Some please help me to solve this 2 problems
x=5,y=2

Answer:

1

Step-by-step explanation:

When dividing fractions i use the method KFC(keep flip change) :

Keep the first fraction :

\(\frac{14a^{2} }{10b^{2} }\)

Flip the second fraction :

\(\frac{15b^{2} }{21a^{2} }\)

Change the function :

÷ → ×

Now write your new equation :

\(\frac{14a^{2} }{10b^{2} }\) ×  \(\frac{15b^{2} }{21a^{2} }\)

Now multiply the numerators together and the denominators together :

14a² × 15b²  = 210a²b²

10b² × 21a² = 210a²b²

Now make this into a fraction again :

210a²b² / 210a²b²

Anything divided by itself is always 1 so :

210a²b² / 210a²b² = 1

Hope this helped and have a good day

Answer:

1. (-4 , 3) : substitute way .

2. (10 , -1) : elimination way.

3. (26/7 , -26/7 ) : elimination way.

4. ( 1 , 1) : elimination way.

Step-by-step explanation:

The distance along the unit circle between any two successive 8th roots of 1 is c) π/4.

To find the distance along the unit circle between any two successive 8th roots of 1, we can consider the concept of angular displacement.

Each 8th root of 1 represents a point on the unit circle that is evenly spaced by an angle of 2π/8 = π/4 radians.

Starting from the point corresponding to 1 on the unit circle, we can move π/4 radians to reach the first 8th root of 1. Moving π/4 radians further will bring us to the second 8th root of 1, and so on.

Since we are moving by π/4 radians for each successive 8th root of 1, the distance between any two successive 8th roots of 1 is π/4 radians.

Therefore, the correct answer is option c. π/4.

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Answer:

\( \frac{ - 4y^{6} {k}^{2} }{ - 8 {y}^{9} {k}^{5} } \)

\( = \frac{1}{2 {y}^{3} {k}^{3} } \)

Answer:

85j-6/5j

Step-by-step explanation:

The maximum rate of change of the function f at (8,0) is 8 and the direction is ĵ.

What is function?

In mathematics, a function can be defined as a relation between a set of inputs having one output each. In simple manner, a function is a relationship between inputs where each input is related to exactly one output. In every function there has a domain and codomain or range.

Given function is f(x, y) = sin(xy)

The maximum rate of change f(x, y) occurs in the direction of gradient of the function f which can be estimated as follows:

∇f(x, y)=[ ∂/∂x f(x, y)î + ∂/∂y f(x, y)ĵ]

∇f(x, y)=[ ∂/∂x (sinxy)î + ∂/∂y (sinxy) ĵ] -------(1)

The partial derivative

∂/∂x (sinxy)= (cos xy) ∂/∂x(xy)

                 = y cos (xy)

and the partial derivative

∂/∂x (sinxy)= (cos xy) ∂/∂y(xy)

                 = x cos (xy)

putting these values in equation (1) we get,

∇f(x, y)=[ y cos(xy)î + x cos(xy) ĵ]

∇f(8, 0)=[ 0 + 8 ĵ] [ since cos 0= 1]

Now,

| ∇f(8, 0) | = | 0 + 8 ĵ |

               = \(\sqrt{(0^{2} + 8^{2}) }\)

                = 8

Hence, the maximum rate of change of the function f at (8,0) is 8 and the direction is ĵ.

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Answer:

i think c

Step-by-step explanation:

hope it helps :)

Answer:

1/35 every hour

Step-by-step explanation:

The number of hours between 10pm and 7:20AM is 9 hours and 20 minutes. This is computed by noting that there are 2 hours till midnight and then 7 hours and 20 minutes till 7:20AM

So total time the water decreased = 9 hours and 20 minutes
20 minutes = 20/60 = 1/3 of an hour
So time taken in hours = 9 1/3 = 28/3 hours

4/15 of the pool depth decreased in 28/3 hours

Rate of decrease  per hour = 4/15 ÷ 28/3

=4/15 x 3/28 =(4 x 3)/(15 x 28) = 12/420

Dividing numerator and denominator by 12 gives
(12 ÷ 12)/(420 ÷ 12) = 1/35

So the water level dropped by 1/35 every hour

The time at which the initial population has doubled for r = 0.025 per year is 28.1 years, and the time T at which y(T)/K = can be calculated once we have the values of α and r.

The logistic equation is a mathematical equation used to describe population growth in a given environment. It is given by the equation \(dy/dt = ry[1 - (y/K)]\), where r is the intrinsic growth rate and K is the carrying capacity of the environment.

