df(0) = [0 0 0; 0 0 0]
d(g o f)(0) = [0 0; 0 0].
We have f: R^3 → R^2 and g: R^2 → R^2.
Using the chain rule, we have:
d(g o f)(0) = dg(f(0)) ◦ df(0)
First, let's find df(0):
df(0) = [∂f₁/∂x₁(0) ∂f₁/∂x₂(0) ∂f₁/∂x₃(0); ∂f₂/∂x₁(0) ∂f₂/∂x₂(0) ∂f₂/∂x₃(0)]
We know that f(0) = (0, 0, 0) and f(0) = (1, 2), so:
f₁(0) = 1, f₂(0) = 2
∂f₁/∂x₁(0) = ∂f₁/∂x₂(0) = ∂f₁/∂x₃(0) = 0
∂f₂/∂x₁(0) = ∂f₂/∂x₂(0) = ∂f₂/∂x₃(0) = 0
Next, let's find dg(f(0)):
dg(x, y) = [∂g₁/∂x ∂g₁/∂y; ∂g₂/∂x ∂g₂/∂y]
dg(1, 2) = [2 1; 6 3]
Finally, we can find d(g o f)(0):
d(g o f)(0) = dg(f(0)) ◦ df(0) = [2 1; 6 3] ◦ [0 0 0; 0 0 0] = [0 0; 0 0]
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The derivative of the composition g o f at (0) given by applying the chain rule is [2 4; 3 1].
The problem requires finding the derivative of the composition g o f at (0).
Using the chain rule, we can express this derivative as the product of the Jacobian matrix of g with respect to its inputs and the Jacobian matrix of f with respect to its inputs, evaluated at (0).
The Jacobian matrix of g is given by:
[ 2y 1 2x ]
[ 3y 3x ]
If T : Rn → R
m is a linear transformation, then T(0) = 0.
Evaluating this at f(0) = (1, 2) gives:
[ 4 2 ]
[ 6 3 ]
The Jacobian matrix of f is given by:
[ 1 0 0 ]
[ 0 1 0 ]
Evaluating this at 0 gives:
[ 1 0 0 ]
[ 0 1 0 ]
Multiplying these two matrices, we get:
[ 2 4 ]
[ 3 1 ]
Therefore, d(g o /)(0) = [2 4; 3 1].
In summary, we used the chain rule to find the derivative of the composition g o f at (0), which is given by the product of the Jacobian matrix of g and the Jacobian matrix of f, both evaluated at the same point.
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Can someone please solve this
Answer:
20
Step-by-step explanation:
a c will have the same angle as b d
A sequence consists of the positive odd integers 1, 3, 5,. What's the sum of the first 12 terms of the
sequence?
hi
we have an aroithmetic serie of first term 1 and pace 2
so sum of 12 first terms, namming 1 as S1 and 12th term as S12
S12 = 1 + 2*11 = 23
formula of summ : number of term * ( final term + first term) / 2
So sum of terms from S1 +S12 = 12 ( S12 +S1 ) / 2 = 12 * ( 23+1) /2
12* 12= 144
-
Owen has enough materials to build up to 10 birdhouses in shop class. each birdhouse needs 12 square feet of wood. the function w(b) = 12b represents the total amount of wood that owen would need to build b birdhouses. what domain and range are reasonable for the function?
Domain of the function is [tex]0\leq b\leq 10[/tex] and range of the function is [tex]0\leq W\leq 120[/tex].
What is domain and range of a function?The range of values that we are permitted to enter into our function is known as the domain of a function.
A function's range is the collection of values it can take as input.
Each birdhouse uses 12 square feet of wood. Owen has enough to build 10 birdhouses, so he has 120 square feet of wood.
The function has an input of the number of birdhouses, b, and W as an output of the amount of wood needed. b is domain, and W is the range. The domain is 0 to 10 and range is 0 to 120.
