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10 months ago

For each problem, identify the variables, write the equations, and solve

Mathematics

1 answer:

Ronch [10]10 months ago

5 0

Let the 4-passenger cars be represented with F

Let the 6-passenger cars be represented with S

Rocket Coaster has 15 cars

So that F + S = 15 ----- Equation 1

Also, we were told that the total room for 72 passenger

so that 4F + 6S = 72 ----- Equation 2

Solving the two equations simultaneously using the substitution method,

Step 1

From equation 1:

Make F the subject of the formula

F = 15 - S ---- Equation 3

Step 2

substitute equation 3 into equation 2

4 (15 - S) + 6S = 72

Step 3

60 - 4S + 6S = 72

6S - 4S = 72 - 60

2S = 12

divide both sides by 2

S = 12/ 2

S= 6

Step 4

Substitute the value of S = 6 into equation 3

F = 15 - 6

F = 9

So the number of 4-passenger cars = 9

the number of 6-passenger cars = 6

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Solve for m and n<br> I been stuck on this question for an hour

Crazy boy [7]

Answer:

m = 10 , n = 5 $\sqrt{2}$

Step-by-step explanation:

using the cosine and tangent ratio in the right triangle and the exact values

cos45° = $\frac{1}{\sqrt{2} }$ and tan45° = 1 , then

cos45° = $\frac{adjacent}{hypotenuse}$ = $\frac{5\sqrt{2} }{m}$ = $\frac{1}{\sqrt{2} }$ ( cross- multiply )

m = 5 $\sqrt{2}$ × $\sqrt{2}$ = 5 × 2 = 10

-----------------------------------------

tan45° = $\frac{opposite}{adjacent}$ = $\frac{n}{5\sqrt{2} }$ = 1 , then

n = 5 $\sqrt{2}$

3 0

1 year ago

3. Convert the measure from radian to degree.

Shalnov [3]

Answer:

Here is the answer...hope it helps

4 0

1 year ago

Select the correct images on the graph.

MatroZZZ [7]

Answer:

the dark purple in the bottom, brown reddish one light purple one in the bottom

Step-by-step explanation:

5 0

2 years ago

In triangle ABC, line A.B.=CB Angle ABC equals 4X -3, and angle CAB equals X -3, what is angle ACB

Soloha48 [4]

Answer:

∠ACB = 28.5

Step-by-step explanation:

In triangle ABC,

angle CAB = x-3

angle ABC = 4X-3

It is also given that AB=CB

We know that if two sides of any triangle are equal then corresponding sides must also be equal.

Hence

angle ACB = angle CAB

angle ACB = x-3 {Given that angle CAB = x-3 }

We know that sum of all three angles of a triangle is 180 degree so let's add given angles

angle ACB + angle CAB + angle ABC = 180

(x-3) + (x-3) + (4x-3) = 180

x-3 + x-3 + 4x-3 = 180

6x-9 = 180

6x = 180+9

6x = 189

x = 189/9

x= 31.5

Now plug value of x into

angle ACB = x-3 = 31.5-3 = 28.5

Hence final answer is

∠ACB = 28.5

3 0

2 years ago

2 points) Sometimes a change of variable can be used to convert a differential equation y′=f(t,y) into a separable equation. One

Stells [14]

$y'=(t+y)^2-1$

Substitute $u=t+y$ , so that $u'=y'$ , and

$u'=u^2-1$

which is separable as

$\dfrac{u'}{u^2-1}=1$

Integrate both sides with respect to $t$ . For the integral on the left, first split into partial fractions:

$\dfrac{u'}2\left(\frac1{u-1}-\frac1{u+1}\right)=1$

$\displaystyle\int\frac{u'}2\left(\frac1{u-1}-\frac1{u+1}\right)\,\mathrm dt=\int\mathrm dt$

$\dfrac12(\ln|u-1|-\ln|u+1|)=t+C$

Solve for $u$ :

$\dfrac12\ln\left|\dfrac{u-1}{u+1}\right|=t+C$

$\ln\left|1-\dfrac2{u+1}\right|=2t+C$

$1-\dfrac2{u+1}=e^{2t+C}=Ce^{2t}$

$\dfrac2{u+1}=1-Ce^{2t}$

$\dfrac{u+1}2=\dfrac1{1-Ce^{2t}}$

$u=\dfrac2{1-Ce^{2t}}-1$

Replace $u$ and solve for $y$ :

$t+y=\dfrac2{1-Ce^{2t}}-1$

$y=\dfrac2{1-Ce^{2t}}-1-t$

Now use the given initial condition to solve for $C$ :

$y(3)=4\implies4=\dfrac2{1-Ce^6}-1-3\implies C=\dfrac3{4e^6}$

so that the particular solution is

$y=\dfrac2{1-\frac34e^{2t-6}}-1-t=\boxed{\dfrac8{4-3e^{2t-6}}-1-t}$

3 0

2 years ago