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3 years ago

Easy maths question I’ll give brainiest

Mathematics

2 answers:

NISA [10]3 years ago

5 0

Answer:

BC ≈ 12.6 m

Step-by-step explanation:

Using the tangent ratio in the right triangle

tan31° = $\frac{opposite}{adjacent}$ = $\frac{AB}{BC}$ = $\frac{7.6}{BC}$ ( multiply both sides by BC )

BC × tan31° = 7.6 ( divide both sides by tan31° )

BC = $\frac{7.6}{tan31}$ ≈ 12.6 m ( to 3 sf )

LUCKY_DIMON [66]3 years ago

4 0

Answer:

Angle BC is 12.6m

Step-by-step explanation:

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Rewrite the system of linear equations as a matrix equation AX = B.

iren2701 [21]

Answer:

$\left[\begin{array}{ccc}1&2&5\\1&1&1\\4&6&5\end{array}\right]*\left[\begin{array}{ccc}x1\\x2\\x3\end{array}\right]=\left[\begin{array}{ccc}5\\6\\7\end{array}\right]$

Step-by-step explanation:

Let's find the answer.

Because we have 3 equations and 3 variables (x1, x2, x3) a 3x3 matrix (A) can be constructed by using their respectively coefficients.

Equations:

Eq. 1 : x1 + 2x2 + 5x3 = 5

Eq. 2 : x1 + x2 + x3 = 6

E1. 3 : 4x1 + 6x2 + 5x3 = 7

Coefficients for x1 ; x2 ; x3

From eq. 1 : 1 ; 2 ; 5

From eq. 2 : 1 ; 1 ; 1

From eq. 3 : 4 ; 6 ; 5

So matrix A is:

$\left[\begin{array}{ccc}1&2&5\\1&1&1\\4&6&5\end{array}\right]$

And the vector of vriables (X) is:

$\left[\begin{array}{ccc}x1\\x2\\x3\end{array}\right]$

Now we can find the resulting vector (B) using the 'resulting values' from each equation:

$\left[\begin{array}{ccc}5\\6\\7\end{array}\right]$

In conclusion, AX=B is:

$\left[\begin{array}{ccc}1&2&5\\1&1&1\\4&6&5\end{array}\right]*\left[\begin{array}{ccc}x1\\x2\\x3\end{array}\right]=\left[\begin{array}{ccc}5\\6\\7\end{array}\right]$

7 0

4 years ago

A 10-foot ramp must make an angle of 30degrees with the ground if it is to reach a certain window. What angle must a 15-foot ram

prohojiy [21]

<span>We know Sin theta is given by Perpendicular/ hypotenuse. Hence in this case the angle given is 30 degree and hypotenuse is given as 10 foot. Hence Sin 30= P/ 10 1/2= P/10 Hence on solving value of P is 5. Now we have to compute the theta value for Perpendicular as 5 and now the height of ramp is increased to 15 foot, hence hypotenuse is now 15 foot. Hence Sin theta= 5/15 On taking inverse of Sin Theta we will get the theta value as 19.47. Hence the angle of ramp should is 19.47 degrees.</span>

4 0

4 years ago

I need help, please and thank you. I know that you have to multiply the diameter by 2 to find the radius, but with the 9 pi, it

andrew11 [14]

Answer:

r=6

Step-by-step explanation:

The area of a circle is given by πr². Note that this uses the radius, not the diameter.

Now, one quarter of this area (ABC) is given to be 9π.

So apparently:

$\frac14 \pi r^2 = 9\pi$

If you solve this:

$\frac14 r^2 = 9$ (divide both sides by π)

$r^2 = 9\cdot4$ (multiply both sides by 4)

r = √36 = 6

so the radius is 6.

4 0

3 years ago

Given the following signal:  x(n) = {4, −1, 2, 5, − 2, 3}  Compute the 6-point DFT of x(n) directly from the DFT equation  −

FrozenT [24]

Answer:

Computing the 6-Point DFT of x(n), where X = 0,1,2,3,4,5

x(0) = 11

x(1) = 21/8 -j13/8

x(2) = 27/8 + j33/32

x(3) = 1139/256 + j91/256

x(4) = 4389/1024

x(5) = 4.14685 - j1379/8192

Step-by-step explanation:

See the picture for workings.

Given X(n) = { 4, -1, 2, 5, -2, 3}

Six point DFT implies that N = 6

Step 1 = write out equation X(k)

Step 2 = substitute "Wn" in the equation X(k) to give a new equation

Step 3 = when N=6, substitute for "N" in the new equation and simplify the new X(k) equation.

Step 4 = use 0, 1, 2, 3, 4, 5 in finding the DFT

4 0

3 years ago

Ethan opens up a new savings account. The account has a 3.5% compound interest per annum. Ethan invests £2,000 into the account

Margarita [4]

$\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &2000\\ r=rate\to 3.5\%\to \frac{3.5}{100}\dotfill &0.035\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{per annum, thus once} \end{array}\dotfill &1\\ t=years\dotfill &2 \end{cases} \\\\\\ A=2000\left(1+\frac{0.035}{1}\right)^{1\cdot 2}\implies A=2000(1.035)^2\implies A=2142.45$

3 0

3 years ago