Therefore, the domain of the function is [tex]0\leq b\leq 10[/tex] and the range of the function is [tex]0\leq W\leq 120[/tex].
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14. The following three lines intersect to form
a triangle.
y = x + 1
2x + y = 4
x + y = 5
a) Find the coordinates of each vertex.
b) Is this a right triangle? Explain how
you know.
The coordinates of the vertices are (-1, 6), (1, 2) and (2, 3)
The coordinates of each vertex?The functions are given as:
y = x + 1
2x + y = 4
x + y = 5
Next, we plot the graph of the lines (see attachment)
From the attached graph, the coordinates of the vertices are (-1, 6), (1, 2) and (2, 3)
The type of triangleRewrite the equations in slope intercept form
y = x + 1 ⇒ Slope = 1
y = -2x + 4 ⇒ Slope = -2
y = -x + 5 ⇒ Slope = -1
The equations y = x + 1 and y = -x + 5 have their slopes to be opposite reciprocals
This means that the lines are perpendicular (they form a right angle)
Hence, the triangle is a right triangle
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What is the best example of elasticity demand in the context university of rwanda
Answer:
Step-by-step explanation:
Elasticity Demand
The flexibility of interest is a significant minor departure from the idea of interest. Request can be delegated as versatile, inelastic, or unitary.Flexible interest is one in which the adjustment of the amount requested because of an adjustment of cost is huge. An inelastic interest is one in which the adjustment of the amount requested because of an adjustment of cost is little.The equation for processing versatility of interest is:(Q1 - Q2)/(Q1 + Q2)
(P1 - P2)/(P1 + P2)
In the event that the recipe makes an outright worth more prominent than 1, the interest is flexible. At the end of the day, the amount changes quicker than the cost. On the off chance that the worth is under 1, the request is inelastic. All in all, the amount changes more slowly than the cost. In the event that the number is equivalent to 1, the flexibility of interest is unitary. All in all, the amount changes at a similar rate as the cost.An illustration of items with a flexible interest is purchaser durables. These are things that are bought inconsistently, similar to a clothes washer or an auto, and can be deferred assuming the cost rises. For instance, vehicle refunds have been extremely fruitful in expanding car deals by diminishing costs.#SPJ10
A tub contains red, blue, green and white counters. 40% of the counters are red or white. The ratio of blue to green counters is 3:2.The ratio of red to white counters is 3: 5. What is the probability of picking a red or green counter?
The probability of randomly getting a red or green counter is:
P = 39%/100% = 0.39
How to get the probability?We know that 40% of the counters are red or white. Then 60% of the counters are blue or green.
Now we know that the ratio of red to white is 3:5
Then the percentage of red counters is:
(3/8)*40% = 15%
And the ratio of blue to green is 3:2
Then the percentage of red counters is:
(2/5)*60% = 24%
Then the percentage of counters that are either red or green is:
15% + 24% = 39%
Then the probability of randomly getting a red or green counter is:
P = 39%/100% = 0.39
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Suppose the length of AC in the triangle below is 15cm. The measure of angle A is 60, sim 60 ≈ 0.866, cos 60 ≈ 0.5 and tan 60 ≈1.73. Determine the length of AB
Answer: Option (4)
Step-by-step explanation:
From the diagram, we know that
[tex]\sin 60^{\circ}=\frac{BC}{15}\\\\\cos 60^{\circ}=\frac{AB}{15}[/tex]
This means we can eliminate options 1 and 2.
Now, if we multiply both sides by 15, we get
[tex]15\cos 60^{\circ}=7.5[/tex].
This gives us Option (4).
Answer:
Step-by-step explanation:
already
The population parameter value and the point estimate differ because a sample is not a census of the entire population, but it is being used to develop the _____. Group of answer choices population parameter point estimate population mean standard error
The population parameter value and the point estimate differ because a sample is not census of the entire population, but it is being used to develop the point estimate.
According to the question,
The population parameter value and the point estimate differ because a sample is not census of the entire population, but it is being used to develop the point estimate.
