Separable differential equation
y’ln^2y+ysqrtx=0 y(0)=e

The value of the composite function f(g(x)) is 2(x-8)^2

Composite functions are functions in another function. Given the following functions

f(x)=2x^2 and

g(x)=x-8

Determine f(g(x))

f(g(x)) = f(x-8)

f(x-8) = 2(x-8)^2

f(g(x)) = 2(x-8)^2

Hence the value of the composite function f(g(x)) is 2(x-8)^2

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The missing value of x will be 9.6 mL.

A ratio is a collection of ordered integers a and b represented as a/b, with b never equaling zero. A proportionate expression is one in which two items are equal.

The equation is given below.

12.5 mg : 5 mL = 24 mg : x mL

Then the value of x will be

12.5 / 5 = 24 / x

          x = (24 × 5) / 12.5

          x = 9.6 mL

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The trigonometry ratios are cos(θ) = -7/√58, sec(θ) = -√58/7 and cot(θ) = -7/3

The point on the terminal side is given as:

(x, y) = (-7, 3)

Start by calculating the hypotenuse using:

[tex]h= \sqrt{x^2 + y^2[/tex]

So, we have:

[tex]h= \sqrt{(-7)^2 + 3^2[/tex]

Evaluate

[tex]h= \sqrt{58[/tex]

The cosine is then calculated using:

cos(θ) = x/h

This gives

cos(θ) = -7/√58

The secant is then calculated using:

sec(θ) = 1/cos(θ)

This gives

sec(θ) = -√58/7

The cotangent is then calculated using:

cot(θ) = cos(θ)/sin(θ)

Where

sin(θ) = y/h

So, we have:

sin(θ) = 3/√58

So, we have:

cot(θ) = (-7/√58)/(3/√58)

This gives

cot(θ) = -7/3

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Let's prove that (sec x)(csc x) is equal to cot x + tan x

[tex]\Longrightarrow \sf (sec(x) )(csc(x))[/tex]

[tex]\Longrightarrow \sf \dfrac{1}{\cos \left(x\right)\sin \left(x\right)}[/tex]

[tex]\Longrightarrow \sf \dfrac{\cos ^2\left(x\right)+\sin ^2\left(x\right)}{\cos \left(x\right)\sin \left(x\right)}[/tex]

[tex]\Longrightarrow \sf \dfrac{\cos ^2\left(x\right)}{\cos \left(x\right)\sin \left(x\right)} + \dfrac{\sin ^2\left(x\right)}{\cos \left(x\right)\sin \left(x\right)}[/tex]

[tex]\Longrightarrow \sf \dfrac{\cos\left(x\right)}{\sin \left(x\right)} + \dfrac{\sin \left(x\right)}{\cos \left(x\right)}[/tex]

[tex]\Longrightarrow \sf cot(x) + tan(x)[/tex]

Hence student A did correctly prove the identity properly.

Also Looking at student B's work, he verified the identity properly.

So, Both are correct in their own way.

Identities used:

[tex]\rightarrow \sf sin^2 (x) + cos^2 (x) = 1[/tex]       (appeared in step 3)

[tex]\sf \rightarrow \dfrac{cos(x) }{sin(x) } = cot(x)[/tex]               (appeared in step 6)

[tex]\rightarrow \sf \dfrac{sin(x )}{cos(x) } = tan(x)[/tex]               (appeared in step 6)

Answer:

3

Step-by-step explanation:

374274 =3.74274 x 100000=3.74272x 10^5

Answer:

jjjijijijiiijijijijijijij no pliss inglés. ;D.

Answer:

x-23=.55

Step-by-step explanation:

Answer: 0.55 = x - 23

Step-by-step explanation:

let his savings = x

The asnwer is C

for finding domain look at just x-axis from left to right , because there are arrows , so domain is all real numbers or from negative infinity to positive infinity

Please give brainliest

The parabola is a downward parabola which is passing through origin and leading coefficient of the negative 2.

It's the locus of a moving point that keeps the same distance between a stationary point and a specified line. The focus is a non-movable point, while the directrix is a non-movable line.

The equation of a quadratic function, of vertex (h, k), is given by:

y = a(x – h)² + k

where a is the leading coefficient.

The equation of the parabola will be

y = -x²

The given parabola is a downward parabola which is passing through origin and leading coefficient of the negative 2.

