that percentage.
To get the decimal form, you need to take the quotient between the percentage and 100%, you will get:
15%/100% = 0.15
Then the discount is:
0.15*$1,725 = $258.75
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Jim usually sails his boat 20 miles from the boat launch to Kingston. Today he is driving the 16 miles from the boat launch to the marina. How far will he sail across the lake to Kingston from the marina?
HURRY PLEASE
Jim will need to sail 4 miles across the lake from the marina to Kingston.
What is miles?Miles is a unit of measurement used to measure the distance between two locations. It is equal to 1.609 kilometers and is commonly used in the United States and the United Kingdom. Miles are frequently used to measure the distance between two cities, the distance a person has traveled, or the length of a road or highway. It is also sometimes used to measure the distance of a flight.
Since he is driving 16 miles from the boat launch to the marina, he will have covered a total of 20 miles by the time he arrives at the marina. From there, it is 4 more miles to Kingston. Therefore, he will need to sail a total of 4 miles to reach his destination.
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The side lengths of a triangle are in the ratio 2 : 3:4.
The longest side has a length of 28 cm.
What is the perimeter of the triangle?
Give your answer in centimetres (cm).
Answer:
It is 63 cm
Step-by-step explanation:
Take 28/4 = 7. That is what1 equals in the proportion. So, we take 2 x 7, 3 x 7, and 4 x 7. Then you just add the sides together and it equals 63 cm.
Answer: 63
Step-by-step explanation:
In the ratio, the longest side is 4. 4x7 is 28, so to make the ratios proportional again, you multiply all the sides by 7, getting 14:21:28.
These are the side lengths of the triangle, and to find the perieter you add all of them up, getting 63.
Hope this helps :)
Need help with another one of these, I still can't seem to understand.
The location of B such that the ratio of AB to BC is given as follows:
B = 28.
How to obtain the location of B?The location of B in the context of this problem is obtained applying the proportion, which is the ratio between the locations.
The coordinates of each point in this problem are given as follows:
A = 4.B = x.C = 36.The length of each segment in this problem is given as follows:
AB = B - A = x - 4.BC = C - B = 36 - x.The ratio of AB to BC is 3 to 1, hence the following proportional relationship is established:
AB/BC = 3.
(x - 4)/(36 - x) = 3.
Applying cross multiplication, we can solve to obtain the value of x, representing the location of B, as follows:
x - 4 = 108 - 3x
4x = 112
x = 112/4
x = 28.
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A manufacturer receives the order of a batch of aluminum panels. A hole should be drilled on the panel in order to bolt it onto other parts. The diameter of the hole is specified as 10.50 +0.50 mm. The population mean of the holes is 10.60 mm, the population standard deviation is 0.30 mm. The data is normally distributed. If the hole is smaller than the lower specification limit, it can be reworked. If the hole is larger than the upper specification limit, the panel is scrapped. So
a) What percentage of the panels will be scrapped? (5 points)
b) What percentage of the panels will need rework? (5 points)
c) In order to reduce the scrap percentage to 1%, the manufacturer re-centers the process with a new mean value, and the standard deviation remains unchanged. So what is the new mean value? (10 points)
d) What will be the rework percentage with the new mean value? (5 points)
Note: maintain at least two digits after the decimal point.
From the given data about population, we found out answers:
a) The percentage of the panels that will be scrapped is 4.55%.
b) The percentage of the panels that will need rework is 45.45%.
c) In order to reduce the scrap percentage to 1%, the manufacturer must re-center the process with a new mean value of 10.50 mm.
d) The rework percentage with the new mean value is 0.33%.
This is because the new mean value (10.60 mm) is within the specified range (10.50 +0.50 mm). Thus, there will be no rework or scraped panels due to the mean being outside of the specified limits.
To better understand this, it is important to consider the normal distribution of the data and the specified limits for the hole size. The normal distribution of the data means that the majority of the holes will be of the mean size, with very few being either significantly larger or smaller.
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One number is 6 more rhan another number. The sum of their squares is 90.