The sample proportion p, is a point estimate of the population proportion.
Hence, the correct answer is point estimate. Thus, the population parameter value and the point estimate differ because a sample is not census of the entire population, but it is being used to develop the point estimate.
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The coordinates of three vertices of a rectangle are (3,7), (-3,5), and (0,-4). What are the coordinates of the fourth vertex
The coordinates of the fourth vertex are (6, -2)
What are the coordinates of the fourth vertex?The coordinates of three vertices of a rectangle are given as: (3,7), (-3,5), and (0,-4).
Calculate the slope of the first two coordinates using
m = (y2 - y1)/(x2 - x1)^2
Substitute the known values in the above equation
d = (7 - 5)/(3 + 3)
Let the fourth coordinate be (x, y)
Calculate the slope of the other two coordinates using
m = (y2 - y1)/(x2 - x1)^2
Substitute the known values in the above equation
m = (y + 4)/x
Equate both slope equations
(y + 4)/x = (7 - 5)/(3 + 3)
Simplify the fraction
(y + 4)/x = 1/3
Cross multiply
x = 3y + 12
Let y = -2
So, we have:
x = 3 *-2 + 12
Evaluate
x = 6
Substitute x = 6 and y = -2 in (x, y)
This gives (6, -2)
Hence, the coordinates of the fourth vertex are (6, -2)
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A submarine model starts at 8 m above the bottom of the pool. It gradually goes down at a rate of 1\2 m\s
a) Graph the relation on the grid provided. Label the axes.
b) Write an equation to represent the relation.
Pleasee
The equation that represents the relation is y = 8 - 0.5x
How to graph the relation?The given parameters are:
Start = 8m
Rate = 1/2 m/s
The linear equation that represents the submarine movement is:
y = Start - Rate * x
This gives
y = 8 - 1/2 * x
Evaluate
y = 8 - 0.5x
Hence, the equation that represents the relation is y = 8 - 0.5x
See attachment for the graph
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there are four elevators in a building. Each elevator makes three stops, which do not have to be on consecutive floors or include the ground floor. For any two floors, there is at least one elevator that stops on both floors. What is the maximum number of floors that this building can have
The maximum number of floors that this building can have is 6
How to determine the maximum number of floors?The given parameters are:
Elevators = 4
Stops = 3
At least one elevator stops on 2 floors
The maximum number of floors is calculated as:
Maximum = Elevators * Stops/2
This gives
Maximum = 4 * 3/2
Evaluate
Maximum = 6
Hence, the maximum number of floors that this building can have is 6
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1. Determine the most precise name for the quadrilateral.
rhumbos
it is the most precise name because it gives more information about the quadrilateral
30 points please help i dont understand
Answer:
502.4 ft²
Step-by-step explanation:
To find the individual area of the ring, you first need to find the area of the white circle. Then, you need to find the area of the circle and the ring (which can be found by adding the width of the ring to the radius of the circle). Finally, you can find the area of the ring through subtraction.
Area (White Circle)
radius = 1/2 diameter
radius = (1/2) x 36 ft
radius = 18 ft
Area = πr²
Area = π(18 ft)²
Area = π(324 ft²)
Area = 1017.36 ft²
Area (White Circle + Ring)
radius = 1/2 diameter + width of ring
radius = (1/2 x 36 ft) + 4 ft
radius = 22 ft
Area = πr²
Area = π(22 ft)²
Area = π(484 ft²)
Area = 1519.76 ft²
Area (Ring)
Area (Ring) = Area (White Circle + Ring) - Area (White Circle)
Area (Ring) = 1519.76 ft² - 1017.36 ft²
Area (Ring) = 502.4 ft²
Solve the equation. Give your simplified answer as an improper fraction.
 -(x-1)+10 = -3(x-2)
A statistical process control monitoring system samples the inside diameter of ball bearing every hour. Measurements were taken every hour for 25 hours. The target thickness, T, is the average.
