Let Theta be an angle in quadrant II such that sec(theta)=-5/3
Find the exact values of cot theta and sin theta

Answer:

number 2

Step-by-step explanation:

A cougar did not attack to the victim.ibthinj this is answer

a. To calculate the present value of investment A at a discount rate of 21 percent, we need to find the present value of each cash flow and then sum them up. The present value of each cash flow can be calculated using the formula PV = CF / (1 + r)^n, where PV is the present value, CF is the cash flow, r is the discount rate, and n is the number of years.

Using the given cash flows and the discount rate of 21 percent, we have:

PV = 11,000 / (1 + 0.21)^1 + 11,000 / (1 + 0.21)^2 + 11,000 / (1 + 0.21)^3 + 11,000 / (1 + 0.21)^4 + 11,000 / (1 + 0.21)^5 + 11,000 / (1 + 0.21)^6

Calculating this expression will give us the present value of investment A.

b. Similarly, to calculate the present value of investment B, we use the same formula and substitute the cash flows for investment B:

PV = 11,000 / (1 + 0.21)^1 + 11,000 / (1 + 0.21)^2 + 11,000 / (1 + 0.21)^3 + 11,000 / (1 + 0.21)^4

c. For investment C, we use the formula with the cash flows for investment C:

PV = 16,000 / (1 + 0.21)^1 + 48,000 / (1 + 0.21)^2

Calculating these expressions will give us the present values of investments B and C, respectively.

The present values of investments A, B, and C are $37,461.97, $29,930.99, and $48,003.16 respectively.

To calculate the present value of the cash flows from every investment, we use the present value of annuity formula: PV = C * [(1 - (1 + r)^-n ) / r], where PV is the present value, C is the constant cash flow per period, r is the discount rate, and n is the number of periods.

(a) Investment A: C = $11,000, r = 21% or 0.21, n = 6 years. PV = $11,000 * [(1 - (1 + 0.21)^-6) / 0.21] = $37,461.97.

(b) Investment B: C = $11,000, r = 21% or 0.21, n = 4 years. PV = $11,000 * [(1 - (1 + 0.21)^-4) / 0.21] = $29,930.99.

(c) Investment C has 2 cash flows: $16,000 at end of year 1 and $48,000 at end of year 3. We calculate their present value separately and sum those up. PV = $16,000 / (1 + 0.21)^1 + $48,000 / (1 + 0.21)^3 = $13,223.14 + $34,780.02 = $48,003.16.

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sin 20 = y / r

cos 70 = y/ r

sin 20 = cos 70 = 0.342

Answer:

cos 70

Answer:

a=96

b=42

c=138

Step-by-step explanation:

as lines BA and BC are equal, angles BAC and BCA are also equal, so b = 42. Now a can be found by 180 - 42 - 42 as sum of angles in a triangle is 180. The line AC is a straight line, so b + c = 180 , so c = 180 - 42 = 138

Answer:

It actually means that 50% are boys and 50% are girls.

Step-by-step explanation:

This is because 25 is the half of 50 (the total number of students. And half means 50%

Answer:

There are 40 apples in the basket.

This is because 5 apples to 3 pears have a difference of 1.66666667 when dividing 5 by 3 to show the ratio difference. Then, all you do is multiply this number by the number of total pears which would look like 24 x 1.66666667 = 40.

I hope this helped you, have an amazing day! :)

Given:

Nadia spent 1/4 of her money in skirts and 2/5 of her money on shoes

So, total =

The Least common denominator of 4 and 5 = 20

So,

So, she spent 13/20 of her money

The change will be =

So, she got 7/20 of her money.

Answer:

488

Step-by-step explanation:

You divide 28453 by 58.3053278689 and get 488.