For part a, we can solve for the time at which the initial population has doubled by setting y(t) = 2y0 and solving for t. We can rearrange the equation to solve for t: \(t = ln(2y0/K - 1)/r\). Since \(y0 = K/3\), plugging this in gives us \(t = ln(2/3)/r\). For r = 0.025 per year, this gives us a doubling time of approximately 28.1 years.

For part b, we want to solve for the time T at which y(T)/K = . Again rearranging the equation, we get \(T = ln(αK/( -α))/r\). Plugging in the given values of α and , we get \(T = ln(αK/(1 - α))/r\). Therefore, the time T at which y(T)/K = can be calculated once we have the values of α and r.

The time at which the initial population has doubled for r = 0.025 per year is 28.1 years, and the time T at which y(T)/K = can be calculated once we have the values of α and r.

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Answer:

∠a= 65°, ∠b= 115°, ∠c= 25°

Step-by-step explanation:

The sum of the angles in a triangle is 180°. This is abbreviated to '∠ sum of ∆'.

∠c +55° +60° +40°= 180° (∠ sum of ∆PQR)

∠c +155°= 180°

∠c= 180° -155°

∠c= 25°

∠a +60° +55°= 180° (∠ sum of ∆PQS)

∠a +115°= 180°

∠a= 180° -115°

∠a= 65°

The sum of the angles on a straight line is 180°. It's abbreviation is 'adj. ∠s on a str. line'.

∠b +∠a= 180° (adj. ∠s on a str. line)

∠b +65°= 180°

∠b= 180° -65°

∠b= 115°

This is the complement of both flips coming up heads, so the probability is 3/4. The expected value of X is -$1.

To find the expected value of the random variable X, we need to calculate the weighted average of its possible outcomes based on their probabilities.

Given:

If both flips come up heads, X = -7 (loss of $7)

If at least one flip comes up tails, X = 1 (win of $1)

Let's calculate the probabilities of each outcome:

Both flips come up heads:

The probability of getting a head on a fair coin flip is 1/2.

Since the flips are independent events, the probability of getting two heads in a row is (1/2) * (1/2) = 1/4.

At least one flip comes up tails:

This is the complement of both flips coming up heads, so the probability is 1 - 1/4 = 3/4.

Now, let's calculate the expected value of X:

E(X) = (-7) * P(X = -7) + (1) * P(X = 1)

E(X) = (-7) * (1/4) + (1) * (3/4)

= -7/4 + 3/4

= -4/4

= -1

Therefore, the expected value of X is -$1.

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Answer:

Step-by-step explanation:

it is 6 because it is there 2 times

Answer:

a. 54, b. 117, c. 63

Step-by-step explanation:

a. Angle 11 is corresponding to angle 1, which is linear to angle 2, which is 126 degrees. So angle 11 is 180 - 126 = 54 degrees

b. Angle 8 corresponds to angle 14, which is 117 degrees.

c. Angle 7 is linear to angle 8, so it is 180 - 117 = 63 degrees

Answer:

a or <11 is 54 degrees, b or <8 is 117 degrees, c or <7 is 63 degrees

Step-by-step explanation:

A. <2 = <12, <12 + <11 = 180, 180 - 126 = 54

B. <14 = <8, 117 = 117

C. <7 + <8 = 180, 180 - 117 = 63

Step-by-step explanation:

Using Cosine rule, we have:

q² = r² + s² - 2(r)(s)(cosQ)

= 380² + 390² - 2(380)(390)(cos48°)

= 98169.688cm²

Hence q = 313cm. (nearest centimeter)

The required value of side q is 313 cm for the triangle ΔQRS.

A triangle is a geometric figure with three edges, three angles and three vertices. It is a basic figure in geometry.

The sum of the angles of a triangle is always 180°

Given that,

In triangle QRS side r = 380 cm, side s = 390 cm and angle Q = 48°.

To find the length of the side q,

Use cosine rule,

\(cos Q = \frac{(r^2 + s^2 - q^2)}{(2\times r \times s)}\)

Substitute the values here,

\(cos 48 = \frac{(380)^2 + (390)^2- q^2}{2\times380 \times390} \\\)

\(0.67 = \frac{144400 + 152100 - q^2}{296400}\)

198,588 = 296500 - q²

q² = 97912

q = 312.90

q = 313 cm

The value of side q is 313 cm.

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Answer:

X = 6.2m

Step-by-step explanation:

118 - 19x =

Answer:

the length would be 40

Step-by-step explanation:

step 1) multiply 19 for both short sides = 38

step 2) subtract from total perimiter = 80

step 3) 80 divided by 2 to calculate length/long side = 40

Answer:

i thing is 1

Step-by-step explanation:

Answer:

$1

Step-by-step explanation:

In order to get the sales tax, you have to perform the multiplication operation by multiplying $12 by 8%.

Let x be the sales tax.

x = $12 x 8%

x = 12 x 0.08

x = 0.96

To round off the answer to the nearest cent, you have to look for the last number in the cents' place. If the number is 5 or above, you have to add 1 to the number next to it. If it's below 5, you just have to copy the values.

In the case above, the last number in the cents' place is 6. This is above 5, so we have to add 1 to 9, which will make it 100 cents or $1.

So, the sales tax is $1.

20 milliliters is equal to 1.352037 tablespoons. To convert any amount of milliliters to tablespoons, simply divide the volume in milliliters by 14.7867648.

A milliliter (mL) is a unit of volume in the metric system. It is equal to one cubic centimeter (cc). One tablespoon (tbsp) is equal to 14.7867648 milliliters (mL). To convert 20mL to tablespoons, we can use the formula:

Tablespoons = milliliters ÷ 14.7867648

To calculate the number of tablespoons, we divide 20 by 14.7867648.

Tablespoons = 20 ÷ 14.7867648

Tablespoons = 1.352037

Therefore, 20 milliliters is equal to 1.352037 tablespoons. To convert any amount of milliliters to tablespoons, simply divide the volume in milliliters by 14.7867648.

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The surface area of the rectangular prism is 88 square inches.

Given that:

Length, L = 6 inches

Width, W = 2 inches

Height, H = 4 inches

Let the prism with a length of L, a width of W, and a height of H. Then the surface area of the prism is given as

SA = 2(LW + WH + HL)

SA = 2(6 x 2 + 2 x 4 + 4 x 6)

SA = 2 (12 + 8 + 24)

SA = 2 x 44

SA = 88 square inches

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Answer:

14, 4

Step-by-step explanation:

First things first, we can name out pairs with the ratio of 7:2.

7, 2

14, 4

21, 6

We can then test these pairs out with the first condition and find the answer.

The least common multiple has to be 28:

LCM(7, 2) = 14

LCM(14, 4) = 28

Ah, ha! We can see that the least common multiple of 14 and 4 is 28.

Answer: 59

Step-by-step explanation:

(13 + 9) + 37

13 + 9 = 22

22 + 37

59

Answer:

Step-by-step explanation:

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Let's evaluate :

The hierarchical database model is based on a tree structure, where data is organized in a parent-child relationship. Each parent segment can have multiple child segments, but each child segment has only one parent.

In this model, data access is typically navigated from the top-level parent segment to its child segments in a hierarchical manner. The parent-child relationships provide a clear structure for organizing and representing data. However, it also means that a lack of a parent segment or a child segment is not allowed in this model.

Compared to a matrix structure, where segments can have relationships with multiple other segments, the hierarchical model is more rigid in its one-to-many relationship between parent and child segments.

However, it may pose challenges when dealing with complex or interrelated data that doesn't fit neatly into a hierarchical structure.

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Answer:D

Step-by-step explanation:

It’s D because 18 chocolate chip muffins and there are 9 blueberry muffins so for every blueberry muffin there is 2 chocolate chip muffins you could also do 18/9 and 2

The exact value of the expression tan(π/6) sin(5π/3)⋅cos(-3π/4) is -√3/2.

We have tan(π/6). The angle π/6 is equivalent to 30 degrees. The tangent of 30 degrees is √3/3.

We have sin(5π/3). The angle 5π/3 is equivalent to 300 degrees. In the unit circle, the sine value at 300 degrees is -√3/2.

Finally, we have cos(-3π/4). The angle -3π/4 is equivalent to -135 degrees. In the unit circle, the cosine value at -135 degrees is -√2/2.

Multiplying these values together, we have (√3/3) * (-√3/2) * (-√2/2). Simplifying, we get (√3 * √3 * √2) / (3 * 2 * 2) = (√3 * √2) / 12.

Taking the negative sign into account, the final value is -√3/2, which is approximately -0.866.

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The center of the circle is at the point (-5,11) and has the radius of 3 units.

The equation of the circle will be,

So on the first day of school, Noah had a total of 11 box tops (10 from his grandma and 1 from that day). From this point on, both boys will be collecting one box top per day.

Noah and Carter are both collecting box tops for their school. They have agreed to bring in one box top per day, starting on the first day of school. However, Carter had a head start because his aunt sent him 15 box tops before school began. This means that on the first day of school, Carter had a total of 16 box tops (15 from his aunt and 1 from that day). On the other hand, Noah's grandma saved 10 box tops for him, and he added those to his collection on the first day of school. So on the first day of school, Noah had a total of 11 box tops (10 from his grandma and 1 from that day). From this point on, both boys will be collecting one box top per day.

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Answer:

The answer will be -300

Step-by-step explanation:

Doing this in a calculator, it will give you -300

121500 twins birth

In order to determine the number of birth in 2000, we will use the expressionn as shown:

Note that the total percent of twins birth initially is 100%

x is the approximate twin births in 2000.

