Mathematics College

Expanded form of 6985062 using exponential notation

Answers

Answer 1

6,000,000 +900,000 +80,000 +5,000 +0 +60 +2

Related Questions

5 hundreds 6 ten thousands 2 ones

Answers

the anwser is 526 because u have 5 hundreds and u have 6 ten thousands 2 ones

60,502 is the answer. (sixty-thousand five hundred and two).

addition or subtraction of unit fractions 1/2-1/8=

Answers

1/2(4/4)= 4/8

4/8-1/8= 3/8

The answer is 3/8. Hope this helps!

gary father dropped him off soccer practice at2:45 pm .his mom picked him up at 5:00 pm.how long did soccer practice last

Answers

2 hours and 15 minutes

Please help me, it's due tomorrow and I haven't gotten any sleep!!!! ); ); );

Answers

Attached the solution and work. Not sure about number 3. You might have to check that one.

x2 + y2 – 10x + 6y = 15.

Answers

Write the equation of this circle in standard form: (x-h)^2 + (y-k)^2 = r^2,
where (h,k) represents the center of the circle.

We must use the "complete the square" approach twice here:

X^2 + y^2 – 10x + 6y = 15

Rewrite this as x^2 - 10x + y^2 + 6y = 15
Complete the square of x^2 - 10x:

x^2 - 10x + 25 - 25

Complete the square of y^2 + 6y:

y^2 + 6y + 9 - 9

Then rewrite X^2 + y^2 – 10x + 6y = 15 as

x^2 - 10x + 25 + y^2 + 6y + 9 = 15 + 25 + 9

Or as (x-5)^2 + (y+3)^2 = 49

Then the equation of the circle in standard form is

(x-5)^2 + (y+3)^2 = 7^2.

The center of this circle is at (5,-3), and its radius is 7.

[tex]x^2 + y^2 - 10x + 6y = 15 [/tex]

Which shows the correct simplification of product of powers?
1.) 78 · 7-4 = 78· (–4) = 7–32
2.)78 · 7–4 = 78 ÷ (–4) = 7–2
3.)78 · 7–4 = 78 + (–4) = 74
4.)78 · 7–4 = 78 - (–4) = 712

Answers

The power symbols are missing.

I can infere that the product intended to simplify is (7^8) * (7^-4)., because that permits you to use the rule of the product of powers with the same base.

That rule is that the product of two powers with the same base is the base raised to the sum of the powers is:

(A^m) * (A^n) = A^ (m+n)

=>(7^8) * (7^-4) = 7^ [8 + (- 4) ] = 7^ [8 - 4] = 7^4, which is the option 3 if the powers are placed correctly.

The answer choice which shows the correct simplification of product of powers is:

78 · 7–4 = 78 + (–4) = 74

What is Product of Powers?

This refers to the mathematical property which states that when there is a multiplication of two powers that have the same base, then there would be the addition of exponents.

From the given choices, we can see that the powers are not given, so we can solve using inference.

This posits that (7^8) * (7^-4) was the product that was intended to be simplified and this law shows:

(A^m) * (A^n) = A^ (m+n)

Hence, if we add the powers, then the correct answer would be option C because they are of the same base.

Read more about product of powers here:

https://brainly.com/question/19517443

at a point P on the parabola x^2=4ay a normal PK is drawn. From vertex O, a perpendicular OM is drawn to meet the normal at M. Show that the equation of the locus of M as P varies on the parabola is x^4-2ax^2y+x^2y^2-ay^3=0

Answers

Answer: Its too long to write here, so I will just state what I did. I let P=(2ap,ap^2) and Q=(2aq,aq^2) But x-coordinates of P and Q differ by (2a) So P=(2ap,ap^2) BUT Q=(2ap - 2a, aq^2) So Q=(2a(p-1), aq^2) which means, 2aq = 2a(p-1) therefore, q=p-1 then I subbed that value of q in aq^2 so Q=(2a(p-1), a(p-1)^2) and P=(2ap,ap^2) Using these two values, I found the midpoint which was: M=( a(2p-1), [a(2p^2 - 2p + 1)]/2 ) then x = a(2p-1) rearranging to make p the subject p= (x+a)/2a

sin pi/4 sin pi/6= 1/2(_____ pi/12-cos 5pi/12)

Answers

Answer:

[tex] sin\frac{\pi}{4}sin\frac{\pi}{6}=\frac{1}{2}(cos\frac{\pi}{12}-cos\frac{5\pi}{12})[/tex]

Step-by-step explanation:

We are given that

[tex] sin\frac{\pi}{4} sin\frac{\pi}{6}[/tex]

We have to correct value in blank space.