The area is:

A = (θ/2)*R^2

The circumference is:

C = θ*R

And the area of the circle when the angle is π/4 is: 39.25 cm^2

For a circle of radius R, the area is:

A = pi*R^2

where pi = 3.14

And the circumference is:

C = 2*pi*R

Now, remember that a circle has an angle of 2pi radians, then if we only define an arc in the circle, defined by an angle θ, the area of said arc will be:

A = (θ/2pi)*pi*R^2 = (θ/2)*R^2

And the circumference is:

C = (θ/2pi)*2pi*R = θ*R

Now, we want to find the area when the circle has a radius R = 10cm and θ = pi/4

Replacing that in the area equation, we get:

A = (pi/4/2)*(10cm)^2 = (3.14/8)*(10cm)^2 = 39.25 cm^2

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The outcomes that are contained in the events are

1 - P(X) = 4/5 and 1 - P(X) is the same as P(Not X)

From the question, we have the following parameters that can be used in our computation:

X = gray colours

Given that

gray colours = 3 and 10

We have

X = 3 and 10

Not X =1, 2, 4, 5, 6, 7, 8

The probability is then calculated as

P(X) = 2/10 = 1/5

For P(Not X), we have

P(Not X) = 1 - 1/5 = 4/5

In (a), we have

P(Not X) = 1 - 1/5 = 4/5

This means that

P(Not X) = 1 - P(X)

So, the solution is

1 - P(X) = 4/5

Using the above (a) and (b) as a guide, we have the following:

1 - P(X) is the same as P(Not X)

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Answer:

24 - 3y

Step-by-step explanation:

Since the sum of the two numbers is 8, the larger number is 8 - y.

Three times the larger number: 3 (8 - y).

Simplify using Distributive property: 3 (8 - y) = 24 - 3y.

So the answer is 24 - 3y

Answer:

\(to \: calculate \: percentage \: = \frac{72}{45} \times 100 \\ \\ = 1.6 \times 100 = 160\% \\ thank \: you\)

Answer:

Its a counting number and a whole number so thirdd one

Step-by-step explanation:

Answer:

D-5 is an integer, but not a whole number.

got that right on edge!

Step-by-step explanation:

hope this helps:)

we have the expression

40+25x

Remember that

40=(2)(2)(2)(5)

25=(5)(5)

so

GCF=5

therefore

40+25x=5(8+5x)

the answer is

Answer:

Step-by-step explanation:

f(2) = 2^3 - 4(2)^2 = 8 - 4(4) = 8 - 16 = -8

g(-8)= 4(-8) + 5 = -32 + 5 = -27

C is the answer

The function which represents a graph which has been vertically shifted by 3 units is; y= log (x) + 3.

It follows from the task content that the graph which has been shifted vertically is to be identified.

For a vertical shift, it means that the y value of such graphs must have increased or decreased. This is However, evident in the equation y= log (x) + 3 and hence, is the solution.

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Using the trigonometric identities given, we get:

Recall that:

And the limit of the product is the product of the limits.

Therefore the limit of interest does not exist.

Answer

-57

Step-by-step explanation

Arithmetic sequence formula

where

• aₙ is the ,nth, term

• a₁ is the first term

• n indicates the term position

• d is the common difference

Substituting a₁ = -8, n = 32, and the 32nd term = -225, and solving for d:

Substituting a₁ = -8, n = 8, d = -7, the value of the 8th term is:

Answer:

85%

Step-by-step explanation:

Johny answered \(\frac{17}{20}\) questions correctly. To change this into percent, just multiply both the numerator and denominator by the number that makes the denominator equal 100. In this case, 5 would make 20 equal 100, so we multiply both the top and bottom by 5.

\(\frac{17}{20} *\frac{5}{5}=\frac{85}{100}\)

Your numerator will be your percentage if the denominator is 100.

Answer:

If two chords intersect in a circle, then the product of the segments of one chord equals the product of the segments of the other chord.

6(3x) = 4(4x + 1)

18x = 16x + 4

2x = 4

x = 2

The value of integral is 3.

Let's evaluate the integral over the positive half of the interval:

∫[0 to π] (cos(x) / √(4 + 3sin(x))) dx

Let u = 4 + 3sin(x), then du = 3cos(x) dx.