The standard deviation is approximately 0.01307. See the explanation below.
What is standard deviation?The square root of the variance is used to calculate the standard deviation, a statistic that expresses how widely distributed a dataset is in relation to its mean.
By calculating the departure of each data point from the mean, the standard deviation may be determined as the square root of variance.
How do we calculate the standard deviation?Step 1: First, lets calculate the variance.
The formula for variance is:
[tex]\sigma^2 = \frac{\sum_{i=1}^{n}(x_i - \mu)^2} {n-1}[/tex]
To get the variance ( s2 ) we must first get the mean. Our mean is 0.99892.
We subtract each value by the mean and square the difference.
(0.978-0.99892)² = 0.0004376464
(0.982-0.99892)² = 0.0002862864
(0.983-0.99892)² = 0.0002534464
(0.984-0.99892)² = 0.0002226064
(0.987-0.99892)² = 0.0001420864
(0.988-0.99892)² = 0.0001192464
(0.989-0.99892)² = 9.84064e-05
(0.99-0.99892)² = 7.95664e-05
(0.992-0.99892)² = 4.78864e-05
(0.992-0.99892)² = 4.78864e-05
(0.993-0.99892)² = 3.50464e-05
(0.994-0.99892)² = 2.42064e-05
(0.996-0.99892)² = 8.5264e-06
(0.997-0.99892)² = 3.6864e-06
(1-0.99892)² = 1.1664e-06
(1.001-0.99892)² = 4.3264e-06
(1.006-0.99892)² = 5.01264e-05
(1.007-0.99892)² = 6.52864e-05
(1.011-0.99892)² = 0.0001459264
(1.015-0.99892)² = 0.0002585664
(1.015-0.99892)² = 0.0002585664
(1.015-0.99892)² = 0.0002585664
(1.018-0.99892)² = 0.0003640464
(1.02-0.99892)² = 0.0004443664
(1.02-0.99892)² = 0.0004443664.
Step 2: Add all these numbers above
0.0004376464+0.0002862864+0.0002534464+0.0002226064+0.0001420864+0.0001192464+9.84064e-05+7.95664e-05+4.78864e-05+4.78864e-05+3.50464e-05+2.42064e-05+8.5264e-06+3.6864e-06+1.1664e-06+4.3264e-06+5.01264e-05+6.52864e-05+0.0001459264+0.0002585664+0.0002585664+0.0002585664+0.0003640464+0.0004443664+0.0004443664
=0.00410184
Step 3: Now we divide the sum by how many numbers there are. In this case we have 25.
We'll call this number n.
So n=25
For a sample (use 0.00410184 divided by (n-1) ):
So s2 =0.00410184 divided by 24
s2 = 0.00017091
Step 4 - Solve for Standard deviation:
The standard deviation is the square root of the variance. Our variance is 0.00017091.
So we only apply a square root on the variance.
= √ 0.00017091
s = 0.0130732551
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Full Question:
A statistical process control monitoring system samples the inside diameter of ball bearing every hour. Measurements were taken every hour for 25 hours. The target thickness, T, is the average.
0.992 1.015 0.988 0.996 1.015 1.000 0.989 0.994 1.018 0.997 1.020 1.007 1.006 0.982 1.001 0.992 1.020 0.993 0.978 0.984 0.990 1.015 0.983 1.011 0.987
What is the population standard deviation, σ?
Solve √5r - 9 - 3 = √r +4-2
Answer:
r = 5
Step-by-step explanation:
Solving radical equations often results in extraneous solutions. These can be avoided by using a graphing calculator for the solution.
GraphThe attached shows that the value of r that makes both sides of the equation have the same value is r = 5.
Check:
√(5·5 -9) -3 = √(5 +4) -2 ⇒ 4 -3 = 3 -2 . . . true
Analytical solutionSolution of an equation like this is typically done by isolating the radical expressions, then squaring the equation.