We know that identity

[tex] sin xsiny=\frac{cos(x-y)-cos(x+y)}{2}[/tex]

Using this identity

[tex] sin\frac{\pi}{4}sin\frac{\pi}{6}=\frac{cos(\frac{\pi}{4}-\frac{\pi}{6})-cos(\frac{\pi}{4}+\frac{\pi}{6})}{2}[/tex]

[tex] sin\frac{\pi}{4}sin\frac{\pi}{6}=\frac{cos(\frac{3\pi-2\pi}{12}-cos(\frac{3\pi+2\pi}{12})}{2}[/tex]

[tex] sin\frac{\pi}{4}sin\frac{\pi}{6}=\frac{1}{2}(cos\frac{\pi}{12}-cos\frac{5\pi}{12})[/tex]

Answer:[tex] sin\frac{\pi}{4}sin\frac{\pi}{6}=\frac{1}{2}(cos\frac{\pi}{12}-cos\frac{5\pi}{12})[/tex]

Approximately how many times greater is 4×107 than 8×103 ?
A.0.5
B.500
C.5000
D.50,000

Answers

The answer is C. 5000

40000000

8000

40000000 / 8000 = 5000

Answer is C. 5000

Uncle drew scored 28 pionts in 5 5\6 minutes how many points did he average

Answers

28 / (5 5/6) =
28 / (35/6) =
28 * 6/35 =
168/35 =
4.8 points per minute <==

Identify the phrase that cannot be described by the same absolute value as the other three. Explain your reasoning.

Answers

The answer would probably be 18 degrees below normal because the absolute values of the rest are 8 not 18 which is the absolute value of 18 degrees below normal.

Students can take MATH 080 between one and four times. The student's tuition for MATH 080 is $ 548.00 If the tuition is increased 6% AFTER 2 ATTEMPTS, what is the student's one semester tuition after the 2nd attempt? In this situation what is the total tuition for taking MATH 080 the allowed four times

Answers

2nd attempt carries a price of 6% extra, so (6/100) * 548 is 32.88, so 548 + 32.88, the price is 580.88.

for the 3rd attempt 6% extra of that, (6/100) * 580.88, is 34.8528, so the price is 615.7328.

4th attempt is 6% extra of that, (6/100) * 615.7328, 36.943968, adding that will give us 652.676768.

At 1pm, there was 16 seagulls on the beach. At 3pm, there were 60 seagulls. What is the constant rate of change

Answers

22 seagulls per hour... cx

1/3 = 16/60
Cross Multiply
48/60=4/5
The constant rate of change is 4/5

how to solve 4+2 - 5/6 - 1/2

Answers

Go to www.symbolab.com

First make everything decimal or whole number

1/2 = 0.5
5/6 = 0.83

4 + 2 - 0.83 - 0.5
6 - 1.33
4.67 is your answer

hope this helps

what inequality represents "a cat weighs no more than 8 pounds"

Answers

Final answer:

The inequality representing "a cat weighs no more than 8 pounds" is expressed as w ≤ 8, where w symbolizes the cat's weight in pounds. This concept illustrates how inequality symbols are applied in algebra to represent the relationship between quantities, applicable in various real-world scenarios.

Explanation:

The question asks which inequality represents "a cat weighs no more than 8 pounds." In mathematical terms, this statement can be translated using an inequality symbol that indicates the cat's weight is either equal to or less than 8 pounds. The appropriate symbol for this is “≤”, which stands for “less than or equal to.” Therefore, the inequality that represents this statement is w ≤ 8, where w represents the weight of the cat in pounds.