Answer:
You know that x = -9, and 3 or The first number is 3, the other -9
Step-by-step explanation:
First number: x
Second: x + 6
(x)^2 + (x + 6)^2 = 90
x^2 + x^2 + 6x + 6x + 36 = 90
Simplify more
2x^2 + 12x + 36 = 90
2x^2 + 12x - 54 = 0
2(x + 9)(x - 3) = 0
The algebraic dimensions of a rectangular prism are:
x, x−2, and x+8
and the volume is 96 square inches.
What are the numeric dimensions of the prism? Work must show evidence of the skills you learned in this chapter. Fill in the blanks in NUMERIC order from least to greatest dimension.
Therefore the numerical order of the dimensions of rectangular prism is 8, 12
What is dimensions?
The minimal set of coordinates required to represent any point inside a mathematical space is known as the dimension of the space in physics and mathematics. As a result, a line has a dimension of one since a point on it may be specified by a single coordinate, such as the point at 5 on a number line.
What is minimal set ?We have a minimum set when a group of words can all be distinguished from one another by altering one phoneme (always in the same location in the word). feat, fit, fat, fate, and foot were used. Big, Pig, Rig, Fig, Dig, and Wig might be included in another minimum list based on consonant phonemes.
The equation for the volume of a rectangular prism:
V = l × w × h
Given dimensions are x, x-2, and x+8
V = (x)(x-2)(x+8) = 96
x^3 - 2x^2 + 8x = 96
x^3 - 2x^2 + 8x - 96 = 0
(x-12)(x+4)(x-8) = 0
Therefore, x = 12, -4, 8
As the dimension of prism can't be negative, we can discard -4 as one of the dimension.
Thus, the numerical order of the dimensions of rectangular prism is 8, 12
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how to evaluate 3x-5/y for x = 3, y = 4
7. Last year Troop No. 113 sold 100 dozen cookies. How
many will they have to sell this year to have a 20% increase
in sales?
does somebody know the answer also please try to explain or show the work worth 40 points help a girl out
Answer:
120 dozen cookies------------------------------------
100 dozen add 20% is:
100 + 100*20/100 = 100 + 20 = 120 dozenhow do you write out 1 and 2 from 1.25??
Answer:
1_ones and 2 _tenth
Step-by-step explanation:
the number in front of the point they start from ones continues
there is a line that includes the point (1, 7) and has a slope of 10. what is its equation in slope-intercept form?
Answer:
y=mx+c
Step-by-step explanation:
Pls help.
Answer and step by step explanation pls
[tex]~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{3(ab^2)^2}{6a^3b^{-3}}\implies \cfrac{3}{6}\cdot \cfrac{(ab^2)^2}{a^3b^{-3}}\implies \cfrac{1}{2}\cdot \cfrac{(a^2b^4)}{a^3b^{-3}}\implies \cfrac{1}{2}\cdot \cfrac{b^4 b^3}{a^{-2}a^3} \\\\\\ \cfrac{1}{2}\cdot \cfrac{b^{4+3}}{a^{-2+3}}\implies \cfrac{1}{2}\cdot\cfrac{b^7}{a^1}\implies \cfrac{b^7}{2a}[/tex]
how is 3^-3 = 1/8. please help
Answer: it's not its [tex]\frac{1}{27}[/tex]
Step-by-step explanation:
Because the negative in the exponent moves it to the denominator then just cube 3 in the denominator
[tex]\frac{1}{3^{3} }[/tex]
[tex]\frac{1}{27}[/tex]
But [tex]2^{-3} =\frac{1}{8}[/tex]
because [tex]\frac{1}{2^{3} }[/tex] = [tex]\frac{1}{8}[/tex]
If a number is added to the numerator of? and the same number is subtracted from the denominator, the result is 2. Find the number.
Answer:
i think it's true am a 6 grader i really try
Step-by-step explanation:
How do you explain a pie chart in a presentation?
Answer: 4 pie chart
Step-by-step explanation:
Each pie chart [tex]\pi[/tex] wil have 4 parts to it depending on how the shape of the pie is
what is the probability that a two-digit number selected at random has a tens digit less than its units digit? express your answer as a common fraction.