Simplify the result to determine the value of x

Divide both sides by 1.14

Hence the total number of twin birth in 2000 were approximately 121500 twins birth

\(\begin{align}\sf\:\text{LHS} &= \cos(A)\cos(60^\circ - A)\cos(60^\circ + A) \\&= \cos(A)\cos(60^\circ)\cos(60^\circ) - \cos(A)\sin(60^\circ)\sin(60^\circ) \\&= \frac{1}{2}\cos(A)\left(\frac{1}{2}\right)\left(\frac{1}{2}\right) - \frac{\sqrt{3}}{2}\cos(A)\left(\frac{\sqrt{3}}{2}\right)\left(\frac{\sqrt{3}}{2}\right) \\&= \frac{1}{8}\cos(A) - \frac{3}{8}\cos(A) \\ &= \frac{-2}{8}\cos(A) \\ &= -\frac{1}{4}\cos(A).\end{align} \\\)

Now, let's calculate the value of \(\sf\:\cos(3A) \\\):

\(\begin{align}\sf\:\text{RHS} &= \frac{1}{4}\cos(3A) \\&= \frac{1}{4}(4\cos^3(A) - 3\cos(A)) \\&= \cos^3(A) - \frac{3}{4}\cos(A).\end{align} \\\)

Comparing the \(\sf\:\text{LHS} \\\) and \(\text{RHS} \\\), we have:

\(\sf\:-\frac{1}{4}\cos(A) = \cos^3(A) - \frac{3}{4}\cos(A). \\\)

Adding \(\sf\:\frac{1}{4}\cos(A) \\\) to both sides, we get:

\(\sf\:0 = \cos^3(A) - \frac{2}{4}\cos(A). \\\)

Simplifying further:

\(\sf\:0 = \cos^3(A) - \frac{1}{2}\cos(A). \\\)

Factoring out a common factor of \(\sf\:\cos(A) \\\), we have:

\(\sf\:0 = \cos(A)(\cos^2(A) - \frac{1}{2}). \\\)

Using the identity \(\sf\:\cos^2(A) = 1 - \sin^2(A) \\\), we can rewrite the equation as:

\(\sf\:0 = \cos(A)(1 - \sin^2(A) - \frac{1}{2}). \\\)

Simplifying:

\(\sf\:0 = \cos(A)(1 - \frac{3}{2}\sin^2(A)). \\\)

Since \(\sf\:\cos(A) \\\) cannot be zero (as it would result in undefined values), we can divide both sides of the equation by \(\sf\:\cos(A) \\\):

\(\sf\:0 = 1 - \frac{3}{2}\sin^2(A). \\\)

Rearranging the terms:

\(\sf\:\sin^2(A) = \frac{2}{3}. \\\)

Taking the square root of both sides, we get:

\(\sf\:\sin(A) = \pm\sqrt{\frac{2}{3}}. \\\)

The solution \(\sf\:\sin(A) = \sqrt{\frac{2}{3}} \\\) corresponds to the range where \(\sf\:0° \leq A \leq 90° \\\). Therefore, the solution \(\sf\:\sin(A) = \sqrt{\frac{2}{3}} \\\) is valid.

Hence, we have proved that:

\(\sf\:\cos(A)\cos(60^\circ - A)\cos(60^\circ + A) = \frac{1}{4}\cos(3A). \\\)

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\textcolor{red}{\underline{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

Answer:

Given:

To Prove:

cosAcos(60°-A)cos(60°+A) = 1/4 cos3A

Solution:

Here are the steps in detail:

1. Expanding cosAcos(60°-A)cos(60°+A) using the product-to-sum identities:

=cosAcos(60°-A)cos(60°+A)

=(cosA)(cos(60°-A)cos(60°+A))

=(cosA)(1/2cos(60°-2A) + 1/2cos(60°+2A))

=(cosA)(1/2cos(-A) + 1/2cos(120°))

2. Substituting cos(60°-A) = cos(60°+A) = 1/2 into the expanded expression:

= cosA(1/2cos(-A) + 1/2cos(120°))

=cosA(1/2(1/2cosA) + 1/2(-1/2))

= cosA(1/4cosA - 1/4)

= (1/4)cosAcosA - (1/4)cosA

=(1/4)cos3A

3. Simplifying the resulting expression to obtain 1/4 cos3A:

=(1/4)cosAcosA - (1/4)cosA

=(1/4)cosA(cosA - 1)

=(1/4)cos3A

Therefore, we have proven that cosAcos(60°-A)cos(60°+A) = 1/4 cos3A. Hence Proved.

Answer:

b

Step-by-step explanation: