what if i wanted to know the instantaneous rate of change at t=2 seconds; how could u go abt determining this value. it says to make an approximation

The amount that she make in a workweek if she sold $4,800 worth of merchandise will be $605.

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.

Here, Mae Ling earns a weekly salary of $365 plus a 5.0% commission on sales at a gift shop.

The amount that she make in a workweek if she sold $4,800 worth of merchandise will be:

= $365 + (5% × $4800)

= $605

The amount is $605.

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SOLUTION

We want to solve the equation

cross multiplying, we have

Hence the answer is x = 2, the first option

Answer:

5,386,830

Step-by-step explanation:

So, on solving the provided question we can say that the rate of change of the volume with respect to radius = \(1770 = 4/3 \pi r^3S = 4 \pi r^2\) \(dS/dt = 8 \pi r dr/dt\)

The length of a circle or sphere, in more contemporary use, is the same as its radius in classical geometry, which is one of the line segments from its center to its circumference. The Latin word radius, which also refers to the spokes of a wagon wheel, gave rise to the term. The distance a circle's center is from any point on its perimeter is its radius. Usually, "R" or "r" is used to indicate it. A radius is a line segment that has one endpoint in the center and one on the circumference of a circle. Circular diameter equals radius The diameter of a circle is the segment that traverses its center and has ends that are on the circle.

Taking the derivative of the volume formula

\(DV/dt = 4\pi r*2 dr/dt\\5471 = 4 \pi r*2 dr/dt\)

This equation  r and dr/dt

We can solve for r...

sphere is 1770 cubic inches

\(1770 = 4/3 \pi r^3S = 4 \pi r^2dS/dt = 8 \pi r dr/dt\)

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Answer:

( a + 5 ) ( a + 6 )

? maybe

Step-by-step explanation:

I really don't know how to explain

On solving the provided question, we can say that integral  =  \(\int\limits^a_b \,\)t√9 + 16t² dt  =   \(\int\limits^a_b \,\)√9 + 16t² d (9 + 16t²)

In mathematics, integrals translate integers into functions that express concepts like displacement, area, and volume that result from the combination of little facts. Integral discovery is a process that is referred to as integration. Integrals are mathematical constructs that, in calculus, have the same meaning as areas or generalized versions of areas. The main goal of calculus is to work with derivatives and integrals. Primitives and inverse derivatives are other terms for integral. Integration is essentially utilized to determine the area of 2D space and determine the volume of 3D objects. As a result, calculating an integral of a function with respect to x entails calculating the area between the curve and the x-axis.

integral

Curves, x = t³ or,

 = 3t²

y = t⁴ or,

  = 4t³  

Now, the line integral along C will be:

→  =  \(\int\limits^a_b \,\)√(3t²)² + (4t³)² dt

            =  \(\int\limits^a_b \,\)√9t⁴ + 16t⁶ dt

            =  \(\int\limits^a_b \,\)√9 + 16t² dt

           =  \(\int\limits^a_b \,\)√9 + 16t² dt

            =  \(\int\limits^a_b \,\)t√9 + 16t² dt

            =   \(\int\limits^a_b \,\)√9 + 16t² d (9 + 16t²)

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Use the edges of the triangles to determine which ones are closest together for the smallest of furthest apart for the largest.

1. Smallest = b

Largest = c

2. Smallest = f

Largest = g

Answer:

= 59.36

Step-by-step explanation:

S = 207

so, tan(16) = H/S

tan(16°) = 0.28674539

so H = tan(16) * S = 0.28674539 * 207 = 59.35629573

so the tree high = 59.36 foot

Ryan will use the multiplication with 0.621 to find the speed in mile per hour.

To find the speed in mile per hour we will convert the unit from mentioned unit to desired unit. As per the known fact, 1 kilometre is 0.621 mile.

Keeping the value of mile in the place of kilometres, we will calculate the speed in miles per hour.

Speed = (100 × 0.621)/1

Performing multiplication in numerator on Right Hand Side of the equation to find the value of speed in miles per hour

Speed = 62.1 miles per hour

Thus, Ryan should multiply the value with 0.621 miles per hour and hence, the value of speed in miles per hour is 62.1.

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Answer:

156 pieces of art is in one classroom alone

Step-by-step explanation:

take 641+490=1,131

then times 1,131 times 8 which gives u 9,048

then divide 9,048 by 58 for the classrooms which gives u 156

Answer:

7a - 4ab + 3b

Step-by-step explanation:

5a - 3ab + 6b - (ab - 2a + 3b)

=5a - 3ab + 6b - ab + 2a - 3b

=7a - 4ab + 3b

Answer:

\(m\angle A\approx112.72^\circ\)

Step-by-step explanation:

Since only side lengths are given and no angles, we are forced to use the Law of Cosines. The equation to find angle A is \(\displaystyle \cos(A)=\frac{b^2+c^2-a^2}{2bc}\):

\(\displaystyle \cos(A)=\frac{b^2+c^2-a^2}{2bc}\\\\\cos(A)=\frac{10.1^2+24.3^2-29.7^2}{2(10.1)(24.3)}\\\\A=\cos^{-1}\biggr(\frac{10.1^2+24.3^2-29.7^2}{2(10.1)(24.3)}\biggr)\\\\A\approx112.72^\circ\)

b=24

Main concepts

Concept 1. Congruent Triangles

Concept 2. Hypotenuse-Leg Congruence

Concept 3. Congruent Triangles implies congruent parts

Concept 4. Solving a one-variable equation

Concept 1. Congruent Triangles

For two triangles to be congruent, the three angles of one triangle must be congruent to the three angles of the other triangle, AND the three side lengths of one triangle must be congruent to the three side lengths of the other triangle.

Fortunately, through various proofs about different types of triangles, it isn't necessary to prove all six of those things.

The 5 cases of triangle Congruence are

Concept 2. Hypotenuse-Leg Congruence

Proving they are both right triangles, and that HL congruence can be used

In this situation, we are given that Angle UVT is a right angle.  Under the assumption that US is a line that contains V, then Angle UVT and Angle SVT form a linear pair and are supplementary (their measures add to 180 degrees).

So, Angle SVT is also a right angle.  This means that both Triangle UVT and Triangle SVT are Right Triangles, since they are each a triangle with a right angle.

To prove HL congruence, we need to prove that one leg of each triangle is congruent to the other, and that the hypotenuse of each triangle is congruent to the other.

Proving Hypotenuse congruence

Note that the Hypotenuse (side across from the right angle) of Triangle UVT is side UT with measure 67 units.

The Hypotenuse of Triangle SVT is side ST, also with measure 67 units.

So the Hypotenuses are congruent.

Proving Leg congruence

Note that one leg of the triangles is shared as a common side:  line segment VT is common to both triangles.  Even though we don't know the actual length of VT, the length of VT for the first triangle is the same as the length of VT for the second triangle.

The official reason that VT is congruent to VT is because of the "Reflexive property".  

Since the Hypotenuses and one leg from each triangle are congruent, the two triangle are congruent.  Specifically, Triangle UVT is congruent to Triangle SVT.

Concept 3. Congruent Triangles implies congruent parts

Even though we didn't prove all 6 congruences, we did prove that the triangles ARE congruent.  Therefore, all 6 congruences are true.  This means that any other pair of corresponding parts is also congruent.

Specifically, we're interested in the last pair of sides, because they have measurements that contain "b" the value we're trying to solve for.

Side UV is congruent to Side SV because Corresponding parts of Congruent triangles are Congruent.

This means that their lengths are equal:

\(Length_{UV}=Length_{SV}\)

\(b+24=2b\)

Concept 4. Solving a one-variable equation

For any equation in math where there is only one item that is unknown, (even if it shows up multiple times in the equation), there are two main steps:

Step 1.  Get the variable to show up exactly once

Step 2.  Isolate the variable

Step 1.  Get the variable to show up exactly once

Since we know that in the very end, we want b=__, we know that the b will appear only once (and thus only on one side of the equation, not both), and will be by itself.

In practice, sometimes there are special tricks that have to be employed to make this step happen.  Generally, this means simplify each side of the equation, and try to group like terms together.

For this equation, observe that b appears twice: once on the left side of the equation, and once on the right side of the equation.  

At some point, we'll need to get the "b"s on the same side of the equation, and hopefully combine like terms into a single term with b.

To get the "b"s on one side, we'll subtract b from both sides:

\((b+24)-b=(2b)-b\)

On the left, the positive b and negative b cancel completely, leaving just 24.  On the right, the 2b subtracted by 1b leaves just 1b, or more simply, b.

\(24=b\)

Step 2.  Isolate the variable

While trying to get the variable to show up exactly once, we also incidentally isolated the variable, as the like terms combined.

So, b=24.

Answer:  Theorem 4 says that the columns of B do NOT span R4. Further, using Theorem 4, since 4(c) is false, 4(a) is false as well, so Bx = y does not have a solution for each y in R4.