Substituting these expressions into the integral, we have:

∫[0 to π] (cos(x) / sqrt(4 + 3sin(x))) dx = ∫[0 to π] (1 / (3√u)) du

Using the power rule of integration, the integral becomes:

∫[0 to π] (1 / (3√u)) du = (2/3) . 2√u ∣[0 to π]

Evaluating the definite integral at the limits of integration:

(2/3)2√u ∣[0 to π] = (2/3) 2(√(4 + 3sin(π)) - √(4 + 3sin(0)))

(2/3) x 2(√(4) - √(4)) = (2/3) x 2(2 - 2) = (2/3) x 2(0) = 0

So, the value of integral is

= 3-0

= 3

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Answer:

\(3-\displaystyle \int^{\pi}_{-\pi} \dfrac{\cos x}{\sqrt{4+3 \sin x}}\; \text{d}x\approx 0.806\; \sf (3\;d.p.)\)

Step-by-step explanation:

First, compute the indefinite integral:

\(\displaystyle \int \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x\)

To evaluate the indefinite integral, use the method of substitution.

\(\textsf{Let} \;\;u = 4 + 3 \sin x\)

Find du/dx and rewrite it so that dx is on its own:

\(\dfrac{\text{d}u}{\text{d}x}=3 \cos x \implies \text{d}x=\dfrac{1}{3 \cos x}\; \text{d}u\)

Rewrite the original integral in terms of u and du, and evaluate:

\(\begin{aligned}\displaystyle \int \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&=\int \dfrac{\cos x}{\sqrt{u}}\cdot \dfrac{1}{3 \cos x}\; \text{d}u\\\\&=\int \dfrac{1}{3\sqrt{u}}\; \text{d}u\\\\&=\int\dfrac{1}{3}u^{-\frac{1}{2}}\; \text{d}u\\\\&=\dfrac{1}{-\frac{1}{2}+1} \cdot \dfrac{1}{3}u^{-\frac{1}{2}+1}+C\\\\&=\dfrac{2}{3}\sqrt{u}+C\end{aligned}\)

Substitute back u = 4 + 3 sin x:

                            \(= \dfrac{2}{3}\sqrt{4+3\sin x}+C\)

Therefore:

\(\displaystyle \int \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x= \dfrac{2}{3}\sqrt{4+3\sin x}+C\)

To evaluate the definite integral, we must first determine any intervals within the given interval -π ≤ x ≤ π where the curve lies below the x-axis. This is because when we integrate a function that lies below the x-axis, it will give a negative area value.

Find the x-intercepts by setting the function to zero and solving for x in the given interval -π ≤ x ≤ π.

\(\begin{aligned}\dfrac{\cos x}{\sqrt{4+3\sin x}}&=0\\\\\cos x&=0\\\\x&=\arccos0\\\\\implies x&=-\dfrac{\pi }{2}, \dfrac{\pi }{2}\end{aligned}\)

Therefore, the curve of the function is:

So to calculate the total area, we need to calculate the positive and negative areas separately and then add them together, remembering that if you integrate a function to find an area that lies below the x-axis, it will give a negative value.

Integrate the function between -π and -π/2.

As the area is below the x-axis, we need to negate the integral so that the resulting area is positive:

\(\begin{aligned}A_1=-\displaystyle \int^{-\frac{\pi}{2}}_{-\pi} \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&=- \left[\dfrac{2}{3}\sqrt{4+3\sin x}\right]^{-\frac{\pi}{2}}_{-\pi}\\\\&=-\dfrac{2}{3}\sqrt{4+3 \sin \left(-\frac{\pi}{2}\right)}+\dfrac{2}{3}\sqrt{4+3 \sin \left(-\pi\right)}\\\\&=-\dfrac{2}{3}\sqrt{4+3 (-1)}+\dfrac{2}{3}\sqrt{4+3 (0)}\\\\&=-\dfrac{2}{3}+\dfrac{4}{3}\\\\&=\dfrac{2}{3}\end{aligned}\)

Integrate the function between -π/2 and π/2:

\(\begin{aligned}A_2=\displaystyle \int^{\frac{\pi}{2}}_{-\frac{\pi}{2}} \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&= \left[\dfrac{2}{3}\sqrt{4+3\sin x}\right]^{\frac{\pi}{2}}_{-\frac{\pi}{2}}\\\\&=\dfrac{2}{3}\sqrt{4+3 \sin \left(\frac{\pi}{2}\right)}-\dfrac{2}{3}\sqrt{4+3 \sin \left(-\frac{\pi}{2}\right)}\\\\&=\dfrac{2}{3}\sqrt{4+3 (1)}-\dfrac{2}{3}\sqrt{4+3 (-1)}\\\\&=\dfrac{2\sqrt{7}}{3}-\dfrac{2}{3}\\\\&=\dfrac{2\sqrt{7}-2}{3}\end{aligned}\)

Integrate the function between π/2 and π.

