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2 years ago

Solve for M in the proportion below

Mathematics

2 answers:

kolbaska11 [484]2 years ago

8 0

Answer:

m = 3 * 51 / 34 = 4.5

Step-by-step explanation:

multiply both sides by 51 to isolate m

tresset_1 [31]2 years ago

3 0

Answer:

m=4.5

Step-by-step explanation:

34*m=3*51 (we cross multiply)

34m=153

m=4.5

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Find a unit vector orthogonal to the plane containing the points A= 1,0,0 , B= 3,−1,−3 , and C= 1,3,−2 .

zysi [14]

Answer:

unit normal vector n will be n=(a,b,c) = (4/√171,11/√171,6/√171)

Step-by-step explanation:

There are several ways to solve this problem

1) build 2 vectors AB and BC such that the vectorial product ABxBC is the orthogonal vector to the plane , then find unit vector

2) since the 3 points belongs to the plane solve a linear system of 4 equation with 4 variables

for the second solution , the equation of the plane with normal vector n=(a,b,c) and containing the point (x₀,y₀,z₀) is

a*(x-x₀)+b*(y-y₀)+c*(z-z₀) =0

and

a²+b²+c² = 1 (unit vector)

then choosing A=(x₀,y₀,z₀)=(1,0,0)

a*(x-1)+b*(y-0)+c*(z-0) =0

for B

a*(3-1)+b*(-1-0)+c*(-3-0) =0

1) 2*a - b - 3*c =0

for C

a*(1-1)+b*(3-0)+c*(-2-0) =0

2) 3*b - 2*c=0 → b= 2/3*c

replacing in 1)

2*a - 2/3*c - 3*c =0

2*a-11/3*c=0 → a=11/6*c

thus

a²+b²+c² = 1

(11/6*c)²+(2/3*c)²+c² = 1

(121/36+4/9+1)*c² = 1

171/36*c²=1 → c= 6/√171

therefore

a=11/6*c = 11/6*6/√171= 11/√171

b=2/3*c= 2/3*6/√171= 4/√171

then the unit normal vector n will be

n=(a,b,c) = (4/√171,11/√171,6/√171)

5 0

4 years ago

The greatest of four consecutive even integers is 14 less than twice the smallest integer. What are the integers

kakasveta [241]

20,22,24,26 is the answer

7 0

3 years ago

El tamaño de cierto cultivo de bacterias se multiplica por 2 cada 30 minutos. Si suponemos que el cultivo tiene inicialmente 256

Oduvanchick [21]

Answer:

La población de bacterias después de tres horas es de $2^{14}$ bacterias.

Step-by-step explanation:

En este enunciado observamos un caso de progresión geométrica, en donde la población de bacterias se duplica cada treinta minutos, es decir:

$\frac{p(n\cdot\Delta t)}{p(0)} = 2^{n}$ (1)

Donde:

$\Delta t$ - Intervalo de tiempo requerido para el incremento geométrico de la población, en minutos.

$n$ - Número de períodos para incremento geométrico, sin unidad.

Sabemos que la población inicial de bacterias es 256 y que 3 horas son 6 veces 30 minutos. Entonces, tenemos la siguiente razón:

$\frac{p(6\cdot \Delta t)}{p(0)} = 2^{6}$ (2)

Si sabemos que $p(0) = 256$ , entonces $p(6\cdot \Delta t)$ es:

$p(6\cdot \Delta t) = 2^{6}\cdot p(0)$

$p(6\cdot \Delta t) = 2^{6}\cdot (256)$

$p(6\cdot \Delta t) = 2^{6}\cdot 2^{8}$

$p(6\cdot \Delta t) = 2^{14}$

La población de bacterias después de tres horas es de $2^{14}$ bacterias.

4 0

3 years ago

PLEASE HELP! PLEASE HELP! PLEASE HELP!<br> The answer choices are in the pictures also.

sashaice [31]

(5 * 3) * 12 = 5 * (3 * 12)

3 0

4 years ago

Herny made muffins, brownies, and cookies to sell at the county fair. He used 5 3/8 cups for mthe muffins, 4 2/3 cups for the br

Delvig [45]

Answer:

17 13/24 cups of sugar

Step-by-step explanation:

Muffins = 5 3/8 cups of sugar

Brownies = 4 2/3 cups of sugar

Cookies = 7 1/2 cups of sugar

Total cups of sugar used = Muffins + Brownies + Cookies

= 5 3/8 + 4 2/3 + 7 1/2

= 43/8 + 14/3 + 15/2

= 129+112+180/24

= 421 / 24

= 17 13/24 cups of sugar

Equivalent to 17.5417 cups of sugar

Approximately about 18 cups of sugar to an whole number

3 0

3 years ago