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Ann [662]
4 years ago
15

Please answer question three and four if you can :) Show full working out ty;)

Mathematics
1 answer:
nikklg [1K]4 years ago
4 0

Step-by-step explanation:

3

Let D be the mid point of side BC, [B(2, - 1), C(5, 2)].

Therefore, by mid-point formula:

D = ( \frac{2 + 5}{2},  \:  \:  \frac{ - 1 + 2}{2} ) = ( \frac{7}{2}, \:  \:  \frac{ 1}{2} ) \\ \therefore D= (3.5, \:  \: 0.5) \\  \& \: A=(-1,\:\:4)...(given) \\\\  now \: by \: distance \: formula \\  \\ Length  \: of \:  segment  \: AD \\  =  \sqrt{( - 1 - 3.5)^{2}  +  {(4 - 0.5)}^{2} }  \\ =  \sqrt{(4.5)^{2}  +  {(3.5)}^{2} }  \\ =  \sqrt{20.25 + 12.25 }  \\  =  \sqrt{32.5}  \\    \red{ \boxed{\therefore Length  \: of \:  segment  \: AD  = 5.7 \: units}}

4 (a)

Equation of line AB[A(2, 1), B(-2, - 11)] in two point form is given as:

\frac{y-y_1}{y_1-y_2} =\frac{x-x_1}{x_1 - x_2} \\\\\therefore \frac{y-1}{1-(-11)} =\frac{x-2}{2 - (-2) } \\\\\therefore \frac{y-1}{1+11} =\frac{x-2}{2 +2} \\\\\therefore \frac{y-1}{12} =\frac{x-2}{4} \\\\\therefore \frac{y-1}{3} =\frac{x-2}{1} \\\\\therefore y-1= 3(x - 2)\\\\\therefore y= 3x - 6+1\\\\\therefore y= 3x - 5\\\\ \huge \purple {\boxed {\therefore 3x - y-5=0}} \\

is the equation of line AB.

Now we have to check whether C(4, 7) lie on line AB or not.

Let us substitute x = 4 & y = 7 on the Left hand side of equation of line AB and if it gives us 0, then C lies on the line.

LHS = 3x - y-5\\=3\times 4-7-5\\= 12-12\\=0\\= RHS

Hence, point C (4, 7) lie on the straight line AB.

4(b)

Like we did in 4(a), first find the equation of line AB and then substitute the coordinates of point C in equation and if they satisfy the equation, then all the three points lie on the straight line.

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Solve the separable differential equation dtdx=x2+164 and find the particular solution satisfying the initial condition x(0)=9
maria [59]
\dfrac{dt}{dx} = x^2 + \frac{1}{64} \Rightarrow\ dt = \left(x^2 + \frac{1}{64}\right)dx \Rightarrow \\ \\ \displaystyle \int 1 dt = \int \left(x^2 + \frac{1}{64}\right)dx \Rightarrow \\ t = \dfrac{x^3}{3} + \frac{x}{64} + C

C = 9 because all the x terms go away.

t = \dfrac{x^3}{3} + \dfrac{x}{64} + 9
3 0
3 years ago
there are 2.54 centimeters in 1 inch. there are 100 centimeters in 1 meter.questionto the nearest meter, how many meters are in
Gre4nikov [31]

There are 7 meters in 279 inches.

  • There are 2.54 centimeters in 1 inch.
  • There are 100 centimeters in 1 meter.
  • The number of inches is given to be 279.
  • Unit conversion is a multi-step procedure that includes multiplying or dividing by a numerical factor, determining the appropriate number of significant digits, and rounding.
  • First of all, we need to convert inches to centimeters.
  • 1 inch equals 2.54 centimeters.
  • 279 inches equals 2.54*279 centimeters.
  • 279 inches equals 708.66 centimeters.
  • Now, we need to convert these centimeters into meters.
  • Meters in 100 centimeters = 1
  • Meters in 1 centimeters = 1/100
  • Meters in 708.66 centimeters = (1/100)*708.66
  • Meters in 708.66 centimeters = 7.0866
  • Thus, there are approximately 7 meters in 279 inches.

To learn more about unit conversion, visit :

brainly.com/question/11543684

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8 0
2 years ago
A manufacturer of banana chips would like to know whether its bag filling machine works correctly at the 421 gram setting. It is
Anastaziya [24]

Answer:

The p-value is approximately 0.0508

Step-by-step explanation:

The given parameters are;

The expected mass of banana chips bag filled by the machine, μ = 421 gams

The number of bags in the sample of bags filled by the machine, n = 26 bags

The mean mass of the bags in the sample, \overline x = 413 grams

The standard deviation of the mass in the bags, s = 24 grams

The level of significance, α = 0.02

The null hypothesis, H₀; μ = 421 grams

The alternative hypothesis, Hₐ; μ < 421 grams

The test statistic is given as follows;

t=\dfrac{\bar{x}-\mu }{\dfrac{s}{\sqrt{n}}}

We get;

t=\dfrac{413-421 }{\dfrac{24}{\sqrt{26}}} \approx -1.6996731712

The t-value = -1.6996731712

The degrees of freedom df = n - 1 = 26 - 1 = 25

From an online source, we get the critical-t =  2.166587

The p-value is obtained using an online source as p(t ≤  -1.6996731712) = 0.0508

From the p-value table, we get

0.05 < p < 0.1

3 0
3 years ago
Show the 64 can be written as either 26 or 43​
xeze [42]

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4 0
3 years ago
"The sum of renting bowling shoes<br><br><br><br><br><br><br><br><br><br><br><br> and $3 per game"
AleksAgata [21]

Answer:

6 dollars

Step-by-step explanation:

if i am wrong tell me pls

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