Step-by-step explanation:

Yes, the column b span r4. Yes, the equation has a solution for each y in r4.

Matrix is defined as a set of numbers consisting of rows and columns elements.

It consists of rows and columns.

The dimensions of the matrix are determined by m×n.

Given matrix,

\(\begin{bmatrix} &1 &3 &-2 &2\\ &0 &1 &1 &-5\\ &1 &2 &-3 &7\\ &-2 &-8 &2 &-1\\\end{bmatrix}\)

R3  → R1

R3→R4+2R1

\(\begin{bmatrix} &1 &3 &-2 &2 \\ &0 &1 &1 &-5 \\ &0 &-1 &1 &5 \\ &0 &-2 &-2 &3\\\end{bmatrix}\)

R3→R3+R2

R4→R4+2R2

\(\begin{bmatrix} &1 &3 &-2 &2 \\ &0 &1 &1 &-5 \\ &0 &-0 &2 &0 \\ &0 &-0 &0 &7\\\end{bmatrix}\)

This is the row echelon form of B. It has four independent columns and the dimension of r4 is 4.

column of B spans r4.

Row of matrix = 4

No of columns of matrix = No of rows of the matrix.

and the columns of B span r4.

thus we can conclude that the columns of b span r4 and the equation

bx =d y have a solution for each y in r4.

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Answer:

32%

Step-by-step explanation:

percent increase = $330-$250 =80

80/250 ×100 = 32%

The Percentage of increase in the price of the car will be; 32.0%.

A percentage is a minimum number or ratio that is measured by a fraction of 100. Suppose the value of which a thing is expressed in percentage is "a'. Suppose the percent that considered thing is of "a" is b%. Then the percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts.

Thus, the thing in number is;  \(\dfrac{a}{100} \times b\)

Given information are;

The price of car last month is: $250

The price of the car this month is: $330

Then, the  Increase in price = $330 - $250 = $80

Therefore, the Percentage increase = (Increase in price/Cost price last month) × 100

= $80 /$250 × 100

= 0.32 × 100

= 32.0%

Hence, The Percentage of increase in the price of the car will be; 32.0%.

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Answer: We can start by using the information given to find the total bill amount.

If the water/sewer/garbage portion of the bill is 72% of the total bill, then the remaining 28% of the bill must be for other utilities. We can use a proportion to set up the equation:

72/100 = 94.41/x

where x is the total bill amount.

We can cross-multiply and solve for x:

72x = 100 * 94.41

x = (100 * 94.41) / 72

x = 123.84

To the nearest cent, the total amount of the utility bill was $123.84.

Step-by-step explanation:

The sampling method used by the researchers from the Department of Education in order to obtain a sample representative of all students is stratified random sampling.

A stratified random sample is a probability sampling method that involves dividing the population into non-overlapping groups, known as strata. The strata are formed based on some variable of interest that is thought to be related to the study's research question, such as age, gender, or geographic location. Within each stratum, a random sample is then selected. By using a stratified random sampling technique.

This method also provides greater precision and reduces the sampling error by taking into account the variability within each stratum separately .The use of stratified random sampling has ensured that the sample taken by the researchers from the Department of Education is more representative of all students. They divided college students into the four classes (freshman, sophomore, junior, and senior) and then took a random sample of students from each class. Hence, the sampling method used by the researchers is stratified random sampling.

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Answer:

Therefore, the 12th term of the geometric sequence 5, 15, 45, ... is 885735.

Step-by-step explanation:

The 12th term of the geometric sequence 5, 15, 45, ... can be found using the general formula for the nth term of a geometric sequence:

an = a1 * r^(n-1)

where:

a1 is the first term of the sequence,

r is the common ratio, and

n is the position of the term that you're trying to find.

In this case,

a1 = 5

r = 15/5 = 3

n = 12

so:

a12 = 5 * 3^(12-1) = 5 * 3^11 = 5 * 177147 = 885735

Therefore, the 12th term of the geometric sequence 5, 15, 45, ... is 885735.

Answer:

12th term = 885735

Step-by-step explanation:

Meaning: A geometric sequence is an ordered set of numbers that progresses by multiplying or dividing each term by the same number.

5 x 3 = 15

15 x 3 = 45

The number we multiply the terms by in this sequence is 3.

