MATHEMATICS HIGH SCHOOL

Solve for y. -3(y-5)=24

Answers

Answer 1

Answer:

-3y+15=24

-3y=9

3y=-9

y=-3

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What is if g(x,y,z) = x + y and S is the first octant portion of the plane 2x + 3y + z = 6 ?

Answers

The question asks for the value of $I=\int\int_Sx+y\textrm{ }dS$ where $S=\{(x,y,z)\mid2x+3z+y=6,x\ge0,y\ge0,z\ge0\}$ .

First let's look at what that surface looks like.

Letting $y=z=0$ yields $x=3$
Letting $x=z=0$ yields $y=2$
Letting $x=y=0$ yields $z=6$

Therefore $S$ is the area of the triangle defined by the three points $(3,0,0),(0,2,0),(0,0,6)$ .

We can thus reformulate the integral as $I=\int_(z=0)^6\int_(x=0)^(6-z)x+ydxdz$ .

By definition on the plane $y=\frac{6-2x-z}3$ thus $I=\int_(z=0)^6\int_(x=0)^(6-z)x+\frac{6-2x-z}3dxdz=\int_(z=0)^6\int_(x=0)^(6-z)2+\frac x3-\frac z3 dxdz$

$I=\int_(z=0)^6\left[2x+\frac{x^2}6-\frac{zx}3\right]_(x=0)^(6-z)dz=\int_(z=0)^62(6-z)+\frac{(6-z)^2}6-\frac{z(6-z)}3\right]dz$

$I=\int_(z=0)^6\frac{z^2}2-6z+18=\left[\frac{z^ 3}6-3z^2+18z\right]_(z=0)^6=36-108+108$

Hence $\boxed{I=\int\int_Sx+y\textrm{ }dS=36}$

How many triangles can be constructed with angles measuring 35º, 62º, and 83º?A. 0

B. 1

C. 2

D. an infinite number

Answers

B)OPTION B only 1 is your answer.

You have 5 pounds and 10 ounces of laundry. Your washer has a capacity of 7 pounds. How many more ounces of laundry would you need to make a full load?

Answers

7 pounds = 16 pounds and 1 pound = 6 pounds and 16 ounces.

(6 pounds + 16 ounces) minus (5 pounds + 10 ounces) = 1 pound + 6 ounces

(6pounds+16ounces)-(5pounds+10ounces)=1pounds +6ounces

What is the closed linear form for this sequence given a1 = 0.3 and an+ 1 = an + 0.75?
A) an = 0.45 - 0.75n
B) an = 0.45 + 0.50n
C) an = -0.45 + 0.75n
D) an = -0.45 - 0.75n

Answers

C) an = -0.45 + 0.75n

What is the solution to the following equation? 5x + 7x = 60

Answers

Answer:

5x+7x=60

12x=60

x=60/12=5

Step-by-step explanation:

The volume of a solid right pyramid with a square base is v units3 and the length of the base edge is y units. which expression represents the height of the pyramid? units (3v – y2) units (v – 3y2) units units

Answers

we know that

The volume of a solid right pyramid with a square base is equal to

$V=(1)/(3)*[ area\ of\ the\ base]*height$

area of the base is the area of a square

$area\ of\ the\ base=y^(2)\ units^(2)\nV=v\ units^(3)$

Substitute the values in the formula of volume

$v=(1)/(3)*[ y^(2)]*height$

solve for the height

$v=(1)/(3)*[ y^(2)]*height\n \nheight=(3v)/(y^(2))\ units$

therefore

the answer is

$height=(3v)/(y^(2))\ units$

3v/y² units

Further explanation

Given:

The volume of a solid right pyramid with a square base is v units³
The length of the base edge is y units.

Question:

Which an expression represents the height of the pyramid?

The Process:

We will solve the problem of a geometric solid.

Let us recall the formula of volume of a right pyramid:

$\boxed{ \ V = (1)/(3) * base \ area * height \ }$

Because the base is square, we use the formula for square area, i.e., side times side.

Let us find out the height of the pyramid.

$\boxed{ \ Height = (3v)/(y * y) \ }$

Thus, an expression represents the height of the pyramid is $\boxed{\boxed{ \ (3v)/(y^2) \ }}$ units

Learn more

What is the volume of each prism? brainly.com/question/414021
The volume of rectangular prism brainly.com/question/11613210
Express the volume of the box as a function of the length of the edge of the base. What is its domain? brainly.com/question/4925904

Keywords: the volume of a solid right pyramid, a square, the length of the base edge, an expression, represent, the height, the formula, a geometric solid, units

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