Using inequality symbols to show how two metric measurements are related is a foundational concept in algebra, and it is crucial when working with real-world scenarios where quantities have upper or lower bounds. For instance, understanding this concept can apply to various situations such as determining the weight of a dog, or comparing soda in a can to ensure it does not exceed a certain weight limit. It's important to grasp how these symbols convey relationships between quantities.

suppose each bag costs $14.99. estimate the total cost of 5 bags

Answers

Round up $14.99 to $15. Then mult. $15 by 5. Result: $75 (approx total cost of 5 bags).

Since you are estimating, I would recommend rounding the $14.99 to a $10.
$10 x 5 would be $50. So, the estimated total cost of 5 bags would be $50.

Use cylindrical coordinates to evaluate the integral where d is the solid bounded above by the plane z=2 and below by the surface 2z=x2+y2

Answers

Answer:

[tex]\displaystyle \iiint_D {z \big( x^2 + y^2 \big)^\big{\frac{-1}{2}}} \, dx \, dy \, dz = \frac{32 \pi}{5}[/tex]

General Formulas and Concepts:

Calculus

Integration

Integrals

Integration Rule [Reverse Power Rule]:
[tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]

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]

Multivariable Calculus

Cylindrical Coordinate Conversions:

[tex]\displaystyle x = r \cos \theta[/tex][tex]\displaystyle y = r \sin \theta[/tex][tex]\displaystyle z = z[/tex][tex]\displaystyle r^2 = x^2 + y^2[/tex][tex]\displaystyle \tan \theta = \frac{y}{x}[/tex]

Volume Formula [Cylindrical Coordinates]:
[tex]\displaystyle V = \iiint_T \, dV \rightarrow V = \iiint_T {r} \, dz \, dr \, d\theta[/tex]

Step-by-step explanation:

Step 1: Define

Identify.

[tex]\displaystyle \text{Region} \ D \left \{ {{2z = x^2 + y^2} \atop {z = 2}} \right.[/tex]

[tex]\displaystyle \iiint_D {z \big( x^2 + y^2 \big)^\big{\frac{-1}{2}}} \, dx \, dy \, dz[/tex]

Step 2: Find Volume Pt. 1

Find θ bound.

[Surface] Substitute in plane z:
[tex]\displaystyle 2(2) = x^2 + y^2[/tex]Simplify:
[tex]\displaystyle x^2 + y^2 = 4[/tex][See 2nd Attachment] Graph[Graph] Identify limits [Unit Circle]:
[tex]\displaystyle 0 \leq \theta \leq 2 \pi[/tex]

Find r bound.

[Surface] Substitute in plane z:
[tex]\displaystyle 2(2) = x^2 + y^2[/tex]Substitute in cylindrical conversions:
[tex]\displaystyle 2(2) = r^2[/tex]Simplify:
[tex]\displaystyle r = \pm 2[/tex][r] Identify:
[tex]\displaystyle r = 2[/tex]Define limits:
[tex]\displaystyle 0 \leq r \leq 2[/tex]

Find z bound.

[Surface] Substitute in cylindrical conversions:
[tex]\displaystyle 2z = r^2[/tex]Rewrite:
[tex]\displaystyle z =\frac{r^2}{2}[/tex]Define limits:
[tex]\displaystyle \frac{r^2}{2} \leq z \leq 2[/tex]

