Which value makes the equation 4× = 48 true?

Answer:

109.17030567685

Step-by-step explanation:

41.68x+2000=60x

-41.68x -41.68x

2000=18.32x

/18.32 /18.32

109.17030567685=x

Answer:

[tex]\displaystyle \int\limits^1_4 {\frac{\cos x}{1 + \frac{e}{x}}} \, dx \approx \boxed{0.862854}[/tex]

General Formulas and Concepts:

Calculus

Differentiation

Derivative Property [Addition/Subtraction]:
[tex]\displaystyle (u + v)' = u' + v'[/tex]

Derivative Rule [Basic Power Rule]:

Integration

Integration Rule [Fundamental Theorem of Calculus 1]:
[tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]

Integration Property [Multiplied Constant]:
[tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]

Integration Property [Addition/Subtraction]:
[tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]

Integration Methods: U-Substitution and U-Solve

Special Integrals:

Step-by-step explanation:

*Note:
The problem is too big to fit all work. I will assume that you know how to do basic calculus.

Step 1: Define

Identify given.

[tex]\displaystyle \int\limits^1_4 {\frac{\cos x}{1 + \frac{e}{x}}} \, dx[/tex]

Step 2: Integrate Pt. 1

Step 3: Integrate Pt. 2

Identify variables for u-substitution.

Step 4: Integrate Pt. 3

Step 5: Integrate Pt. 4

Identify variables for u-substitution for the 1st integral.

Use another variable besides u to avoid confusion with earlier substitutions.

Step 6: Integrate Pt. 5

Solve the 1st integral using basic integration techniques listed under "Calculus":
[tex]\displaystyle \begin{aligned}\int\limits^{x = 1}_{x = 4} {\cos (u - e)} \, du & = \int\limits^{x = 1}_{x = 4} {\cos v} \, dv \\& = \sin v \bigg| \limits^{x = 1}_{x = 4} \\& = \sin (u - e) \bigg| \limits^{x = 1}_{x = 4} \\& = \sin (x) \bigg| \limits^{x = 1}_{x = 4} \\& = \sin 1 - \sin 4\end{aligned}[/tex]

Step 7: Integrate Pt. 6

To solve the 2nd integral, we use the same methods as "Step 6":

[tex]\displaystyle\begin{aligned}\int\limits^{x = 1}_{x = 4} {\frac{\cos (u - e)}{u}} \, du & = \int\limits^{x = 1}_{x = 4} {\frac{\sin e \sin u + \cos e \cos u}{u}} \, du \\& = \sin e \int\limits^{x = 1}_{x = 4} {\frac{\sin u}{u}} \, du + \cos e \int\limits^{x = 1}_{x = 4} {\frac{\cos u}{u}} \, du \\& = \sin (e) \text{Si} (u) \bigg| \limits^{x = 1}_{x = 4} + \cos (e) \text{Ci} (u) \bigg| \limits^{x = 1}_{x = 4} \\\end{aligned}[/tex]

[tex]\displaystyle\begin{aligned}\int\limits^{x = 1}_{x = 4} {\frac{\cos (u - e)}{u}} \, du & = \sin (e) \text{Si} (x + e) \bigg| \limits^{x = 1}_{x = 4} + \cos (e) \text{Ci} (x + e) \bigg| \limits^{x = 1}_{x = 4} \\& = \bigg[ \sin (e) \text{Si} (1 + e) - \sin (e) \text{Si} (4 + e) \bigg] + \bigg[ \cos (e) \text{Ci} (1 + e) - \cos (e) \text{Ci} (4 + e) \bigg] \\\end{aligned}[/tex]

Step 8: Integrate Pt. 7

Combine our 2 integral values to obtain a final answer:

[tex]\displaystyle \int\limits^1_4 {\frac{\cos x}{1 + \frac{e}{x}}} \, dx & = \int\limits^{x = 1}_{x = 4} {\cos ( u - e)} \, du - e \int\limits^{x = 1}_{x = 4} {\frac{\cos (u - e)}{u}} \, du \\\begin{aligned}& = \sin 1 - \sin 4 - e \bigg[ \sin (e) \text{Si} (1 + e) - \sin (e) \text{Si} (4 + e) + \cos (e) \text{Ci} (1 + e) - \cos (e) \text{Ci} (4 + e) \bigg] \\& \approx \boxed{0862854} \\\end{aligned}[/tex]

∴ we have evaluated the given special definite integral.