The graph of the function is given below.

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We have that O(n²) is the theta notation for 7n² + 4n + 2.

Let's give big-Oh a formal definition:

O(g(n)) = {the set of all f such that 0 [tex]\leq[/tex] f(n) [tex]\leq[/tex] cg(n) for any n >= n₀ fulfilling positive constants c and n₀}

To show this

We need to find c and n₀ such that:

7n² + 4n + 2 <= cn² for all n >= n₀ .

Divide both sides by n², getting:

7 + 4/n + 2/(n²) <= c for all n >= n₀ .

If we choose n₀ equal to 1, then we need a value of c such that:

7 + 4 + 2 <= c

We can set c equal to 13. Now we have:

7n² + 4n + 2 <= 13n² for all n >= 1 .

Hence, 7n² + 4n + 2=O(n²)

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Caden needs to grow 4 inches tall enough to ride the Super Slide.

Multiplication or division by a numerical factor, selection of the correct number of significant figures, and unit conversion are all steps in a multi-step procedure.

Given that:-

Caden's height = 4 feet

Min height to ride the Super slide is = 52 inches

Caden's height in inches will be:-

1 feet = 12 inches

4 feet = 12 x 4 = 48 inches.

The difference between the height will be given as:-

D = 50 - 48 = 4 inches

So Caden should grow his height by 4 inches to ride the super slide.

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Answer:

4 kg

Step-by-step explanation:

........................

Answer:

4 kg

Explanation:

Let the mass of tank be 't' and water 'w'

First equation :              (when it is 1/4 filled with water)

Second equation :        (when it is filled fully with water)

Insert second equation into first equation :

[tex]\rightarrow \sf t + \dfrac{1}{4} (10.4 - t) = 5.6[/tex]

[tex]\rightarrow \sf t - \dfrac{1}{4} t + 2.6 = 5.6[/tex]

[tex]\rightarrow \sf \dfrac{3}{4} t = 5.6 - 2.6[/tex]

[tex]\rightarrow \sf \dfrac{3}{4} t = 3[/tex]

[tex]\rightarrow \sf t = 4[/tex]

The tank weights 4 kg when it is empty.

Answer:

Step-by-step explanation:

The area of Maria’s circle is 18π square units option fourth is correct.

It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)

The figure is missing.

Please refer to the attached picture for the figure.

We have given the radius of the circle as 3 units

r = 3 units

Area of circle = πr² = π(3)² = 9π square units

The area of Maria’s circle = 2(9π) = 18π square units

Thus, the area of Maria’s circle is 18π square units option fourth is correct.

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Step-by-step explanation:

On a polar plane, the shape will be a line that goes through the pi/2- pi quadrant , and 3pi/2- 2pi quadrant

On a Cartesian or rectangular plane, the shape will be a line as well passing through 2nd and 4th quadrant

Answer:

Answers are 20, 12 and 16

Step-by-step explanation:

Y=4x

for x = 5

y=4(5)

y=20

for x = 3

y=4(3)

y=12

for x = 4

y=4(4)

y=16

Answer:

X I Y

5 20

3 12

4 16

Step-by-step explanation:

since y=4 multiplied by x

so, 5x4=20

3x4=12

4x4=16

Answer:

[tex] \cfrac{61}{24} [/tex]

Step-by-step explanation:

Given expression:

[tex] \cfrac{2}{3} + \bigg(\cfrac{5}{2} \bigg) {} ^{ 2} \times \cfrac{3}{10} [/tex]

Solution:

Simplify using PEMDAS.

[tex] = \sf \cfrac{2}{3} + \cfrac{25}{4} \times \cfrac{3}{10} \\ \\ = \cfrac{2}{3} + \cfrac{15}{8} \\ \\ = \cfrac{16 +45 }{24} \\ \\ = \boxed{\cfrac{61}{24} }[/tex]

Done!

Answer:

[tex]\frac{61}{24}[/tex]

Step-by-step explanation:

[tex]\frac{2}{3}[/tex] + ( [tex]\frac{5}{2}[/tex] )² × [tex]\frac{3}{10}[/tex] ← evaluate exponent

= [tex]\frac{2}{3}[/tex] + [tex]\frac{25}{4}[/tex] × [tex]\frac{3}{10}[/tex] ← evaluate multiplication ( cancel 25 and 10 by 5 )

= [tex]\frac{2}{3}[/tex] + [tex]\frac{5}{4}[/tex] × [tex]\frac{3}{2}[/tex]

= [tex]\frac{2}{3}[/tex] + [tex]\frac{15}{8}[/tex] ← evaluate addition

= [tex]\frac{2(8)}{3(8)}[/tex] + [tex]\frac{15(3)}{8(3)}[/tex]

= [tex]\frac{16}{24}[/tex] + [tex]\frac{45}{24}[/tex]

= [tex]\frac{61}{24}[/tex]

Answer:

219,221

Step-by-step explanation:

the second number can be represented by the equation n1+2=n2

adding these expressions together you get

(n+2)+n=440

youre going to think of n now as just your first number because the equation solves for n1

with that you will get a number valued at 219

you then solve the first equation n1+2=n2 because we now know the value of n1

219+2=221

so the second numbers value is 221

Answer:

5. 540°

Step-by-step explanation:

m<a + m<c = 180°

m<h + m<f = 180°

m<k + m<m = 180°

Then m<a + m<c + m<h + m<f + m<k + m<m = 180° x 3 = 540°

Answer:

-2(10(-4))²

-2(-40)²

-2 × 1600

= -3200

Answer: = -3200

Step-by-step explanation:

took the test

Answer: 10

Step-by-step explanation:

The sum of the roots is [tex](5+3i)+(5-3i)=10[/tex], so the answer is 10

Two (2) lines are considered to be parallel if their slopes are the same (equal) and they do not intersect.

In Geometry, two (2) lines are considered to be parallel if their slopes are the same (equal) and they've different y-intercepts.

This ultimately implies that, two (2) lines are parallel under the following conditions:

m₁ = m₂

Note: m is the slope.

In conclusion, two (2) parallel lines are shown in the image attached below for more understanding,

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Answer:

∠a = 50°

∠b = 130°

∠c = 130°

Explanation:

Following Vertical Angles Theorem:

A straight line has 180° angle measure, ∠c and ∠a lies on a straight line

Also, following vertical angle theorem:

The expression are; [tex](h - g) (x) = 3x^{3} -x^{2}[/tex], [tex](h + g) (x) = 3x^{3} +x^{2}[/tex] , [tex](h.g) (-1) = -3[/tex].

The function is a type of relation, or rule, that maps one input to specific single output.

Given function;

g(x) = [tex]x^{2}[/tex]

h(x) = [tex]3x^{3}[/tex]

The expression;

[tex](h - g) (x) = 3x^{3} -x^{2}[/tex]

[tex](h + g) (x) = 3x^{3} +x^{2}[/tex]

[tex](h.g) (-1) = x^{2} .3x^{3} \\\\(h.g) (-1) = 3x^5\\\\(h.g) (-1) = 3(-1)^5\\\\(h.g) (-1) = -3[/tex]

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The composite function is given as follows:

[tex](f \circ g)(x) = \frac{2x + 6}{3x + 22}[/tex]

The domain of the composite function is: [tex]\mathbb{R} - \left\{-\frac{22}{3}, 3\right\}[/tex]

The composite function is given by:

[tex](f \circ g)(x) = f(g(x))[/tex]

In this problem, the functions are:

Hence the composite function is:

[tex](f \circ g)(x) = f\left(\frac{13}{x + 3}\right) = \frac{2}{\frac{13}{x + 3} + 3} = \frac{2(x + 3)}{13 + 3(x + 3)} = \frac{2x + 6}{3x + 22}[/tex]

For the domain, we have to remove the points outside the domain of both the primitive and the composite functions, that is, the zeroes of the denominators, hence:

[tex]x + 3 \neq 0 \rightarrow x \neq 3[/tex]

[tex]3x + 22 \neq 0 \rightarrow x \neq -\frac{22}{3}[/tex]

Hence the domain is:

[tex]\mathbb{R} - \left\{-\frac{22}{3}, 3\right\}[/tex]

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The total distance travelled is 1075.91 km.

The average speed is the total distance traveled by the object in a particular time interval. The average speed is a scalar quantity.

45 * (x +12)= 50* 1/5 + 1/2 *x

45x + 540= 10+ 0.5 x

44.5 x = 530

x= 11.91 (neglect the negative sign cause time can't be negative)

So, distance= 45* 23.91 = 1075.91 Km

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