Step 3: Find Volume Pt. 2

[Integrals] Substitute in cylindrical conversions:
[tex]\displaystyle \iiint_D {z \big( x^2 + y^2 \big)^\big{\frac{-1}{2}}} \, dx \, dy \, dz = \iiint_D {z \big( r^2 \big)^\big{\frac{-1}{2}}} \, dx \, dy \, dz[/tex][Integrals] Simplify:
[tex]\displaystyle \iiint_D {z \big( x^2 + y^2 \big)^\big{\frac{-1}{2}}} \, dx \, dy \, dz = \iiint_D {\frac{z}{r}} \, dx \, dy \, dz[/tex][Integrals] Convert [Volume Formula - Cylindrical Coordinates]:
[tex]\displaystyle \iiint_D {z \big( x^2 + y^2 \big)^\big{\frac{-1}{2}}} \, dx \, dy \, dz = \iiint_T {\frac{zr}{r}} \, dz \, dr \, d\theta[/tex][Integrals] Simplify:
[tex]\displaystyle \iiint_D {z \big( x^2 + y^2 \big)^\big{\frac{-1}{2}}} \, dx \, dy \, dz = \iiint_T {z} \, dz \, dr \, d\theta[/tex][Integrals] Substitute in region T:
[tex]\displaystyle \iiint_D {z \big( x^2 + y^2 \big)^\big{\frac{-1}{2}}} \, dx \, dy \, dz = \int\limits^{2 \pi}_0 \int\limits^2_0 \int\limits^2_{\frac{r^2}{2}} {z} \, dz \, dr \, d\theta[/tex][dz Integral] Integrate [Integration Rules and Properties]:
[tex]\displaystyle \iiint_D {z \big( x^2 + y^2 \big)^\big{\frac{-1}{2}}} \, dx \, dy \, dz = \int\limits^{2 \pi}_0 \int\limits^2_0 {\frac{z^2}{2} \bigg| \limits^{z = 2}_{z = \frac{r^2}{2}}} \, dr \, d\theta[/tex]Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]:
[tex]\displaystyle \iiint_D {z \big( x^2 + y^2 \big)^\big{\frac{-1}{2}}} \, dx \, dy \, dz = \int\limits^{2 \pi}_0 \int\limits^2_0 {\bigg( 2 - \frac{r^4}{8} \bigg)} \, dr \, d\theta[/tex][dr Integral] Integrate [Integration Rules and Properties]:
[tex]\displaystyle \iiint_D {z \big( x^2 + y^2 \big)^\big{\frac{-1}{2}}} \, dx \, dy \, dz = \int\limits^{2 \pi}_0 {\bigg( 2r - \frac{r^5}{40} \bigg) \bigg| \limits^{r = 2}_{r = 0}} \, d\theta[/tex]Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]:
[tex]\displaystyle \iiint_D {z \big( x^2 + y^2 \big)^\big{\frac{-1}{2}}} \, dx \, dy \, dz = \int\limits^{2 \pi}_0 {\frac{16}{5}} \, d\theta[/tex][dθ Integral] Integrate [Integration Rules and Properties]:
[tex]\displaystyle \iiint_D {z \big( x^2 + y^2 \big)^\big{\frac{-1}{2}}} \, dx \, dy \, dz = \frac{16}{5} \theta \bigg| \limits^{\theta = 2 \pi}_{\theta = 0}[/tex]Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]:
[tex]\displaystyle \iiint_D {z \big( x^2 + y^2 \big)^\big{\frac{-1}{2}}} \, dx \, dy \, dz = \frac{32 \pi}{5}[/tex]

∴ the integral bound by region D is equal to [tex]\displaystyle \bold{\frac{32 \pi}{5}}[/tex].

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Learn more about cylindrical coordinates: https://brainly.com/question/24004264

Learn more about multivariable calculus: https://brainly.com/question/17203772

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Topic: Multivariable Calculus

Unit: Triple Integrals Applications

What was the most direct effect of the establishment of the Queen’s Men?

a. New plays were written every year.

b. The queen visited Whitehall Palace.

c. The Puritans were outraged.

d. Drama received royal approval.

Answers

Answer:

C) The Puritans were outraged.

Step-by-step explanation:

Answer:

Step-by-step explanation:

trust

what is the value of 6 in 89.6

Answers

That 6 represents 6/10 (six tenths).

that’s the tenth place or 6/10 or 6/100

Loretta deposited $429 in a new savings account at Henry County Bank and Trust. She made no other deposits or withdrawals. After 6 months, the interest was computed at an annual rate of 6 .25%. How much simple interest did her money earn?