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Topic: Calculus

Answer:

1. 71^3 = 71 * 71 * 71 = 357,911

2. 52^4 = 52 * 52 * 52* 52 = 7,311,616

3. 99^5 = 99 * 99 * 99 * 99* 99 = 9,509,900,499

4. 78^4 = 78 * 78* 78* 78 = 37,015,056

5. 8^2 = 8 * 8 = 64

6. 80^5 = 80 * 80 * 80 * 80 * 80 = 3,276,800,000

7. 98^1 = 98 = 98

8. 15^1 = 15 = 15

9. 7^3 = 7 * 7 * 7 = 343

10. 55^4 = 55 * 55 * 55 * 55 = 9,150,625

11. 67^1 = 67 = 67

12. 50^4 = 50 * 50 * 50 * 50 = 6,250,000

Answers:

1)  71^3 = 71 * 71 * 71 = 357,911

2)  52^4 = 52 * 52 * 52* 52 = 7,311,616

3)  99^5 = 99 * 99 * 99 * 99* 99 = 9,509,900,499

4)  78^4 = 78 * 78* 78* 78 = 37,015,056

5)  8^2 = 8 * 8 = 64

6)  80^5 = 80 * 80 * 80 * 80 * 80 = 3,276,800,000

7)  98^1 = 98 = 98

8)  15^1 = 15 = 15

9)  7^3 = 7 * 7 * 7 = 343

10)  55^4 = 55 * 55 * 55 * 55 = 9,150,625

11)  67^1 = 67 = 67

12)  50^4 = 50 * 50 * 50 * 50 = 6,250,000

Answer:

81.75%

Step-by-step explanation:

98 percent on a 60 point test is 59/60

65.50+98/2 = 81.75%

Answer:

6

Step-by-step explanation:

so if she has $65 and she spent 38.50 you find the difference which is   $26.50 then you divide it by 4 which is 6.62 so yes your right its 6 if you round it

Answer:

6 boxes.

Step-by-step explanation:

65 ≥ 38.50 + 4x    where x is the number of boxes of mints.

65 - 38.50  ≥ 4x

(65-38.40/ 4 ≥ x

x  ≤ 6.625

so the answer is 6 boxes.

Answer:

6

Step-by-step explanation:

It may be confusing to see why it would 6 instead of -6. The missing value in the X already includes the negative symbol. So if the 6 was the X value, then the negative sign would apply to the 6 making it - 6. The results would be:

⇒ [tex]-x = -6[/tex]

⇒ [tex]-6=-6[/tex]

Answer:

It would be 1/4 or 25%

Step-by-step explanation:

done this before

Answer: 1/3

Step-by-step explanation:

The correct answer to this question is a 1/3.

Hope this helps a lot of people (please like and give brainliest)!

Answer:

18 degrees

Step-by-step explanation:

6 hours times 3 Fahrenheit every hour is 18 Fahrenheit

Answer:

70 years

Step-by-step explanation:

28 cm more to reach 1 meter (100 cm)

  28 cm / 4 mm/year =

   280 mm   /   4mm/year = 70 years

Answer:

12.5 unit square

Step-by-step explanation:

The area of a trapezoid is calculated with the following formula:

(b1 + b2)*h/2 (b1: base, b2: base, h: height)

(4+6)*(2.5)*2 = 12.5

Answer:

c

Step-by-step explanation:

it's 3 calories per grape

57/19= 3

Answer: 3 calories per grape

Step-by-step explanation:

ur welcome

Answer:

61/2

Step-by-step explanation:

Answer:

4!