We can add 3, square the equation, then isolate the radical and square again:
[tex]\displaysyle \sqrt{5r-9}-3=\sqrt{r+4}-2\\\\\sqrt{5r-9}=\sqrt{r+4}+1\qquad\text{add 3}\\\\5r-9=(r+4)+2\sqrt{r+4}+1\qquad\text{square both sides}\\\\(4r-14)^2=4(r+4)\qquad\text{subtract $(r+5)$ and square again}\\\\16r^2-116r+180=0\qquad\text{rewrite in standard form}\\\\4(4r -9)(r -5) = 0\qquad\text{factor}\\\\r=\{\dfrac{9}{4},\ 5\}\qquad\text{solutions to the factored form}[/tex]
Trying these values in the original equation, we get ...
√((5(9/4) -9) -3 = √(9/4 +4) -2 ⇒ 1.5 -3 = 2.5 -2 . . . . . false
√(5(5) -9) -3 = √(5 +4) -2 ⇒ 4 -3 = 3 -2 . . . . . true
The solution is r = 5.
A rectangular block of candy 10 inches by 10 inches by 5 inches is coated on all faces with a very thin layer of chocolate. The block of candy is then cut into cubes measuring 1 inch by 1 inch by 1 inch. What percent of the cubes have no chocolate on them
38.2% of the cubes are without chocolate coated.
CalculationGiven that,
The length ,l= 10 inch
The width ,b=10 inch
The height, h=5 inch
We know that the lateral surface area of the cuboid or rectangular block,
SA= 2(lh+lb+hb)
⇒ SA = 2( 10*5 +10*10+5*10)
⇒ SA =2*200=400 [tex]inch^{3}[/tex]
The volume of the cuboid,V= 10*10*5 =500 [tex]inch^{3}[/tex]
The block of candy is then cut into another small cube 1 inch per side.
length,l=1 inch
width, b=1 inch
height,h=1 inch
So, the surface area of each small cube ,sa= 2(1+1+1) = 6 [tex]inch^{3}[/tex]
Volume of each candy,v= 1*1*1=1 [tex]inch^{3}[/tex]
So, the total number of candy= 500/1 =500 nos.
There is chocolate on each and every piece on the exterior inch. But those who are totally within do not.
A cube measuring 8 inches by 8 inches by 3 inches makes up the inside.
So, the total no of boxes that have no chocolate =8*8*3=192 boxes
So, the percentage = 192*100/500= 38.2 %
Therefore, it is concluded that 38.2% of cubes are without chocolate.
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For limit of startfraction x squared minus 4 x minus 12 over x minus 2 endfraction as x approaches 2 minus = and limit of startfraction x squared minus 4 x minus 12 over x minus 2 endfraction as x approaches 2 plus= . these limits indicate there is an asymptote of .
The given limit indicates that there is a vertical asymptote at x = 2.
What are the vertical asymptotes of a function f(x)?The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator. When x tends to these values laterally, the limit of f(x) goes to infinity.
In this problem, the function is:
[tex]f(x) = \frac{x^2 - 4x - 12}{x - 2}[/tex]
The vertical asymptote is:
x - 2 = 0 -> x = 2.
Hence:
[tex]\lim_{x \rightarrow 2^+} f(x)[/tex] and [tex]\lim_{x \rightarrow 2^-} f(x)[/tex] are either positive infinity or negative infinity.
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What is the simplified base for the function f(x) = 2rootindex 3 startroot 27 endroot superscript 2 x?
