Simplify using order of operations. Show all of your work and do ONE operation at a time to receive all possible points. 90 ÷ [ 10 + ( 3 2 − 4 ) ]

Answer:

[tex]\displaystyle \int \sec\left(\frac{x}{2}\right)\tan^5\left(\frac{x}{2}\right)dx=\frac{2\sec^5\left(\dfrac{x}{2}\right)}{5}-\frac{4\sec^3\left(\dfrac{x}{2}\right)}{3}+2\sec\left(\frac{x}{2}\right)+C[/tex]

Step-by-step explanation:

We want to find the integral:

[tex]\displaystyle \int \sec\left(\frac{x}{2}\right)\tan^5\left({\frac{x}{2}\right)dx[/tex]

First, perform the substitution y = x / 2. This yields:

[tex]\displaystyle dy = \frac{1}{2} \, dx \Rightarrow dx = 2\, dy[/tex]

Hence, the integral becomes;

[tex]\displaystyle =2\int \sec y\tan^5 y \, dy[/tex]

Next, as you had done, let's expand the tangent term but to the fourth:

[tex]\displaystyle =2\int \sec y\tan^4 y\tan y\, dy[/tex]

Recall that:

[tex]\tan^2(y)=\sec^2(y)-1[/tex]

Hence:

[tex]\displaystyle =2\int \sec y(\sec^2 y-1)^2\tan y\, dy[/tex]

We can use substitution once more. This time, let u = sec(y). Hence:

[tex]\displaystyle du = \sec y \tan y \, dy[/tex]

Rewrite:

[tex]\displaystyle =2\int \left((\sec^2y-1)^2\right)\left(\sec y \tan y\right)dy[/tex]

Therefore:

[tex]\displaystyle = 2\int (u^2 - 1)^2\, du[/tex]

Expand:

[tex]\displaystyle =2\int u^4-2u^2+1\, du[/tex]

Reverse Power Rule:

[tex]\displaystyle = 2\left(\frac{u^5}{5} - \frac{2u^3}{3} + u\right) + C[/tex]

Simplify:

[tex]\displaystyle = \frac{2u^5}{5} - \frac{4u^3}{3} + 2u + C[/tex]

Back-substitute:

[tex]\displaystyle = \frac{2\sec^5 y }{5}-\frac{4\sec^3 y}{3}+2\sec y+C[/tex]

Back-substitute:

[tex]\displaystyle =\frac{2\sec^5\left(\dfrac{x}{2}\right)}{5}-\frac{4\sec^3\left(\dfrac{x}{2}\right)}{3}+2\sec \left(\frac{x}{2}\right)+C[/tex]

Therefore:

[tex]\displaystyle \int \sec\left(\frac{x}{2}\right)\tan^5\left(\frac{x}{2}\right)dx=\frac{2\sec^5\left(\dfrac{x}{2}\right)}{5}-\frac{4\sec^3\left(\dfrac{x}{2}\right)}{3}+2\sec\left(\frac{x}{2}\right)+C[/tex]

Answer:

= 2 (sec (x/2) - 2sec³(x/2) +  sec⁵(x/2) ) + C

                              3                     5

Step-by-step explanation:

∫sec(x/2) tan⁵(x/2) dx

apply u substitute u = x/2

= ∫sec(u) tan⁵(u) * 2du

= 2 *  ∫sec(u) tan⁴(u) tan(u) du

= 2 *  ∫sec(u) (tan²(u))² tan(u) du

= 2 *  ∫sec(u) (-1 + sec²(u))² tan(u) du

apply u substitute v = sec(u)

= 2 * ∫(-1 + v²)² dv

expand

= 2 * ∫1 - 2v² + v⁴ dv

sum

= 2 (v - 2v³ + v⁵ )

             3      5

substitute it back

= 2 (sec (x/2) - 2sec³(x/2) +  sec⁵(x/2) )

                              3                     5

add constant to the solution.

= 2 (sec (x/2) - 2sec³(x/2) +  sec⁵(x/2) ) + C

                              3                     5

Answer:

92%

Step-by-step explanation:

Answer:4782984

Step-by-step explanation:

Answer:4782984

Step-by-step explanation:

Answer:

4/5*3/4&6/7*2/5

Step-by-step explanation:

4/5*3/4=12/20

6/7*2/5=12/35

Answer:

[tex]n=26[/tex]

Step-by-step explanation:

So we have the equation:

[tex]-413.4=-15.9n[/tex]

To figure out the value of n, divide both sides by -15.9. The right will cancel. Thus:

[tex]n=(-413.4)/(-15.9)[/tex]

Use a calculator:

[tex]n=26[/tex]

So, the answer is 26.

So, yes, you are very correct!

