someone please help me in this question i need step by step sol with explaination

a. The area on [0, 10] is that of a trapezoid with bases 5 and 15 and height 10, so

[tex]\displaystyle \int_0^{10} f(x) \, dx = \frac{5+15}2\cdot10 = \boxed{100}[/tex]

b. By linearity of the definite integral, we have

[tex]\displaystyle \int_0^{25} f(x)\,dx = \int_0^{10} f(x)\,dx + \int_{10}^{25} f(x)\,dx[/tex]

and the area on [10, 25] is another trapezoid with bases 15 and 7.5 and height 15, so that

[tex]\displaystyle \int_{10}^{25} f(x)\,dx = \frac{15+7.5}2\cdot15 = 168.75[/tex]

Then the total area on [0, 25] is

[tex]\displaystyle \int_0^{25} f(x)\,dx = \boxed{268.75}[/tex]

c. The area on [25, 35] is that of a triangle with base 10 and height 15. However, [tex]f(x)<0[/tex] on this interval, so we multiply this area by -1 to get

[tex]\displaystyle \int_{25}^{35} f(x)\,dx = -\frac{10\cdot15}2 = \boxed{-75}[/tex]

d. The area on [15, 25] is the same as the area on [25, 35] because it's another triangle with the same dimensions. But the area on [15, 25] lies above the horizontal axis, so

[tex]\displaystyle \int_{15}^{25} f(x)\,dx = \int_{15}^{25} f(x)\,dx + \int_{25}^{35} f(x)\,dx = \boxed{0}[/tex]

e. The plot of [tex]|f(x)|[/tex] lies above the horizontal axis. We know the area on [15, 25] is the same as the area on [25, 35], but now both areas are positive, so

[tex]\displaystyle \int_{15}^{35} |f(x)| \, dx = \int_{15}^{25} f(x)\,dx - \int_{25}^{35} f(x)\,dx = 2 \int_{15}^{25} f(x)\,dx = \boxed{150}[/tex]

f. Changing the order of the limits in the integral swaps the sign of the overall integral, so

[tex]\displaystyle \int_{10}^0 f(x)\,dx = -\int_0^{10} f(x)\,dx = \boxed{-100}[/tex]

Considering the definition of mass volume percent, the percent composition of lactose in skim milk is 28%.

The concentration of solutions is the amount of solute contained in a given amount of solvent or solution. In other words, the relationship between the amount of solute and the amount of solvent is called concentration.

Mass volume percent (% m/V) is a measure of concentration that indicates the number of grams of solute in each 100 mL of solution.

In other words, mass-volume percent is an intensive property that is defined as the mass of solute (in grams) that there are in 100 mL of solution and it is calculated by applying the following equation:

[tex]Mass volume percent=\frac{mass solute (grams)}{volume solution (mL)}x100[/tex]

This is, mass volume percent is defined as the ratio of the mass of solute that is present in a solution, relative to the volume of the solution, as a whole.

In this case, you know:

Replacing in the definition of mass volume percent:

[tex]Mass volume percent=\frac{0.28 grams}{1 mL}x100[/tex]

Solving:

mass volume percent= 28 %

Finally, the percent composition of lactose in skim milk is 28%.

Learn more about mass volume percent:

brainly.com/question/19038237

brainly.com/question/14707974

#SPJ1

Answer:

v = -3w

Step-by-step explanation:

water level/volume = -3 x weeks

v = -3w

Answer:

4x³ + 4x² + 5

Step-by-step explanation:

3x³ - 2x + 8 + 2x² + 5x + x³ + 2x² - 3x - 3.

4x³ - 2x + 8 + 2x² + 5x + 2x² - 3x - 3

4x³ + 4x² - 2x + 8 + 5x - 3x - 3

4x³ + 4x² + 8 - 3

4x³ + 4x² + 5

The missing angles are listed below:

sin 27.818° = 21 / 45

tan 26.565° = 8 / 16

cos 57.607° = 15 / 28

tan 38.956° = 38 / 47

sin 44.901° = 12 / 17

cos 52.398° = 36 / 59

tan 19.477° = 29 / 82

sin 16.601° = 8 / 28

tan 10.008° = 9 / 51

cos 36.870° = 16 / 20

sin 35.538° = 60 / 84

cos 53.576° = 19 / 32

tan 40.101° = 64 / 76

cos 39.571 = 37 / 48

cos 69.605° = 23 / 66

In this question we must find the measure of the angle associated to the rational numbers seen in the statement. There are two methods to estimate such measures: (i) Drawing an equivalent right triangle and estimate the measure of the angle by definition of trigonometric functions, (ii) Using inverse trigonometric functions and numerical methods since they are trascendent variables.