Applying exponential properties, the simplified base for the function is given as follows:
[tex]f(x) = 2(3)^{2x}[/tex]
What is the function?The function is represented by the following definition:
[tex]f(x) = 2\sqrt[3]{27^{2x}}[/tex]
As an exponent, the function is given by:
[tex]f(x) = 2(27)^{\frac{2x}{3}}[/tex]
27 can be simplified as follows:
27 = 3 x 3 x 3 = 3³
Hence:
[tex]f(x) = 2(3^3)^{\frac{2x}{3}}[/tex]
Then, the 3 at the exponent multiplies 2x and can be simplified with the 3 of the root, hence:
[tex]f(x) = 2(3)^{\frac{3 \times 2x}{3}} = 2(3)^{2x}[/tex]
Hence the simplified base for the function is given as follows:
[tex]f(x) = 2(3)^{2x}[/tex]
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What is the inverse of the equation y=x^2+9,x>0
The inverse of the equation y = x^2 + 9 is [tex]x = \sqrt{y - 9[/tex]
How to determine the equation inverse?The equation is given as:
y = x^2 + 9
Subtract 9 from both sides
x^2 = y - 9
Take the square root of both sides
[tex]x = \sqrt{y - 9[/tex]
Hence, the inverse of the equation y = x^2 + 9 is [tex]x = \sqrt{y - 9[/tex]
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On a coordinate plane, kite U V W X with diagonals is shown. Point U is at (negative 2, 5), point V is at (5, 4), point W is at (8, negative 5), and point X is at (negative 1, negative 2).
Prove that the diagonals of kite UVWX are perpendicular.
Step 1: Determine the slope of XV.
The slope of XV is
.
Step 2: Determine the slope of UW.
The slope of UW is
.
Step 3: The slopes of the diagonals are
.
The diagonals of kite UVWX are
.
The information about the coordinate plane shows that the slope of XV is 1.
How to illustrate the information?From the information, the slopes of the diagonals are negative reciprocals. Therefore, the slope of UW is -1 and the slope of XV is 1.
The diagonals of kite UVWX are perpendicular.
It should be noted that negative reciprocals in a kite create a perpendicular bisector. So the two lines share a midpoint so they are perpendicular.
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Answer:
Step-by-step explanation:
The slope of XV is
1
The slope of UW is
–1
The slopes of the diagonals are
negative reciprocals
The diagonals of kite UVWX are
perpendicular
.
Chandra invests $75 every month at 4.8% compounded monthly for 8 years. What is the total amount of Chandra's investments after 8 years?
The total amount of Chandra's investments after 8 years exists $110.03.
How to estimate the compound interest?The formula for calculating the compound interest exists defined as;
[tex]$A = P(1+r/n)^{nt[/tex]
where, P exists the amount invested = $75
r exists the rate. = 0.048
t exists the time = 8 years
n = 12 (monthly)
The formula for calculating the compound interest,
[tex]$A = P(1+r/n)^{nt[/tex]
Substitute the value in the above equation, and we get
[tex]$A = 75(1+0.048/12)^{96[/tex]
A = 75(1.467)
A = 110.03
Hence the total amount of Chandra's investments after 8 years exists $110.03
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With a perfectly balanced roulette wheel, in the long run, red numbers should turn up 18 times in 38. To test its wheel, one casino records the results of 3,800 plays, finding 1,890 red numbers. Is that too many reds
It is not too many reds, but it is also not a perfectly balanced roulette wheel.
How to find whether the roulette wheel is balanced or not?It is given that the red numbers should come up 18 times when the roulette wheel is played 38 times.
Therefore, the ratio of red numbers to the total number of plays is = 18:38
It is also given that a casino tests the wheel with 3800 plays and noticed that the red numbers came up 1890 times.
The ratio is given as 1890:3800.
We have to simplify this.
1890/3800 = 18.9/38
If the roulette wheel was perfect, it should've been 18:38.
Therefore, we can say that the roulette wheel is not perfectly balanced.
Therefore we have found that it is not too many reds, but it is also not a perfectly balanced roulette wheel.
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Find the missing side length of the triangle.
Answer:
a = 1.5 in.
Step-by-step explanation:
Use the Pythagoras Theorem:
1.7^2 = a^2 + 0.8^2
a^2 = 1.7^2 - 0.8^2
= 2.25
a = 1.5 in.