The probability that a two-digit number selected at random has a tens digit less than its units digit is 0.2667 (4/15).
What is a probability simple definition?
A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%
P= A/B
= 4/15
There are 90 two-digit numbers (99-9). Of these, six numbers are divisible by 15 (15, 30, 45, 60, 75, 90). This is also divisible by 5. Therefore, the preferred case is 30-6 = 24. Therefore, the required probability is 24/90 = 4/15.
The probability of an event can be calculated by simply dividing the number of favorable results by the total number of possible results using a probabilistic expression. Whenever you are uncertain about the outcome of an event, you can talk about the probability of a particular outcome, that is, its potential.
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If you divided the number of letters in “MerryChristmas” by the number of thieves in the first “Home Alone” movie, what would be the answer
If you divided the number of letters in “Merry Christmas” by the number of thieves in the first “Home Alone” movie, then the answer will be 7.
What is Division ?Multiplication is the opposite of division. If 3 groups of 4 add up to 12, then 12 split into 3 groups of equal size results in 4 in each group. Creating equal groupings or determining how many people are in each group after a fair distribution is the basic objective of division.
One of the four fundamental arithmetic operations, or how numbers are joined to create new numbers, is division. The other operations are multiplication, addition, and subtraction.
A division problem has three primary components: the dividend, the divisor, and the quotient. The amount that will be shared is the dividend. The quantity of "people" among whom the number is split is referred to as the divisor. The answer is the quotient.
Number of letters in Merry Christmas is 14
Number of thieves in Home Alone is 2
The quotient is given as 14/2 = 7
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PLEASE HELP
question 5,
The average starting salary for a lawyer is $79,590 but can vary by as much as $4,236. Which inequality could be used to determine the average salary range, if x represents the starting salary?
|x − 4,236| ≥ 79,590
|x − 4,236| ≤ 79,590
|x − 79,590| ≥ 4,236
|x − 79,590| ≤ 4,236
Graph the curve x = cos t + 2 cos 2t, y = sin t + 2 sin 2t to discover where it crosses itself. Find equations of both tangents at that point.
For given parametric curve the equations of both tangents at point where it crosses itself are: y = ± (√15x + 2√15)
The graph of parametric curve x = cos t + 2 cos 2t, y = sin t + 2 sin 2t (t ∈ [0, 2π]) is as shown below.
From the graph we can observe that, the curve crosses itself at (-2, 0).
Let x = -2
cos t + 2 cos 2t = -2,
and y = 0
sin t + 2 sin 2t = 0
sin t + 2 (2 sin(t) cos(t)) = 0
sin t + 4 sin t cos t = 0
sin t(1 + 4 cos t) = 0
sin(t) = 0 OR 1 + 4 cos(t) = 0
sin(t) = 0 OR cos(t) = -1/4
From sin(t) = 0
⇒ t = 0 or t = π,
but for these values of t, cos t + 2 cos 2t = -2 is not true.
This means, the point (-2, 0) must corresponds to cos(t) = -1/4
[tex]\Rightarrow t=cos^{-1}(\frac{1}{4} )[/tex]
When cos(t) = -1/4,
sin(t) = [tex]\frac{\sqrt{15} }{4}[/tex] ..............(by identity sin²(t) + cos²(t) = 1)
And
[tex]sin(2t) = 2sin(t)cos (t)\\sin(2t) = 2\times \frac{\sqrt{15} }{4} \times (\frac{-1}{4} )\\\\sin(2t) = -\frac{\sqrt{15} }{8}[/tex]
[tex]\\\\cos(2t)=2cos^2{t} - 1\\\\cos(2t)=2(\frac{-1}{4} )^2 - 1\\\\cos(2t)=\frac{1}{8}-1\\\\ cos(2t)=\frac{-7}{8}[/tex]
Now we find derivative of given parametric equations with respect to t.