4th term = 45 x 3 = 135

5th term = 135 x 3 = 405

6th term = 405 x 3 = 1215

7th term = 1215 x 3 = 3645

8th term = 3645 x 3 = 10935

9th term = 10935 x 3 = 32805

10th term = 32805 x 3 = 98415

11th term = 98415 x 3 = 295245

12th term = 295245 x 3 = 885735

5, 15, 45, 135, 405, 1215, 3645, 10935, 32805, 98415, 295245, 885735

hope this helps :)

Answer:

il say its B

Step-by-step explanation:

Answer:

zfsdfsdf

Step-by-step explanation:

dfsdfsf

Answer: y = 5x + 26

Step-by-step explanation:

To find the equation of a line that is perpendicular to the given line y = -1/5x + 1 and passes through the point (-5, 1), we need to determine the slope of the perpendicular line. The given line has a slope of -1/5. Perpendicular lines have slopes that are negative reciprocals of each other. So, the slope of the perpendicular line will be the negative reciprocal of -1/5, which is 5/1 or simply 5. Now, we have the slope (m = 5) and a point (-5, 1) that the perpendicular line passes through.

We can use the point-slope form of a linear equation to find the equation of the line:

y - y1 = m(x - x1)

Substituting the values, we get:

y - 1 = 5(x - (-5))

Simplifying further:

y - 1 = 5(x + 5)

Expanding the brackets:

y - 1 = 5x + 25

Rearranging the equation to the slope-intercept form (y = mx + b):

y = 5x + 26

Therefore, the equation of the perpendicular line that passes through the point (-5, 1) is y = 5x + 26.

A two-sample t-test is the inferential statistical test that would be best suitable to this situation.

The area of mathematics known as probability deals with numerical representations of how likely it is for an event to happen or for a claim to be true. A number between 0 and 1 is the probability of an occurrence, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

A t-test is a method for evaluating hypotheses that involve examining the means of one or more populations. A t-test can be used to determine if one group deviates from a predetermined value, whether two groups diverge from one another (an independent two-sample t-test), or whether paired measurements reveal a statistically significant difference.

According to the question, we can say

With 12 technicians each, there are two techniques. To put it another way, the sample sizes are really small. Aside from that, there is no connection between the two samples. A two-sample t-test should be used as a result.

Thus, a two-sample t-test is the inferential statistical test that would be best suitable to this situation.

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Answer:

-7/9

Step-by-step explanation:

= (-4/9) x (7/4)

= -4/9 x 7/4

= -28/36 (simplifying gives -7/9)

The area of the region enclosed by the graphs of y=x^3+8 and y=x+8 is 24. This is found by calculating the area under each graph and subtracting the area of the overlap and the area outside the region.

The area of the region can be calculated by finding the area under the two graphs, subtracting the area of the overlap and then subtracting the area outside the region bounded by the two graphs.

First, find the area under the graph of y=x^3+8 and above the x-axis. This can be calculated using the definite integral

∫ y dx from 0 to 8, which is equal to 8^4/4+8 = 288.

Next, find the area under the graph of y=x+8 and above the x-axis. This can be calculated using the definite integral

∫ y dx from 0 to 8, which is equal to 8^2/2+8 = 72.

The area of the overlap between the two graphs is the area of the region below both graphs and above the x-axis. This can be calculated using the definite integral

∫ y dx from 0 to 8, which is equal to 8^3/3+8 = 168.

Finally, subtract the area outside the region bounded by the two graphs, which is the area below the line y=x+8 and above the x-axis. This can be calculated using the definite integral

∫ y dx from 0 to 8, which is equal to 8^2/2 = 32.

Therefore, the area of the region in the first quadrant that is enclosed by the graphs of y=x^3+8 and y=x+8 is 288 - 72 - 168 + 32 = 24.

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Answer:

Step-by-step explanation:

thats it

Therefore , the solution of the given problem of unitary method  comes out to be total cost for to make 15 jars is  12,386.25 euroes.

After calculating the size of a small slice, multiply the quantity by two to complete a task using the unitary technique. Simply expression, the unit variable technique works to separate a coded item from a certain group or collection of groups. For instance, 40 pens would cost Rs. 400 (or 400 pounds, $1.01). It's possible that one country will have total control over the method employed to do this. Almost every living creature has a distinctive quality.

Here,

Given :

cost of blackberry = 88 euroes

cost of sugar = 650 euroes

Jam bottles costs =87.75

total cost for to make 15 jars is

=> 15 * (87.75+650+88)

=> 15 * 825.75

=>  12,386.25 euroes

Therefore , the solution of the given problem of unitary method  comes out to be total cost for to make 15 jars is  12,386.25 euroes.