Answer:

n=26

Step-by-step explanation:

We are given the equation:

[tex]-413.4=-15.9n[/tex]

We want to solve for the unknown variable, which is n. Therefore, we must isolate n on one side of the equation.

n is being multiplied by -15.9. The inverse of multiplication is division. Divide both sides of the equation by -15.9

[tex]\frac{-413.4}{-15.9} =\frac{-15.9n}{-15.9}[/tex]

[tex]\frac{-413.4}{-15.9}=n[/tex]

[tex]26=n[/tex]

Let's check our solution. Plug 26 in for n and solve.

[tex]-413.4=-15.9n[/tex]

[tex]-413.4=-15.9(26)[/tex]

Multiply -15.9 and 26.

[tex]-413.4=-413.4[/tex]

This checks out, so we know our solution is correct.

The solution to this equation is n=26 and you are correct!

Answer:

the last one is the only one with a y intercept of -1

Step-by-step explanation:

Answer:

$50 is profit because every $50 it intersects.

X would be the $50 so 10x50=500-150=which would be $350.

I think this is right hope this helps!

Answer:

false or not true

Step-by-step explanation:

5x + 8x < 4x + -7

combine like terms

13x<4x+-7

4x divided by 4  -7 divided by 4

x= -7/4

13x<-7/4

Answer:

x^2 - 8x + 9

Step-by-step explanation:

Please write x2+9-8x as x^2 + 9 - 8x.  The " ^ " indicates exponentiation.

Next, please write x^2 + 9 - 8x in descending powers of x:

x^2 - 8x + 9

Answer:

Equation to represent all number of points = |4|

Step-by-step explanation:

We are told that a player either wins or loses 4 points during each turn. This means a player could either gain 4 points or loose 4 points. When writing this in Mathematical terms its means either -4 or +4.

Now, since possible number of turns is -4 or 4, then we can represent this with the absolute value symbol.

Thus, it's |4|

Answer:

Step-by-step explanation:

The answer to your question is 4.8 kilometers. Brainliest?

Answer:

1.86

Step-by-step explanation:

Answer:

$4.44

Step-by-step explanation:

Cost per yard = $10/2.25

= $4.44 (nearest cent)

the answer $ 4.44

explanation :

so first of all you need to divide 10 by 2 1/4

when you divide both number you'll get 4 4/9

4 4/9 can also be written as 4.44444444444

which is also 4.4 recurring

now we can round this off

when you round it off, you should round it off to two decimal points cause the answer should be in dollars

you should get 4.44 as an answer

so the answer will be $ 4.44

really hope that helped :)

Answer:

20

Step-by-step explanation:

The total gains of Jack if, In the first play, he gained 12 yards, in the second play lost 15 yards, in the third play gained 25 yards, and in the fourth play lost 2 yards is 20 yards.

The action of subtracting a matrix, vector, or other quantity from another according to predetermined rules in order to find the difference.

In math, addition is the process of adding two or more integers together. Addends are the numbers that are added, while the total refers to the outcome of the operation.

Given:

In the first play, he gained 12 yards, in the second play lost 15 yards, in the third play gained 25 yards, and in the fourth play lost 2 yards.

Assume the gains can be denoted by positive and loss by negative,

Gains = 12 yards, 25 yards.

Total gain = 12 + 25 = 37 yards

Loss = -15 yards, -2 yards

Total loss = -15 + (-2) = -17 yards

Calculate the total gain as shown below,

Total gain = total gain + total loss

Total gain = 37 + (-17)

Total gain = 20 yards.

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Answer:

X * 12 = 9

Step-by-step explanation:

The required model of the given situation is given as y = 9 (x + 12).

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
the product of 9 and the sum of the number x and 12 is given as
Let the product is equal to y
y = 9 (x + 12)

Thus, the required model of the given situation is given as y = 9 (x + 12).

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Answer:

4096

Step-by-step explanation:

Answer:

4096

Step-by-step explanation:

4 to the third power is 64 and 64 to the 2nd power is 4096 so that should be your answer

Answer:

4 pints

Step-by-step explanation:

16 oz in a pint

Answer:

0.00000014 x

Step-by-step explanation:

Answer:

The coordinates of point P are (2,5)

Step-by-step explanation:

We know that point P divides AB internally in the ratio 3:2, that is AP/PB = 3/2,

we thus use the formula for internal division.