for x = cos t + 2 cos 2t,
dx/dt = -sin(t) -4 sin(2t)
y = sin t + 2 sin 2t
dy/dt = cos(t) + 4 cos(2t)
Consider dy/dx
[tex]= \frac{\frac{dy}{dt} }{\frac{dx}{dt} }\\\\= \frac{cos(t) + 4 cos(2t) }{-sin(t) -4 sin(2t)}\\\\=\frac{\frac{-1}{4}+4~\frac{-7}{8} }{-\frac{\sqrt{15} }{4}-4~\frac{\sqrt{15} }{8} }\\\\=-\sqrt{15}[/tex]
This means, slope m = -√15
We have the point (−2,0)
Using equation of line y=mx+b the y-intercept would be,
0 = -√15 (−2) + b
b = -2√15
So, the equation for this tangent line :
y = -√15x - 2√15
And the equation of other tangent would be,
y = √15x + 2√15
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please help quickly
The polygons are similar. x = ___ Write your answer as a decimal
The value of x of the quadrilateral using the concept of similar quadrilaterals is; x = 1.5
How to interpret Similar Quadrilaterals?Two quadrilaterals are referred to as similar quadrilaterals when the three corresponding angles are the same and as a result the fourth angles automatically become the same due to the fact that the interior angles of a quadrilateral sum up to 360 degrees and two adjacent sides have equal ratios.
Thus, we can say by the concept of similar quadrilaterals that;
AB/LM = BC/MN
Thus;
14/(x + 9) = 10/(x + 6)
14(x + 6) = 10(x + 9)
14x + 84 = 10x + 90
14x - 10x = 90 - 84
4x = 6
x = 1.5
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Derek is riding his bicycle with a 36-in. diameter wheel in a
10-mi race How many revolutions will each wheel make in the
race?. Round your answer to the nearest tenth. Use 3.14 for T
(Hint: 12 in. = 1 ft; 5280 ft = 1 mi)
6-7
The number of revolution each wheel make is 5605.
What is a circle?A circle is a two-dimensional figure with a radius and circumference of 2πr.
The area of a circle is given as πr².
We have,
Diameter of the wheel = 36 inches
The radius of the wheel = 18 inches
The circumference of the wheel = 2πr.
The total distance traveled = Circumference of the wheel x Number of revolutions (N).
Now,
10 miles = 10 x 5280 ft = 10 x 5280 x 12 inches
10 miles = 2πr x N
N = (10 x 5280 x 12) / (2 x 3.145 x 18)
N = 633600 / 113.04
N = 5605
Thus,
The number of revolutions is 5605.
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Two square stepping stones are placed in a garden as shown below. Each stepping stone has a side length of 2 feet. The rest of the garden will have flowers in it.
How many square feet of the garden could contain flowers?
20 ft²
32 ft²
16 ft²
24 ft²
The square feet of the garden that could contain flowers, given the side lengths of the stepping stone and the garden, is C. 16 ft².
How to find the square feet of the garden ?To find the portion of the garden that could contain flowers, first find the total area of the entire garden ;
= Length of garden x Width
= 4 x 6
= 24 ft ²
The stepping stones will not contain flowers so their area should be deducted from the area of the garden :
= 24 - ( 2 x ( 2 x 2 ))
= 24 - ( 2 x 4 )
= 24 - 8
= 16 ft²
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25% discount, the price of a t shirt was 15$. What was the price before the discount
The charge for the t-shirt earlier than the cut price of 25 percent is $20.
What is percentage?A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.
Given, the 25% discount, the price of a t-shirt was 15$.
Since, After 25% discount price of t-shirt = 15
Thus
Original price of t-shirt = 15 * 100/75
Original price of t-shirt = 20
Therefore, the price before the discount of 25 percent is $20.
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The radius of a wheel is 28cm. How many revolutions will it make in travelling 3.52km?
Answer:
2001
Step-by-step explanation:
First, let us find the circumference of the wheel ( circle ) using the below formula.
C = 2πr
Here,
r ⇒ radius ⇒ 28 cm
Let us solve it now.
C = 2 × π × 28
C = 175.93 cm
And now let us covert the travelling distance to centimeters.