Answers

i = prt

Simple interest is the product of the principal (the money deposited), the annual interest rate, and the time.

p = $429
i = 6.25% = 0.0625
t = 0.5 year

i = $429 * 0.0625 * 0.5

i = 13.40625

The interest is $13.41

Interest can be calculated by the following equation.
Interest = Principal x rate p.a x time
Now we can sub the numbers in.
Interest = 429 x (6.25% / 12) x 6
Note that u have to divide the annual rate by 12, which is the number of months in a year, as the amount time in this question is counted by months
Interest = 429 x (6.25% / 12) x 6
Interest = $ 13.406249914
Round up if needed.

The cost of producing x pumpkin pies at a small bakery is given by c(x)=49+1.75x. Find the cost of producing 25 pies A. $74.00 B.$81.50 C.$92.75 D.$108.25

Answers

So basically you wanna look at the equation like this, you have the base price of 49$ no matter what. Now you need to find what 1.75 x 25 is which is 43.75. So now you add the 49 and 43.75 giving you C: $92.75. Hope this helps :D

A function is defined as a relation between a set of inputs having one output each.

Input = 25 and output = $92.75

The cost of 25 pies is $92.75

What is a function?

A function is defined as a relation between a set of inputs having one output each.

The inputs are called the domain of the function.

The outputs are called the range of the function.

Example: f(x) = 2 + 3x

x = 1

f(1) = 2 + 3x1 = 2 + 3 = 5

1 = Domain

5 = Range

We have,

c(x) = 49 + 1.75x

x = number of pies

The cost of producing 25 pies:

c(25) = 49 + 1.75 x 25

= 49 + 43.75

= $92.75

Thus the cost of 25 pies is $92.75

Learn more about functions here:

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perform the following conversions convert 5.0 cm to m

Answers

5 centimeters is 0.05 meters

To convert 5.0 cm to m, use the conversion factor of 1 m = 100 cm to get the result of 0.05 m.

Convert 5.0 cm to m:

1 m = 100 cm, which means 1 cm is 0.01 m.

Therefore, 5.0 cm is equal to 5.0 x 0.01 m = 0.05 m.

Carly is making 3 1/2 batches of biscuits. If one batch calls for 2 1/3 cups of floor, how much flour will she need?

Answers

In this question, Carly needs to make 3.5 batches of biscuit and one batch equal to 2 1/3 cups of flour. Then you will get an equation look like this:

1 batch of biscuit= 2 1/3 cups of flour

Then 3.5 batches of cookies would be:
3.5 batches of biscuit * (2 1/3 cups of flour/ batch of biscuit)= 49/6 cups of flour= 8.16 cups of flour

Which of the numbers below correctly describes 5,000 µf?

Answers

Final answer:

The number 5,000 µF represents a capacitance, indicating that the capacitor can store 5,000 microcoulombs of electric charge at an electric potential difference of 1 volt.

Explanation:

The number 5,000 µF describes a capacitance. Capacitance is a measure of a capacitor's ability to store an electric charge. It can be defined as the ratio of the change in an electric charge in a system to the corresponding change in its electric potential. So, when we say a capacitor has a capacitance of 5,000 µF (microfarads), it means the capacitor can store 5,000 micro coulombs of electric charge at an electric potential difference of 1 volt. It's important to know that the typical range of capacitors can vary from fractions of a picofarad (pF) to a milifarad (mF).

Learn more about Capacitance here:

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A customer pays $1,100 in state taxes on a newly purchased car. What is the value of the car if state taxes are 8.9% of the value?
$9,765.45
$10,876.90
$12,359.55
$14,345.48
$15,745.45

Answers

Final answer:

To find the value of the car, divide the amount of state taxes paid by the tax rate percentage. The value of the car is $12,359.55.

Explanation:

To find the value of the car, we need to divide the amount of state taxes paid by the tax rate percentage. In this case, the state taxes paid is $1,100 and the tax rate is 8.9%.