Herein we decided to use the second method by reasons of rapidness and effectivity:

sin 27.818° = 21 / 45

tan 26.565° = 8 / 16

cos 57.607° = 15 / 28

tan 38.956° = 38 / 47

sin 44.901° = 12 / 17

cos 52.398° = 36 / 59

tan 19.477° = 29 / 82

sin 16.601° = 8 / 28

tan 10.008° = 9 / 51

cos 36.870° = 16 / 20

sin 35.538° = 60 / 84

cos 53.576° = 19 / 32

tan 40.101° = 64 / 76

cos 39.571 = 37 / 48

cos 69.605° = 23 / 66

To learn more on inverse trigonometric functions: https://brainly.com/question/1143565

#SPJ1

Answer:

x+(x+5)=28

Step-by-step explanation:

girls(g)should be equal to x

boys(b) will therefore be x+5

x+(x+5)=28

Answer:

16 packages

Step-by-step explanation:

5 2/5 + 2 1/4  Use the common denominator of 20

5 8/20 + 2 5/20  

7  13/20

I know that I will need 14 packages for the 7 pounds.  For the fraction part, 10/20 would be half, so I would need to buy a half pound for that, but I need 13/20 which would be more than a half pound, so I will need to buy 2 more pounds for the fraction part.

14 + 2 = 16

Answer:

x ≤ −8

Step-by-step explanation:

Let's solve your inequality step-by-step.

3 - 3x/4 ≥ 9

Step 1: Simplify both sides of the inequality.

-3/4x + 3 ≥ 9

Step 2: Subtract 3 from both sides.

-3/4x + 3 - 3 ≥ 9 − 3

-3/4x ≥ 6

Step 3: Multiply both sides by 4/(-3).

(4/-3) * (-3/4x) ≥ (4/-3) * (6)

x ≤ −8

Answer:

x ≤ −8

Answer: 4

Step-by-step explanation:

x - (1/3)x - (1/6)x = 2

(6x - 2x - x)/6 = 2

3x/6 = 2

x=4

The distance that he has traveled exists 73km 500m.

Distance exists described as the amount of space between two items or the condition of existing far apart. The distance of an object can be described as the complete path traveled by an object.

Given: A motorist travels from town A to town B, which exists 84km apart. He has finished 7/8 of his journey.

To estimate the distance that he has traveled

He covered 7/8 out of 84 km

So, 7/8 × 84 = 73.5 km

The distance he has traveled = 73 km 500 m

Therefore, the distance that he has traveled exists 73km 500m.

To learn more about distance refer to:

https://brainly.com/question/26550516

#SPJ9

Answer:

A child ticket costs $16.50 and an adult ticket costs $25.45.

It is found that the child ticket costs $16.50 and an adult ticket costs $25.45.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Given that  4 children and 2 adults are $116.90. For 6 children and 3 adults, the admission is $175.35.

Assuming a different price for children and adults,

Let the children are x and the adult is y.

Therefore,

4x + 2y = 116.90

6x + 3y = 175.35

Hence, the child ticket costs $16.50 and an adult ticket costs $25.45.

To learn more about the unitary method, please visit the link given below;

https://brainly.com/question/23423168

#SPJ2

Answer:

Step-by-step explanation:

answer: 47

add the heights then divide by 5

Answer:

45:315

Step-by-step explanation:

Add up the ratio to get the total ratio.

1+7=8

Divide the 360 by the total ratio.

360÷8=45

The number 45 tells you how many times to multiply both sets of the ratio to get a total of 360.