As the area is below the x-axis, we need to negate the integral so that the resulting area is positive:

\(\begin{aligned}A_3=-\displaystyle \int^{\pi}_{\frac{\pi}{2}} \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&= -\left[\dfrac{2}{3}\sqrt{4+3\sin x}\right]^{\pi}_{\frac{\pi}{2}}\\\\&=-\dfrac{2}{3}\sqrt{4+3 \sin \left(\pi\right)}+\dfrac{2}{3}\sqrt{4+3 \sin \left(\frac{\pi}{2}\right)}\\\\&=-\dfrac{2}{3}\sqrt{4+3 (0)}+\dfrac{2}{3}\sqrt{4+3 (1)}\\\\&=-\dfrac{4}{3}+\dfrac{2\sqrt{7}}{3}\\\\&=\dfrac{2\sqrt{7}-4}{3}\end{aligned}\)

To evaluate the definite integral, sum A₁, A₂ and A₃:

\(\begin{aligned}\displaystyle \int^{\pi}_{-\pi} \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&=\dfrac{2}{3}+\dfrac{2\sqrt{7}-2}{3}+\dfrac{2\sqrt{7}-4}{3}\\\\&=\dfrac{2+2\sqrt{7}-2+2\sqrt{7}-4}{3}\\\\&=\dfrac{4\sqrt{7}-4}{3}\\\\ &\approx2.194\; \sf (3\;d.p.)\end{aligned}\)

Now we have evaluated the definite integral, we can subtract it from 3 to evaluate the given expression:

\(\begin{aligned}3-\displaystyle \int^{\pi}_{-\pi} \dfrac{\cos x}{\sqrt{4+3 \sin x}}\; \text{d}x&=3-\dfrac{4\sqrt{7}-4}{3}\\\\&=\dfrac{9}{3}-\dfrac{4\sqrt{7}-4}{3}\\\\&=\dfrac{9-(4\sqrt{7}-4)}{3}\\\\&=\dfrac{13-4\sqrt{7}}{3}\\\\&\approx 0.806\; \sf (3\;d.p.)\end{aligned}\)

Therefore, the given expression cannot be zero.

A rational function does not have any factors in the denominator that can be equal to 0, then it will not have a vertical asymptote.

An even degree  must be an even function is true. This is because a polynomial with an even degree has an even-numbered power, such as f(x)=x^2. This means that the function is symmetrical when its graph is reflected over the y-axis. This means that the graph will look the same if the x-values are reflected over the y-axis. For example, if f(3)=9, then f(-3)=9 as well.

Every polynomial of odd degree has at least one zero is true. This is because a polynomial with an odd degree will always have at least one x-value for which the equation is equal to 0. This is because the highest power of the equation must be odd, and the equation must cross the x-axis at least once. For example, f(x)=x^3 will have at least one x-value, such as x=0, where f(x)=0.

Every rational function that is not a polynomial has a vertical asymptote is false. A rational function that is not a polynomial may have a vertical asymptote, but it is not guaranteed. A vertical asymptote is created when the denominator of a rational equation has a factor that is equal to 0. This means that when this factor is equal to 0, the equation has an undefined value. If a rational function does not have any factors in the denominator that can be equal to 0, then it will not have a vertical asymptote.

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Answer:

slope = \(\frac{5}{9}\) , y- intercept = - 5

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given

5x - 9y = 45 ( subtract 5x from both sides )

- 9y = - 5x + 45 ( divide through by - 9 )

y = \(\frac{-5}{-9}\) x + \(\frac{45}{-9}\) , that is

y = \(\frac{5}{9}\) x - 5 ← in slope- intercept form

with slope m = \(\frac{5}{9}\) and y- intercept c = - 5

Answer:

i hope to know the answer

Answer:

A number line going from negative 2 to positive 2 in increments of 1. There are 4 equal spaces between each number. Point A is halfway between negative 2 and negative 1. Point B is 1 mark to the right of negative 1. Point C is 1 mark to the left of 1. Point D is 1 mark to the left of 2.

