Find the value of each variable. I’ll mark you as a brainliest

Answer:

a) 12cm

b) 3cm

c)12cm

brainliest plzz

Answer:

Answer for a)12 b)3 c)12

Step-by-step explanation:

a)12 b)3 c)12

Answer: D

Step-by-step explanation: y=2 so 2+2=4+1=5

Answer: Step-by-step explanation:

To find the average rate of change of a function over an interval, we can use the following formula:

average rate of change = (y2 - y1)/(x2 - x1)

Where x1 and x2 are the values of x at the beginning and end of the interval, and y1 and y2 are the corresponding values of the function at those points.

In this case, we are asked to compare the average rate of change of the functions g(x) and f(x) over the interval where -1≤x≤3.

For the function g(x) = x²+6x, we can plug in the given values for x1, x2, y1, and y2 to find the average rate of change:

average rate of change = (g(3) - g(-1))/(3 - (-1))

= (9 + 18 - (1 - 6))/(4)

= 27/4

= 6.75

For the function f(x) = 2, we can plug in the given values for x1, x2, y1, and y2 to find the average rate of change:

average rate of change = (f(3) - f(-1))/(3 - (-1))

= (2 - 2)/(4)

= 0

Since the average rate of change of the function g(x) is greater than the average rate of change of the function f(x), the function g(x) has a greater average rate of change over the interval where -1≤x≤3.

I hope this helps clarify the comparison of the average rate of change for these two functions. Do you have any other questions?

The volume of the composite figure is 6,330.24 in^3

We know that the volume of half a sphere of radius R is:

V = (2/3)*pi*R^3

Here we know that pi = 3.14 and R = 12 inches, then the volume is:

V = (2/3)*3.14*(12 in)^3 = 3,617.28 in^3

And the volume of a cone of height H and radius R is:

v = (1/3)*pi*R^2*H

So here the volume is:

v = (1/3)*3.14*(12in)^2*18in = 2,712.96 in^3

Then the total volume is:

3,617.28 in^3 +  2,712.96 in^3 = 6,330.24 in^3

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Answer:

7x+5-3x+12

7x-3x+12+5

4x+17

Answer:

P=3, q=-1

Step-by-step explanation:

4p+3q=9 equation 1

2p+3q=3 equation 2

-4p-3q=-9 multiply equation 1 by -1 to eliminate q

-2p+0=-6 add above 2 equations

-2p=-6

p=3

solve for q by inserting p value into either equation

2p+3q=3

2(3)+3q=3

6+3q=3

3q=-3

q=-1

The coordinates of the reflected point P' will be (4, -3).

When a point is reflected over the x-axis, its y-coordinate changes sign.

In this case, the point P has coordinates (4,3).

To reflect it over the line x=3, we need to keep its x-coordinate the same and change its y-coordinate to its opposite.

So, the x-coordinate of the reflected point will still be 4, but the y-coordinate will become -3.

Therefore, the coordinates of the reflected point P will be (4, -3).

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Answer:

Step-by-step explanation:

The value of surface integral using the Divergence Theorem is \(729\pi\) .

Divergence Theorem states that the surface integral of a vector field over a closed surface, is equal to the volume integral of the divergence over the region inside the surface. Mathematically the it can be calculated using the formula:\(\int\int\int\limit{ }_V(\delta \cdot F)=\int\int(F \cdot n)dS\)

The divergence of F is

\(div F=\frac{d}{dx}(2x^{3}+y^{3})+\frac{d}{dy}( y^{3} +z^{3})+\frac{d}{dz}3y^{3} z\)

\(div F=6x^{2}+3y^{2}+3y^{2}\)

Let E be the region \({(x,y,z):0\leq z\leq 9-x^{2} -y^{2}\) then by divergence theorem we have \(\int \int\limits^{}_s {F\cdot n\times dS} =\int\int\int\limits^{}_E divFdV=\int\int\int\limits^{}_E(6x^2+6y^2)dV\)

Now we find the value of the integral:

\(=\int\limits^{2\pi}_0\int\limits^3_0\int\limits^{9-r^2}_0(6r^2)rdzdrd{\theta}\\=\int\limits^{2\pi}_0 \int\limits^3_0(9-r^2)6r^3drd{\theta}\\=2\pi\int\limits^3_0 {(54r^3-6r^5)} dr\\\)

\(=2\pi\times \frac{729}{2}\\=729\pi\)

Thus we can say that the value of the integral for the surface around the paraboloid is given by \(729\pi\).