Step-by-step explanation:

its 0.05 not 0.5! instead of it being 40, its 4

4 freight cars can be filled by 120 scoops of excavator having a total mass of 156 tons and a volume of 3120 ft³.

In three-dimensional space, volume refers to the entire amount of space occupied by an item. Capacity refers to an object's capacity to contain, absorb, or accept anything (such as a solid material, gas, or liquid).

The amount of matter in a substance or object is measured by its mass.

In the question, we are given that the scoop of an excavator holds 26 ft³of sand.

We are asked if the capacity of a freight car is 39 tons of sand, then how many freight cars can be filled with 120 scoops.

We are also informed that 1 ft³ of sand weighs 0.05 tons.

We first find the mass of sand in one scoop of an excavator.

The volume of sand in one scoop of an excavator = 26 ft³.

Mass of 1 ft³ of sand = 0.05 tons.

∴ Mass of 26 ft³ of sand, that is, the mass of sand in one scoop of an excavator = 26*0.05 tons = 1.3 tons.

∴ Mass of 120 scoops = 120*1.3 tons = 156 tons.

The capacity of one freight car = 39 tons

∴ Number of freight cars in 156 tons = 156/39 = 4.

∴ 4 freight cars can be filled by 120 scoops of excavator having a total mass of 156 tons and a volume of 3120 ft³.

Learn more about the mass and volume of a substance at

https://brainly.com/question/1354972

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Answer

(B) 1.2

Step-by-step explanation:

Step-by-step explanation:

we are using the right triangle altitude theorem. it means that in a right-angled triangle the geometric mean of the two segments of the Hypotenuse (the baseline opposite of the 90° angle) equals the altitude.

in other words

h² = p×q

h = height

p, q are the 2 segments of the Hypotenuse.

so, in our case we have

100 = x(x + 21) = x² + 21x

that gives us the following quadratic equation

x² + 21x - 100 = 0

the general solution to a quadratic equating is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

a = 1

b = 21

c = -100

so,

x = (-21 ± sqrt(21² - 4×1×-100))/(2×1) =

= (-21 ± sqrt(441 + 400))/2 = (-21 ± sqrt(841))/2 =

= (-21 ± 29)/2

x1 = (-21 + 29)/2 = 8/2 = 4

x2 = (-21 - 29)/2 = -50/2 = -25

x2 would give us negative lengths for the triangle, which does not make sense.

so, x = 4 is our solution.

that makes the segments of the Hypotenuse 4 and (4+21) = 25 units long (the whole baseline is then 4+25 = 29).

Hope u can see it : )

Answer: 65...

Step-by-step explanation: (65 is not on there but..)

35x2= 70 (correct)

5x1= 5 (incorrect)

70-5= 65 (total)

Answer:

if you calculate 6-[(-3)+(-7)]-[(-1)-(-5)-(-8)] you get 4

Step-by-step explanation:

step by step by step

Answer: :

If the average out of 5 numbers is 17 then to know the sum

Step-by-step explanation:

Answer:

The one in the bottom right hand corner.

Step-by-step explanation:

The one in the bottom shows a perfectly symmetric standard curve. In a standard curve, the mean and median and mode are equal.

In a right skewed curve, the median is less than the mean. An example of a right skewed curve is the bottom left hand corner.

In a left skewed curve, the mean is less than the median. An example of a left skewed curve is the top left hand corner.

I hope this helps! Let me know if you have any further questions.

Answer:

x

Step-by-step explanation:

angle bac and bca need to be acute and similar in size and angle abc needs to be an obtuse angle. This is the only triangle where angle abc is obtuse.

Answer: Yes the triangles are the same, just one is smaller than the other

Step-by-step explanation: if you flip tringle y, you get the same messurments, its just smaller.

Answer: the answer is 440 cm sq

Step-by-step explanation: since the formula is a+b/2 x h

where a is 19 cm ,

b is 25 cm and

h is 20 cm

Answer: this answer is A

Step-by-step explanation:

Length: Length, Width:Width