Answer:
a = 1.5 in.
Explanation:
Using Pythagoras theorem:
a² + b² = c²
insert values
a² + 0.8² = 1.7²
a² = 1.7² - 0.8²
a² = 2.89 - 0.64
a² = 2.25
a = √2.25
a = 1.5
Page 3. Calculate the semi inter quartile range and its coefficients from the table Marks (below) 20 30 40 50 60
No of students 5 12 27 40 50
SOMEONE HELP ME
1. The semi inter quartile range is 10
2. The coefficient of quartile deviation is 0.2
1. How to determine the semi inter quartile rangeMark: 20, 30, 40, 50, 60Freq: 5, 12, 27, 40, 50Com. freq: 5, 17, 44, 84, 134Semi inter quartile range =?1st quartile (Q₁) = (134 + 1) / 4 = 33.75th = 40
3rd quartile (Q₃) = 3 (134 + 1) / 4 = 3 × 33.75 = 101.25th = 60
Semi inter quartile range = (Q₃ - Q₁) / 2
Semi inter quartile range = (60 - 40) / 2
Semi inter quartile range = 10
2. How to determine the coefficient1st quartile (Q₁) = 403rd quartile (Q₃) = 60Coefficient of quartile deviation =?Coefficient of quartile deviation = (Q₃ - Q₁) / (Q₃ + Q₁)
Coefficient of quartile deviation = (60 - 40) / (60 + 40)
Coefficient of quartile deviation = 0.2
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Simplify the expression. (5k2)3
Answer:
25k x 3
Step-by-step explanation:
URGENT!!! PLEASE HELP!!!
Find the value of x that makes the parallelogram a square. Show your steps.
(13x + 5.5)°
You will be awarded 5 points for the correct answer and 5 points for the supporting
work.
Answer: 6.5
Step-by-step explanation:
Since all squares are rhombi, and diagonals of a rhombus intersect at right angles, this means that
[tex]13x+5.5=90\\\\13x=84.5\\\\x=6.5[/tex]
the price for 5/6 l of liquid x is $80. what is the price per litre of liquid x
Answer:
$96.
Step-by-step explanation:
5/6 costs 80
Multiply both parts by 6/5:
5/6 * 6/5 ( = 1 ) costs 80 * 6/5
= 16 * 6
= $96.
Maria buys some soft drinks for her friends. she buys a total of 13 drinks for a total of $32. if medium drinks, m, cost $3 and small, s, drinks $2, write a system of equations which can be used to find how many small drinks and medium drinks she bought.
The total number of small drinks 's' bought by Maria is 7.
The total number of medium drinks 'm' drinks bought by Maria is 6.
What is system of linear equations?A collection of one or more linear equations containing the same variables is known as a system of linear equations (or linear system).
Formation of the linear equation for the drinks bought by Maria:
The total number of drinks bought by the Maria is 13.
Lets say 'm' represents the number of medium drink.
's' represents the number of small drink.
Total drinks comprises of medium drinks and small drinks.
Thus,
s + m = 13, is the first linear equation.
Now medium drinks cost $3.
Total cost for purchasing medium drinks = (price of one medium drink)×(total number of medium drinks)
Total price for medium drinks = 3×m
Similarly,
Total cost for purchasing small drinks = (price of one small drink)×(total number of small drinks)
Total price for small drinks = 2×s
Total cost = total cost of medium drink + total cost of small drink
32 = 3×m + 2×s, is second linear equation.
From equation first substitute the value of 'm' in second equation to fine the total number of drink.
32 = 3×(13 - s) + 2×s
32 = 39 - 3s + 22
s = 7
Put s = 7 in first equation and calculate 'm'.
m = 13 -7
m = 6
Therefore, The total number of small drinks 's' bought by Maria is 7.
The total number of medium drinks 'm' drinks bought by Maria is 6.
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What is the type? f(x)=-1/5x³-5+10x²