( For that, multiply km by 100000 )
3.52km = 352000 cm
Now, to find the number of revolution, divide the total distance travelled by its circumference.
352000/175.93 = 2000.79
Approximately, 2001 revolutions
The number of revolutions made by a wheel of 28cm radius covering a distance of 3.52km is 2000.8.
Given,
Radius, r = 28cm
Circumference = 2πr = 56π cm
Circumference = Distance traveled in one revolution
The distance traveled by wheel = 3.52km = 3520m = 352000cm
Let N = number of revolution
Now we know that,
Total distance = Number of revolutions × 1 revolution distance(circumference)
or 352000 = N × 56π
or N = 352000/56π
or N = 2000.8
Therefore, the number of revolutions made by a wheel of 28cm radius covering a distance of 3.52km is 2000.8.
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Find the domain in interval notation of (f/g)(x)
The domain of (f/g)(x) in interval notation is [-3, 6].
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
From the graph,
f(x) has x values from x = -1 to x = 6
g(x) has x values from x = -3 to x = 5
The function f(x) is f(x) = mx + c
Find two coordinates from the graph of f(x).
= (-1, 3) and (6, 4)
m = (4 - 3) / (6 + 1) = 1/7
Now,
3 = (1/7) x -1 + c
3 = -1/7 + c
c = 3 + 1/7
c = 22/7
f(x) = (1/7)x + 22/7 _____(1)
The function g(x) is f(x) = mx + c
Find two coordinates from the graph of g(x).
= (-3, 2) and (5, 4)
m = (4 - 2) / (5 +3) = 2/8 = 1/4
Now,
2 = 1/4 x (-3) + c
2 = -3/4 + c
c = 2 + 3/4
c = 11/4
g(x) = (1/4)x + 11/4 _______(2)
Now,
From (1) and (2)
(f/g)(x)
= f(x)/g(x)
= ((1/7)x + 22/7) / ((1/4)x + 11/4)
The domain of f(x) and g(x) will include the domain of both f(x) and g(x).
So,
x = -1 to x = 6 and x = -3 to x = 5
This can be written as,
[-3, 6]
Thus,
The domain of (f/g)(x) is [-3, 6].
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0 Arrange the numbers shown in descending order.
9
13
312' 4'
312%,
4.2 x 10-2,
TT
The bot won’t input the equation right so can anyone pls help me
312%, 312' 4', 13, 9, 4.2 x 10-2. This is a decending order.
What is meant by decending?
Moving downward, tiny, or least from the top, big, or large, is referred to as descending.Descending order refers to arranging items, such as numbers, amounts, lengths, etc., from a higher value to a lower one. The diminishing order is an alternative name for it.In general, the phrases Ascending and Descending denote the smallest to largest, 0 to 9, and/or A to Z, and the largest to smallest, 9 to 0, and/or Z to A, respectively.In contrast to ascending order, descending order lists character data types from lowercase z to uppercase A and numerical data types from highest to lowest.The order of date and datetime data is from most recent to earliest, and the order of interval data is from longest to shortest duration of time.To learn more about decending refer to
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Give the slope-intercept form of the equation of the line that is perpendicular to 2x – 4y = 17 and contains p(–8, –2).a.y 2 = −2(x 8)c.y = −2x − 12b.y = −2x − 18d.y 8 = −2(x 2) please select the best answer from the choices providedgive the slope-intercept form of the equation of the line that is perpendicular to 2x – 4y = 17 and contains p(–8, –2). a.y 2 = −2(x 8)c.y = −2x − 12b.y = −2x − 18d.y 8 = −2(x 2) please select the best answer from the choices provided brainly
The equation of the line that is perpendicular to 2x – 4y = 17 and contains p(-8, -2) is y = -2x - 18.
Therefore, the answer is b) y = −2x − 18.
The slope-intercept form of a line's equation is y = mx + b, where m is the slope of the line and b is the y-intercept, which is the point where the line crosses the y-axis.