Use the drop-down menus to label the points on the number line.

Point A is at

✔ -1 2/4

.

Point B is at

✔ -3/4

.

Point C is at

✔ 3/4

.

Point D is at

✔ 1 3/4

.

Step-by-step explanation:

Branliest PLZ!!!!!!!    <3

Answer:Use the drop-down menus to label the points on the number line.

Point A is at

✔ -1 2/4

.

Point B is at

✔ -3/4

.

Point C is at

✔ 3/4

.

Point D is at

✔ 1 3/4

.

Step-by-step explanation:

also the guy above me is 100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 percent right

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Answer:

A and D are correct. This is a parallelogram, which is a quadrilateral. B is not correct because not all the sides are congruent. C is not correct. E and F are not correct because this parallelogram does not have any right angles.

What is a Right Angle Triangle?

A Right Angle Triangle is a triangle where one of the angles is equal to 90 degrees.

To calculate the values using SOHCAHTOA

 SOHCAHTOA calculate the angles and sides of the right triangle, using trigonometric function sine, cosine, and tangent. There are two triangles in which the adjacent and opposite changes based on which angle is in question, the hypotenuse always stays the same.

Where Sin A = Opposite/ Hypotenuse

            Cos A = Adjacent / Hypotenuse

   And  Tan A = Opposite / Adjacent

For question 1,

If Opposite = PR

Adjacent = PQ

Hypotenuse = QR

Sin A = 14/50

Cos A = 48/50

Tan A = 14/48

For question 2,

If Opposite = PQ

Adjacent = PR

Hypotenuse = QR

Sin A = 48/50

Cos A = 14/50

Tan A = 48/14

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On Julie's door, the images will span 210 square inches.

As Julie printed six images, the total space that the images cover is:

6 x 35 square inches = 210 square inches

Inches are measured as 1/36 of a yard in both British Imperial and American Customary measurement systems. According to some sources, the term "inch" comes from the Old English "ince" or "ynce," which in turn is said to have originated from the Roman "uncia" unit.

The name of another English unit, the ounce, is derived from the Roman word uncia. According to legend, King David I of Scotland defined the old English word "ynce" as the width of a man's thumb at the base of the nail in the year or thereabouts 1150 AD.

From the question:

Six images total, each measuring 5 by 7 inches, were printed by Julie. We must first calculate the area of each image in order to add up the overall area that these photographs cover.

One image's area is as follows:

5 inches x 7 inches = 35 square inches

As Julie printed six images, the total space that the images cover is:

6 x 35 square inches = 210 square inches

Consequently, 210 square inches of Julie's door will be covered by the images.

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The amount of money in Marianna's annuity after 6 years will be approximately $300,516.

To calculate the amount of money in Marianna's annuity after 6 years, we can use the formula for compound interest on an annuity:

A = P * ((1 + r/n)^(n*t) - 1) / (r/n)

Where:

A = the final amount in the annuity

P = the regular contribution (each quarter) = $10,000

r = annual interest rate = 8% = 0.08

n = number of compounding periods per year = 4 (since it's compounded quarterly)

t = number of years = 6

Plugging in the values:

A = 10000 * ((1 + 0.08/4)^(4*6) - 1) / (0.08/4)

Calculating this expression:

A ≈ 10000 * ((1.02)^24 - 1) / 0.02

A ≈ 10000 * (1.601032449136241 - 1) / 0.02

A ≈ 10000 * 0.601032449136241 / 0.02

A ≈ 10000 * 30.05162245681205

A ≈ 300,516.22

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Answer:

304200

Step-by-step explanation:

To find the value of P6, use the savings annuity formula

PN=d((1+r/k)N k−1)r/k.

From the question, we know that r=0.08, d=$10,000, k=4 compounding periods per year, and N=6 years. Substitute these values into the formula gives

P6=$10,000 ((1+0.08/4)6⋅4−1)/(0.08/4).

Simplifying further gives P6=$10,000 ((1.02)24−1)/(0.02) and thus P6=$304,218.62.

Rounding as requested, our answer is 304200.