Let A = (x₁, y₁) = (-4, 8), B = (x₂, y₂) = (6, 3) and P = (x, y)  

So x = (mx₂ + nx₁)/(m + n)

y = (my₂ + ny₁)/(m + n)

where m = 3 and n = 2

Substituting the values of the x coordinates of A and B into x, we have

x = (mx₂ + nx₁)/(m + n)

x = (3 × 6 + 2 × (-4))/(3 + 2)

x = (18 - 8)/5

x = 10/5

x = 2

Substituting the values of the y coordinates of A and B into y, we have

y = (my₂ + ny₁)/(m + n)

y = (3 × 3 + 2 × 8)/(3 + 2)

y = (9 + 16)/5

y = 25/5

y = 5

Therefore, the coordinates of point P are (2,5)

Answer:

You spent $1349

Step-by-step explanation:

sweaters s = $29

t-shirts t = $16

pants p = $25

Cost = C

28s + 7t + 17p = C

28 ($29) + 7 ($16) + 17 ($25) = C

$812 + $112 + $425 = C

$1349 = C

Answer:

21

Step-by-step explanation:

The answer is negitive 21 becuase it you sub and

After conducting some mathematical operations, we can conclude that Florida is warmer than Texas by 21°F.

So, Florida is warmer than Texas by:

Now, calculate as follows:

Therefore, after conducting some mathematical operations, we can conclude that Florida is warmer than Texas by 21°F.

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Answer: 3 seconds

Step-by-step explanation: the pump fills 1 tire per second

Answer:

The number of years needed is 15.75 years.

Step-by-step explanation:

The investment amount (present value) = $200

Interest rate =4.5%

Double of investment = $400

Now we have to find the time or number of years in which the investment amount will be doubled. So, just use the below formula to find the number of years.

Future value = present value ×(1+interest rate)^n

400 = 200×(1+4.5%)^n

N = 15.75 years

The number of years required to double the amount is 15.75 years.

Answer:

thousands place

Step-by-step explanation:

Answer:

$170.14

Step-by-step explanation:

4,861 / 1,000 = $4.861 per gallon

35 x $4.681 = $170.135, so you need to round up to the nearest penny

Step-by-step explanation:

For 1000 gallons=$4861

For 1 gallon =$4861/1000

For 35 gallons=$4861/1000 x 35=170.135

Answer:

[tex]90^\circ[/tex]

Step-by-step explanation:

Given two non zero vectors, [tex]\vec a, \vec b[/tex].

Let the angle between the two vectors = [tex]\theta[/tex]

Given that:

[tex]|\vec a+\vec b|=|\vec a-\vec b|[/tex]

Let us have a look at the formula for magnitude of addition of two vectors:

[tex]|\vec x+\vec y|=\sqrt{x^2+y^2+2xycos\theta}[/tex]

Where [tex]\theta[/tex] is the angle between the two vectors.

formula for magnitude of subtraction of two vectors:

[tex]|\vec x-\vec y|=\sqrt{x^2+y^2-2xycos\theta}[/tex]

As per the given condition:

[tex]\sqrt{a^2+b^2+2abcos\theta}=\sqrt{a^2+b^2-2abcos\theta}[/tex]

Squaring both sides:

[tex]a^2+b^2+2abcos\theta=a^2+b^2-2abcos\theta\\\Rightarrow 2abcos\theta=-2abcos\theta\\\Rightarrow cos\theta = -cos\theta\\\Rightarrow 2cos\theta = 0\\\Rightarrow cos\theta = 0\\\Rightarrow \theta = 90^\circ[/tex]

So, the angle between the two vectors is: [tex]90^\circ[/tex]

Answer:

(a) Shown below

(b) Positively Skewed

(c) No Outlier

(d) 15%

Step-by-step explanation:

Arrange the data set in ascending order as follows:

S = {5.7 , 6.2 , 6.3 , 6.5 , 6.8 , 6.8 , 7 .0, 7 .0, 7.2 , 7.3 , 7.4 , 7.6 , 7.7 , 7.7 , 7.8 , 7.8 , 7.9 , 8.1 , 8.2 , 8.7 , 9 .0, 9.7 , 9.7 , 10.6 , 11.5 , 11.6 , 11.8}

(a)

Construct a stem-and-leaf display of the data as follows:

5 | 7

6 | 2  3  5  8  8

7 | 0  0  2  3  4  6  7  7  8  8  9

8 | 1  2  7

9 | 0  7  7

10 | 6

11 | 5  6  8

The representative strength value is the mid-value.

The mid-value is: 7.7

Thus, the representative strength value is 7.7.

(b)

No, the data does not appear to be highly concentrated about the representative value or rather spread out.

As we take the stem-and-leaf plot into consideration we observe that most of the observations are concentrated towards the right of the graph.

So, the data is right or positively skewed.

(c)

No, there doesn't appear to be any outlying strength values.

This is because all the values are closer to each other and none of the observations are too extreme.

(d)

The number of observations more than 10 MPa is, 4.

Total number of observations, 27.

Compute the proportion of strength observations that exceed 10 MPa as follows:

[tex]P(>10\ \text{MPa})=\frac{4}{27}=0.14815\approx 0.15[/tex]

Thus, the proportion of strength observations that exceed 10 MPa is 15%.