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The third approximate solution is x = (869/1024, -707/1024, 867/1024, 0). The Gauss-Seidel iterative method can be used to find the third approximate solution to 2x₁ + x₂2x3 = 1, 2x₁3x₂ + x₃ = 0, and x₁x₂ + 2x₃ = 2. We will begin with x = (0, 0, 0, 0)*.*

The asterisk indicates that x is the starting point for the iterative method.

The process is as follows: x₁^(k+1) = (1 - x₂^k2x₃^k)/2,x₂^(k+1) = (-3x₁^(k+1) + x₃^k)/3, and x₃^(k+1) = (2 - x₁^(k+1)x₂^(k+1))/2.

We'll first look for x₁^(1), which is (1 - 0(0))/2 = 1/2.

Next, we'll look for x₂^(1), which is (-3(1/2) + 0)/3 = -1/2.

Finally, we'll look for x₃^(1), which is (2 - 1/2(-1/2))/2 = 9/8.

Thus, the first iterate is x^(1) = (1/2, -1/2, 9/8, 0).

Next, we'll look for x₁^(2), which is (1 - (-1/2)(9/8))/2 = 25/32.

Next, we'll look for x₂^(2), which is (-3(25/32) + 9/8)/3 = -31/32.

Finally, we'll look for x₃^(2), which is (2 - (25/32)(-1/2))/2 = 54/64 = 27/32.

Thus, the second iterate is x^(2) = (25/32, -31/32, 27/32, 0).

Now we'll look for x₁^(3), which is (1 - (-31/32)(27/32))/2 = 869/1024.

Next, we'll look for x₂^(3), which is (-3(869/1024) + 27/32)/3 = -707/1024.

Finally, we'll look for x₃^(3), which is (2 - (25/32)(-31/32))/2 = 867/1024.

Thus, the third iterate is x^(3) = (869/1024, -707/1024, 867/1024, 0).

Therefore, the third approximate solution is x = (869/1024, -707/1024, 867/1024, 0).

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Answer:

Step-by-step explanation

b/sin(102°) =27/sin(28°)
⇔b ≈56,2548

Using sine rule of triangles, the length of the hypotenuse is 56.3 rounded to the nearest tenth

Sine rule of triangles is related using the formula :

Inputting values into the relation

b/sin(102) = 27/sin(28)

cross multiply

b * sin(28) = 27 * sin(102)

divide both sides by sin(28)

b = 26.40998/sin(28)

b = 56.254

Therefore, the length of b in the figure given is 56.3

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Swimmers jump from a railroad bridge to river. Using equations of motion, the height of the bridge is calculated to be 17.8m, their speed when hitting the water is 18.6m/s. If the bridge were twice as high, the drop time would be 4.18s.

We can use the equations of motion to solve this problem. Let h be the height of the bridge, g be the acceleration due to gravity, and t be the time taken by the swimmers to fall from the bridge to the water. We can assume that the swimmers start from rest.

(a) Using the equation h = (1/2)gt^2, we can find the height of the bridge:

h = (1/2)gt^2 = (1/2)(9.81 m/s^2)(1.9 s)^2

h = 17.8 m

Therefore, the height of the bridge is 17.8 meters.

(b) Using the equation v = gt, we can find the speed of the swimmers just as they hit the water:

v = gt = (9.81 m/s^2)(1.9 s)

v = 18.6 m/s

Therefore, the swimmers were moving at a speed of 18.6 m/s when they hit the water.

(c) If the bridge were twice as high, the time taken by the swimmers to fall would be:

t' = sqrt(2h/g) = sqrt(2(2h)/g) = sqrt(4h/g) = 2sqrt(h/g)

Using this equation, we can find the new drop time:

t' = 2sqrt(h/g) = 2sqrt(17.8 m / 9.81 m/s^2)

t' = 4.18 s

Therefore, if the bridge were twice as high, the swimmers would take 4.18 seconds to fall from the bridge to the water.

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Answer:

\(83f+49.8b \leq 560\)

Step-by-step explanation:

Given that the cost of 1 floor ticket = $ 83.

Cost for f floor tickets = $ 83f

Ticket for 1 balcony ticket = 60% of floor ticket.

= 0.60 x 83 = $49.8

Cost for b balcony tickets = $ 49.8b.

Total cost for f floor tickets and b balcony tickets, C= 83f+49.8b.

As the person can spend a maximum of $560,

So, \(C\leq 560\)

\(\Rightarrow 83f+49.8b \leq 560\).

Hence, the required inequality is \(83f+49.8b \leq 560\).

Answer:

RM=12m

Step-by-step explanation:

You can set up a proportion of 9/15 on one side and RM/20 on the other. you would then cross multiply and solve for RM