So, the value of the car can be calculated as follows:

Value of the car = State taxes paid / Tax rate percentage

= $1,100 / 0.089

= $12,359.55

Therefore, the value of the car is $12,359.55

Please help???
Which of the following equations represents the graph shown?
A) f(x)=-x+2
B) f(x)=-x-2
C) f(x)=x+2
Okay it's not C, it's wrong

Answers

The answer is: [A]: " f(x) = x + 2 " .
_________________________________
Notice the points on the graph shown:
_________________________________
(0, 2) ; and (2, 0).

Answer choice: [A]: is the only function, among the answer choices given, that has BOTH of these coordinates when you plug in these values.
_________________________________

Answer:

the answer is f(x) = -x + 2

Step-by-step explanation:

because i got it right

Is the ratio 35 to 10 proportional to the ratio 7 to 5? Explain.

Answers

35/10 = 7/5
35*5 = 10*7 ... cross multiply
175 = 70
the last equation is false so the first equation is false. The original two ratios are NOT proportional

Another way to see this is to use a calculator to get the decimal form of each fraction
35/10 = 3.5
7/5 = 1.4

The results 3.5 and 1.4 are not the same so this is more confirmation that they are not proportional

Use the chinese remainder theorem to solve the systems of congruences:
a. find x mod 77 if x ≡ 2 (mod 7) and x ≡ 4 (mod 11).
b. x ≡ 2 (mod 3), x ≡ 3 (mod 4), x ≡ 1 (mod 5).

Answers

(a) Suppose we let

[tex]x=2+4=6[/tex]

Modulo 7, we're left with [tex]x\equiv2+4\pmod7=6\mod7[/tex], but we want a remainder of 2, so multiply 4 by 7 to assure that that remainder vanishes. So now

[tex]x=2+4\cdot7=30[/tex]

and [tex]x\equiv2\pmod7[/tex], but modulo 11, we have [tex]x=\equiv2+28\equiv2+4\equiv6\pmod{11}[/tex]. But we want the remainder to be 4, so multiply the first term by 11 to guarantee this. So we write

[tex]x=2\cdot11+4\cdot7=50[/tex]

but now, we get a remainder of 1 modulo 7 and 6 modulo 11. To fix the first case, multiply the first term by 2. For the second case, first find the inverse of 6 modulo 11. We have [tex]2\cdot6=12[/tex], and [tex]12\equiv1\pmod{11}[/tex], so the inverse is 2. Multiply the second term by 2, so that the second term's remainder modulo 11 becomes 1. Then multiply by 4, so that now

[tex]x=2\cdot11\cdot2+4\cdot7\cdot2\cdot4=268[/tex]

We have

[tex]x=268=3\cdot77+37\implies x\equiv37\pmod{77}[/tex]

(b) This is done similarly. Modulo 3, we want a remainder of 2, so we can start with

[tex]x=2+3+3=8[/tex]

Then taken modulo 4, we need to multiply the first term by 2 and the third term by 4 to ensure the remainder becomes 3. The second term can be left alone.

[tex]x=2\cdot2+3+3\cdot4=19[/tex]

Now taken modulo 5, we can multiply the first two terms by 5 and the third term by the inverse of [tex]3\times2\equiv12\equiv2\pmod5[/tex]. We have [tex]3\cdot2\equiv6\equiv1\pmod5[/tex], so we multiply by 3.

[tex]x=2\cdot2\cdot5+3\cdot5+3\cdot4\cdot3=71[/tex]

Now

[tex]x=71=1\cdot(3\cdot4\cdot5)+11=1\cdot60+11[/tex]

which means the smallest positive solution for the system would be [tex]x=11[/tex].

Select from the drop-down menu to correctly identify the property shown.

(−5.2+ (−8.4)) + (−2.8) = −(5.2 + 8.4) + (−2.8)

Associative property

Commutative property

Opposite of sum property

Answers

Opposite of sum property

Sara can type 90 words in 4 minutes about how many words would you expect her to type in 10 minutes at this rate

Answers

first divide 90 by 4 to see how many words per minute

90 ÷ 4 = 22.5

then multiply 22.5 by 10 to get your answer

so your answer is;

225 words per 10 minutes

Answer:

C. 225 words

Step-by-step explanation:

90 / 4 = 22.5

22.5 x 10 = 225 words

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