To find the equation of a line that is perpendicular to another line, we can use the fact that the slopes of perpendicular lines are negative reciprocals of each other. This means that if the slope of one line is m, the slope of a line perpendicular to it is -1/m.
The equation of the line that is perpendicular to 2x – 4y = 17 and contains p(-8, -2) can be found by first finding the slope of the line 2x – 4y = 17. We can do this by rearranging the equation to the slope-intercept form:
2x – 4y = 17
-4y = -2x + 17
y = (1/2)x - (17/4)
The slope of the line 2x – 4y = 17 is (1/2). Therefore, the slope of a line perpendicular to it is -2.
To find the equation of the line that is perpendicular to 2x – 4y = 17 and contains p(-8, -2), we can use the slope-intercept form of a line's equation and plug in the slope (-2) and the coordinates of the point p(-8, -2):
y = -2x + b
-2 = -2×(-8) + b
b = -18
--The question is incomplete, the complete question is given below--
"Give the slope-intercept form of the equation of the line that is perpendicular to 2x – 4y = 17 and contains p(–8, –2).
a. y = −2x + 8
b. y = −2x − 18
c. y = −2x − 12
d. y = −2x + 2"
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The equation of the line that is perpendicular to 2x – 4y = 17 and contains p(-8, -2) is y = -2x – 18
y = mx + b is the slope intercept form of a line’s equation. Here, m = slope of the line and b = y-intercept.
The equation of the line that is perpendicular to 2x – 4y = 17 and contains p(-8, -2) can be found by first finding the slope of the line 2x – 4y = 17. We can do this by rearranging the equation to the slope-intercept form:
2x – 4y = 17
-4y = -2x + 17
y = (1/2)x - (17/4)
The slope of the line is 1/2. Hence m = ½
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The triangle to the right has an area of 35 square units. What would be the area of a new triangle if the scale factor were 2? Show your work with one equation
The area of triangle will be 140 square units.
What is scale factor?The scale factor of a shape refers to the amount by which it is increased or shrunk. It is applied when a 2D shape, such as a circle, triangle, square, or rectangle, needs to be made larger.
K is the scaling factor for x in the equation y = Kx. This expression can also be visualised in terms of proportionality:
y ∝ x
K can therefore be regarded as a proportionality constant in this context.
Given the area of triangle = 35 sq. units
and scale factor is 2
The base times the height of a triangle equals its area. Triangle ABC's base and height each double when a scale factor of 2 with centre A is used, increasing the area by a factor of 4 as a result.
area of triangle = 1/2bh
where b = base and h = height
given 1/2bh = 35
when scale factor is 2
new base = 2b
new height = 2h
area will be 1/2(2b)(2h) = 4/2bh
so 1/2bh = 35
4/2bh = 35 x 4 = 140 square units.
Hence the area is 140 square units.
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1. A car has a mass of 1200 kg.
The Change
in Momentum
a. If the braking force for a car is 10,000 N, calculate the impulse if
the brake is applied for 1.2 s.
b. What is the change in velocity of the car over this 1.2 s time
interval?
(a) The impulse of the car of mass 1200 kg is 12000 Ns.
(b) The change in velocity of the car is 10 m/s.
What is an impulse?Impulse is the product of force and time.
(a) To calculate the impulse of the force, we use the formula below
Formula:
I = Ft................. Equation 1Where:
I = ImpulseF = Forcet = TimeFrom the question,
Given:
F = 10000 Nt = 1.2 sSubstitute these values into equation 1
I = 1.2×10000 = 12000 Ns(b) To calculate the change in velocity of the car, we use the formula below
ΔV = I/m.................... Equation 2Where:
ΔV = Change in velocitym = Mass of the carFrom the question,
Given:
m = 1200 kgI = 12000 NsSubstitute these values into equation 2
ΔV = 12000/1200ΔV = 10 m/sHence the change in velocity of the car is 10 m/s.
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Solve for y: 2x + y = 7 and -2x + 3y = -3
Answer:
[tex]y=1[/tex]
Step-by-step explanation:
Adding the equations yields [tex]4y=4[/tex]. Therefore, [tex]y=1[/tex].