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Answer:

80%

Step-by-step explanation:

The simplified expression of \(\frac{x^{3}-8x^{2}}{x^2-64}\) is \(\frac{x^2}{x + 8}\)

The expression is given as:

\(\frac{x^{3}-8x^{2}}{x^2-64}\)

Factor the numerator

\(\frac{x^{2}(x-8)}{x^2-64}\)

Express the denominator as a difference of two squares

\(\frac{x^{2}(x-8)}{(x-8)(x + 8)}\)

Cancel out the common factor

\(\frac{x^2}{x + 8}\)

Hence, the simplified expression of \(\frac{x^{3}-8x^{2}}{x^2-64}\) is \(\frac{x^2}{x + 8}\)

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Answer:

2.460375e+15

Step-by-step explanation:

HOPE THIS HELPS

:)

Answer:

Step-by-step explanation:

To solve this problem, we can use the following formulae for the volume of a cylinder and a hemisphere:

Volume of a cylinder = πr²h

Volume of a hemisphere = 2/3πr³/2

where r is the radius of the cylinder or hemisphere, and h is the height of the cylinder.

(a) To find the length of the cylinder, we can subtract the combined length of the two hemispheres from the total length of the capsule:

Length of cylinder = Total length of capsule - 2 × radius of hemisphere

Length of cylinder = 20 mm - 2 × 3 mm (radius of hemisphere)

Length of cylinder = 14 mm

(b) To find the volume of the cylinder, we need to know the radius and height. Since the width of the capsule is given as 6 mm, and we know that the cylinder runs the full length of the capsule, we can use the following formula to find the radius of the cylinder:

Width = 2 × radius of hemisphere + diameter of cylinder

6 mm = 2 × 3 mm + diameter of cylinder

Diameter of cylinder = 6 mm

Radius of cylinder = 3 mm

Now we can use the formula for the volume of a cylinder to find the volume of the cylinder:

Volume of cylinder = πr²h

Volume of cylinder = π(3 mm)² × 14 mm

Volume of cylinder ≈ 395.8 mm³ (to 3 significant figures)

(c) The radius of each hemisphere is 3 mm (since they have the same radius as the cylinder), so we can use the formula for the volume of a hemisphere to find the volume of each hemisphere:

Volume of hemisphere = 2/3πr³/2

Volume of hemisphere = 2/3π(3 mm)³/2

Volume of hemisphere ≈ 56.55 mm³ (to 3 significant figures)

(d) To find the total volume of the capsule, we can add the volumes of the cylinder and the two hemispheres:

Total volume of capsule = Volume of cylinder + 2 × Volume of hemisphere

Total volume of capsule ≈ 509.9 mm³ (to 3 significant figures)

Therefore, the length of the cylinder is 14 mm, the volume of the cylinder is approximately 395.8 mm³, the volume of each hemisphere is approximately 56.55 mm³, and the total volume of the capsule is approximately 509.9 mm³.

Step-by-step explanation:

\(\frac{8}{5}\)÷6\(\frac{3}{4}\)

First, simplify the 6\(\frac{3}{4}\) to an improper fraction, which is:

\(\frac{27}{4}\)

Next rewrite the equation using the improper fraction:

\(\frac{8}{5}\)÷\(\frac{27}{4}\)

Now, in order to divide the fraction, we will need to flip the second fraction over, and then multiply the two fractions together. A great way to remember this is the phrase Copy Dot Flip - Copy the first fraction, put a dot for multiplication, and flip the second fraction.