1×45=45

7×45=315

so,

45:315

Hope this helped. Comment below if you need more assistance! :)

Based on the given parameters, the length of c is 8.0 units

The given parameters are

Angle c = 76 degrees

Side a = 20

Side b = 13

The length of c is then calculated using the following law of sines

c^2 = a^2 + b^2 - 2absin(C)

Substitute the known values in the above equation

So, we have

c^2 = 20^2 + 13^2 - 2 * 20 * 13 * sin(76)

Express 20^2 as 400

c^2 = 400 + 13^2 - 2 * 20 * 13 * sin(76)

Express 13^2 as 169

c^2 = 400 + 169 - 2 * 20 * 13 * sin(76)

Evaluate the product and sin(76)

c^2 = 400 + 169 - 520 * 0.9703

Evaluate the product

c^2 = 400 + 169 - 504.55

Evaluate the exponents

c^2 = 400 + 169 - 504.55

So, we have

c^2 = 64.45

Evaluate the square root

c = 8.0

Hence, the length of c is 8.0 units

Read more about law of sines at:

https://brainly.com/question/16955971

#SPJ1

Answer:

The percentage of the students that can swim is 75%

The percentage of students that can't swim is 25%

Step-by-step explanation:

100÷40=2.5

2.5×30=75

The percentage of the students that can swim is 75%

100-75=25

The percentage of students that can't swim is 25%

Please comment below if you don't understand or want me to clarify. :)

The conversion of "z = 2(cos(π/3))" in polar form to rectangular form is equal to 1.

A polar coordinate can be defined as a two-dimensional coordinate system, wherein each point on a plane is typically determined by a distance (r) from the pole (origin) and an angle (θ) from a reference direction (polar axis).

In geometry, the relationship between a polar coordinate (r, θ) and a rectangular coordinate (x, y) based on the conversion rules is given by the following polar functions:

a = rcos(θ)    ....equation 1.

b = rsin(θ)     ....equation 2.

Where:

Note: The exact value of cos(π/3) is equal to ½.

Substituting the given parameters into the formula, we have;

z = 2(½)

z = 2/2

z = 1.

In conclusion, we can logically deduce that the conversion of "z = 2(cos(π/3))" in polar form to rectangular form is equal to 1.

Read more on polar coordinates here: https://brainly.com/question/2193539

#SPJ1

Complete Question:

Convert z = 2(cos(π/3)) in rectangular form

The amount that Karsten's estate should pay his younger daughter each month over 20 years so that the accumulated present value will be equal to $50,000 is $358.22.

The monthly payments out of the present value of $50,000 can be computed using an online finance calculator.

The periodic payment represents the equal amount that can be paid to the daughter monthly so that it equals the PV of $50,000 of the estate share.

N (# of periods) = 240

I/Y (Interest per year) = 6%

PV (Present Value) = $50,000

FV (Future Value) = $0

Results:

Monthly Payment = $358.22

Sum of all periodic payments = $85,971.73 ($358.22 x 2400

Total Interest = $35,971.73

Thus, Karsten's younger daughter can be paid $358.22 to equal the accumulated present value of $50,000.

Learn more about periodic payments at https://brainly.com/question/13098072 and https://brainly.com/question/13031679

#SPJ1

Step-by-step explanation:

Let's solve for the first one,

[tex]R.H.S. = Cos²A + cos²A.cot²A[/tex]

Step 1- Take Cos²A common,

[tex] = Cos²A( 1+ cot²A)[/tex]

[tex] \small \sf \: Now \: we \: know \: that \\ \small (1 + Cot^{2} \theta = Cosec^{2} \theta)[/tex]

Step 2 - Substituting above value in step 1,

[tex] = Cos^{2} A(Cosec^2A)[/tex]

[tex] \small \sf \: We \: know \: that \: Cosec \theta= \frac{1}{Sin \theta} [/tex]

Step 3 - Substitute Cosec²A with 1/Sin²A

[tex] = \frac{Cos^2A}{Sin^2A} [/tex]

[tex] \small \sf \: Now \: the \: basic \: trigonometric \: function \: is \\ \small \frac{Cos\theta}{Sin \theta} = Cot\theta[/tex]

Step 4 - Replacing the product of step 3 with above function,

[tex] = {Cot}^{2} A[/tex]

Hence proved,

[tex]R.H.S = L.H.S[/tex]

﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌

Now let's prove the second relation,

[tex](1-sin²A)(1+cot²A)=cot²A[/tex]

Let's solve for R.H.S.,

[tex]R.H.S.= (1-sin^{2} A)(1+cot^{2} A)[/tex]

As I told above,

[tex]\small(1+cot^{2} \theta) = cosec^{2} \theta[/tex]

Another important relation is,

[tex] \small sin^2\theta + cos^2\theta= 1 \: or \: \\ \small cos^2\theta = 1 - sin^2\theta[/tex]

Replacing both the above brackets with this relation we get,

[tex] = Cos^2A \cdot Cosec^2A [/tex]

Now follow the step 3 and step 4 of first question and you will get,

[tex]R.H.S. = L.H.S.[/tex]

﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌

Some important trigonometric relations that you must learn,

[tex]Sin^2\theta + Cos^2\theta = 1 \\ 1 + Cot^2\theta = Cosec^2\theta \\ 1+Tan^2\theta = Sec^2\theta[/tex]

[tex] \small\sf \: Thanks \: for \: joining \: brainly \: community! [/tex]

Answer:

40 liters of 30% solution.

20 liters of 60% solution.

Step-by-step explanation:

Let x = amount of 30% solution.

Let y = amount of 60% solution.

Equation of amounts of solutions.

x + y = 60

Equation of amounts of alcohol in the solutions.

0.3x + 0.6y = 0.4 × 60

x = 60 - y

0.3(60 - y) + 0.6y = 24

18 - 0.3y + 0.6y = 24

0.3y = 6

y = 20

x + y = 60

x + 20 = 60

x = 40

Answer:

40 liters of 30% solution.

20 liters of 60% solution.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

The number of liters of the 30% solution and the number of liters of the 60% solution to mix to make the 40% solution is 40 liters and 20 liters.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 7 is an equation.

We have,

Let 30% solution = m

Let 60% solution = n

Now,

A scientist needs 60 liters of a 40% solution of alcohol.

He has a 30% solution and a 60% solution available.

This means,

m + n = 60 _____(1)

30% of m + 60% of n = 40% of 60

0.30m + 0.60n = 0.40 x 60

0.30m + 0.60n = 24 ____(2)

From (1) and (2) we get,

m + n = 60

m = 60 - n _____(3)

Putting (3) in (2) we get,

0.30m + 0.60n = 24

0.30(60 - n) + 0.60n = 24

18 - 0.30n + 0.60n = 24

18 + 0.30n = 24

0.30n = 24 - 18

0.30n = 6

n = 6/0.30

n = 20

Putting n = 20 in (3) we get,

m = 60 - 20

m = 40

Now,

The number of liters of the 30% solution is 40.

The number of liters of the 60% solution is 20.

Thus,

The number of liters of the 30% solution and the number of liters of the 60% solution to mix to make the 40% solution is 40 liters and 20 liters.

Learn more about equations here:

https://brainly.com/question/17194269

#SPJ6

Hey there!

8!
= 8(7)(6)(5)(4)(3)(2)(1)

= 56(6)(5)(4)(3)(2)(1)

= 336(5)(4)(3)(2)(1)

= 1,680(4)(3)(2)(1)

= 6,720(3)(2)(1)

= 20,160(2)(1)

= 40,320(1)

= 40,320

Therefore, your answer should be:

40,320

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

The dimensions of the pool would give a quadratic equation x² + 28x - 770 = 0

For the pool, we have that;

Let the width = x feet

Length = (x+8) feet

The pool alongside the walkway gives;

Width = x + 5 + 5 = (x + 10) feet

Length = x + 8 + 5 + 5 = (x + 18) feet

Total area of the pool with walkway = 950 square feet

Note that formula for area is given as

Area = length * width = 950

Equate the length and width

(x+18)  × (x + 10) = 950

Using the  FOIL method, we have;

(x × x )+ (x × 10) + (18 × x) + (18 × 10) = 950

x² + 10x + 18x + 180 -950 = 0  

collect like terms

x² + 28x - 770 = 0

Thus, the dimensions of the pool would give a quadratic equation x² + 28x - 770 = 0

Learn more about area of a rectangle here:

https://brainly.com/question/14137384

#SPJ1

The answer to these questions are

How to find the point where the distribution lies at 99.7%. The data is 3 sd from mean

Hence

39 - 3*(5) = 24

39 + 3*(5) = 54

The widget lies between 24 and 54

c. P(29.0 < x < 54.0)

= 29 - 39 / 5 and 54 - 39 / 5

= -2.0 and 3.0

We have to find P(Z < 3.0) - P(Z < -2.0)

= 0.9987 - 0.0228

= 97.59%

d. x = 44

= 44 - 39/ 5

= 1

We are to find P(z < 1.0)  = 84.13%

Read more on standard deviation here: https://brainly.com/question/475676

#SPJ1

Answer:

x ≤ 4

Step-by-step explanation:

the solid dot at 4 indicates that x can equal 4

the arrow points to the left indicating values less than 4 , then

x ≤ 4

Answer:

8

Step-by-step explanation:

let the number=x

8(x-2)=16(x-5)

divide by 8

x-2=2(x-5)

x-2=2x-10

2x-x=-2+10

x=8

Considering the given function, we have that:

The function is:

f(x) = 4 - 2x + 6x².

When x = a, we have that:

f(a) = 4 - 2a + 6a².

When x = a + h, we have that:

f(a + h) = 4 - 2(a + h) + 6(a + h)² = 6a² + 12ah + 6h² - 2a - 2h + 4.

For the fraction, we have that:

[f(a + h) - f(a)]/h = [6a² + 12ah + 6h² - 2a - 2h + 4 - 4 + 2a - 6a²]/h = [12ah + 6h² - 2h]/h = h(12a + 6h - 2)/h

Hence:

[f(a + h) - f(a)]/h = 12a + 6h - 2.

More can be learned about functions at https://brainly.com/question/25537936

#SPJ1

Answer:

7×10³+3×10²+4×10¹+2×10 or 7.342×10³

Answer:

4*1/1000+6*100+8*10+5*1

Step-by-step explanation:

No, we are unable to produce an endless amount in a given space. because the function is at its highest point when x is equal to 70, and its highest point of output is 2300.

We are unable to produce zero items in one day.

Maximum available output = 2300

The graph of the function is quadratic (parabolic), and the point at which it reaches its highest value, denoted by the vertex x = 70,

Generally, The greatest level of production that a firm is able to maintain in order to provide its goods or services is referred to as its capacity. Capacity may refer to a manufacturing process, the distribution of human resources, technological thresholds, or any one of a number of other related ideas, depending on the sort of company being discussed.

In conclusion, No, we are unable to produce an endless amount in a given space. because the function is at its highest point when x is equal to 70, and its highest point of output is 2300.

We are unable to produce zero items in one day.

Maximum available output = 2300

The graph of the function is quadratic (parabolic), and the point at which it reaches its highest value, denoted by the vertex x = 70,

Read more about Capacity

https://brainly.com/question/15158174

#SPJ1

Answer:

- [tex]\sqrt{2}[/tex]

Step-by-step explanation:

cos90° - 2sin45° + 2tan180°

= 0 - ( 2 × [tex]\frac{\sqrt{2} }{2}[/tex] ) + 2(0)

= 0 - [tex]\sqrt{2}[/tex] + 0

= - [tex]\sqrt{2}[/tex]

Answer:

5

Step-by-step explanation:

Gradient (slope) of the curve can be found by deriving a curve function.

In this scenario, the given function is a polynomial function which we can use Power Rules to derive it.

Power Rules

[tex]\displaystyle{y=ax^n \to y' = nax^{n-1}}[/tex]

Thus, using the power rules, we will have:

[tex]\displaystyle{y'=3x^2-4x+5}[/tex]

Note that deriving a constant will always result in 0.

Then the problem gives us that we want to find the slope or gradient at where the curve crosses y-axis.

The curve crosses y-axis at x = 0 only. Therefore, we substitute x = 0 in a derived function.

[tex]\displaystyle{y'(0) = 3(0)^2-4(0)+5}\\\\\displaystyle{y'(0) = 5}[/tex]

Therefore, the slope at the point where a curve crosses y-axis will be 5.