\(\frac{8}{5}\)·\(\frac{4}{27}\)

Finally, multiply together and simplify/reduce if needed:

The final answer is \(\frac{32}{135}\) and no simplification or reduction is needed

Answer:

C

Step-by-step explanation:

Formula for the volume of a cone :

Volume (cone) = 1/3πr²h

===========================================================

Given :

⇒ r = 4 units

⇒ h = 21 units

============================================================

Solving :

⇒ Volume (cone) = 1/3 × π × (4)² × 21

⇒ Volume (cone) = 16 × 7 × π

⇒ Volume (cone) = 112π units²

Answer:

\(\sf C. \quad 112 \pi \:units^2\)

Step-by-step explanation:

\(\textsf{Volume of a cone}=\sf \dfrac{1}{3} \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}\)

Given:

Substituting the given values into the formula:

\(\implies \sf Volume=\dfrac{1}{3} \cdot \pi \cdot 4^2 \cdot 21\)

\(\implies \sf Volume=112 \pi \:units^2\)

Answer:

4^19

Step-by-step explanation:

The answer is 1.C 2.$500

Answer:

to convey the parametric expression to be use the explosions

Answer:

6 and 2

Step-by-step explanation:

Let the first and second numbers be x and y respectively.

x = 4 + y..... (1)

2x = 4 + 4y...... (2)

Using the substitution method from Eqn(1) into (2)

Anywhere we see x in Eqn(2) we substitute it with 4 + y

I. E. 2(4 + y) = 4 + 4y

8 + 2y = 4 + 4y

Collect like terms.

8 - 4 = 4y - 2y

4 = 2y

.: y = 2

Put y = 2 in Eqn(1), and we have;

x = 4 + 2

x = 6.

.: the first number is 6 and the second number is 2.

Option C is correct.

The perimeter of a rectangle is given by two times the length plus two times the width, so we have:

Therefore the perimeter's expression is 26u + 14v

Answer:

come india

Step-by-step explanation:

ok

Check the picture below.

so the parabolic path of the object is more or less like the one shown below in the picture, now this object has an initial of 1240 ft, as it gets thrown from the ski lift, so from 0 seconds is already higher than 1000 feet.

\(h=-16t^2+32t+1240\hspace{5em}\stackrel{\textit{a height of 1000 ft}}{1000=-16t^2+32t+1240} \\\\\\ 0=-16t^2+32t+240\implies 16t^2-32t-240=0\implies 16(t^2-2t-15)=0 \\\\\\ t^2-2t-15=0\implies (t-5)(t+3)=0\implies t= \begin{cases} ~~ 5 ~~ \textit{\LARGE \checkmark}\\ -3 ~~ \bigotimes \end{cases}\)

now, since the seconds can't be negative, thus the negative valid answer in this case is not applicable, so we can't use it.

So the object on its way down at some point it hit 1000 ft of height and then kept on going down, and when it was above those 1000 ft mark  happened between 0 and 5 seconds.

Alex can buy at most 4 pounds of tomatoes

Let:

a represent pounds of tomatoes to buy

3a represent pounds of black beans to buy

Total cost of each ingredient that can be bought = number of pounds x price per pound

Tomatoes = a x $1.60 = 1.60a

Black beans = 3a x $1.70 = 5.1a

1.60a + 5.1a = 26.80

Add similar terms

6.7a = 26.80

Divide both sides of the equation by 6.7

a = 4 pounds

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The algebraic expression for 5 more than z is Z + 5.

Given,

5 more than z.

We need to find the algebraic expression.

What are the different algebraic expressions?

We have,

Examples:

- 3 more than M =  M + 3

- 3 less than M =  M - 3

- 3 times M = 3 x M

- 3 times M less than 2 = 3M - 2

- 3 times M more than 2 = 3M + 2

Find the algebraic expression for 5 more than Z.

We have,

5 more than Z = Z + 5

Thus the algebraic expression for 5 more than z is Z + 5.

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Answer:

The answer is 7

Step-by-step explanation:

Answer:

3(x-9)=40

Step-by-step explanation:

Because distributive property is when you doe something that is in parenthesis. and it's in parenthesis.

A rational number is a number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q.

Irrational numbers are all the real numbers which are not rational numbers. That is, irrational numbers cannot be expressed as the ratio of two integers.

Remember that decimals with repeating patterns

Answer: 90.95

Step-by-step explanation:

85x0.07= 5.95(tax)

85+5.95=90.95(total)

Answer:

See below.

Step-by-step explanation:

Divide to turn the percentage into a decimal.

\(\frac{7}{100} =0.07\)

Multiply to find the total amount of tax.

\(85*0.07=5.95\)

Add it to the total.

\(85+5.95=90.95\)

Answer: \(90.95\)

:)

Answer:

B

Step-by-step explanation:

25/10=2.5

Answer:

2.5

Step-by-step explanation: