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4 years ago

The figure below is formed by 8 identical rectangles and 1 triangle. Find the

Mathematics

1 answer:

Aliun [14]4 years ago

3 0

Answer:

Step-by-step explanation:

Base of triangle = length of the rectangle

Since, all are identical rectangles,

Length of a rectangle= 36/2 = 18 cm

Base of triangle = 18 cm

Height of triangle = length of the rectangle + width of the rectangle

Width of 6 rectangles = 36

Width of 1 rectangle = 36/ 6 = 6 cm

Height of the triangle = 18 + 6 = 24 cm

Area of the shaded triangle = $\frac{1}{2}base*height$

= $\frac{1}{2}*18*24$

= 9 * 24

= 216 cm²

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Can you solve -4a^ - (6a-2) + 3 (a^-1).the arrows that are pointing up is exponent 2.also please show work

Burka [1]

First step is to distribute.
-4a^2 - 6a +2 + 3a^2 -3
Combine like terms
-a^2 -6a -1

5 0

3 years ago

4. Evaluate f(x) = - 9x + 8 at the given value

allsm [11]

Answer:

y= 9x + 8

Step-by-step explanation:

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3 years ago

How do you solve the equation -7/8k=21

loris [4]

$- \frac{7}{8} k$ = 21

First, simplify $\frac{7}{8} k$ to $\frac{7k}{8}$ / Your problem should look like: $-\frac{7k}{8}$ = 21
Second, multiply both sides by 8. / Your problem should look like: -7k = 167
Third, divide both sides by -7. / Your problem should look like: k = $\frac{168}{-7}$
Fourth, simplify $\frac{168}{-7}$ to $\frac{168}{7}$ / Your problem should look like: k = $- \frac{168}{7}$
Fifth, simplify $\frac{168}{7}$ to 24. / Your problem should look like: k = -24

Answer: k = -24

4 0

3 years ago

Find the solution of the given initial value problem:<br><br> y''- y = 0, y(0) = 2, y'(0) = -1/2

igor_vitrenko [27]

Answer: The required solution of the given IVP is

$y(x)=\dfrac{3}{4}e^x+\dfrac{5}{4}e^{-x}.$

Step-by-step explanation: We are given to find the solution of the following initial value problem :

$y^{\prime\prime}-y=0,~~~y(0)=2,~~y^\prime(0)=-\dfrac{1}{2}.$

Let $y=e^{mx}$ be an auxiliary solution of the given differential equation.

Then, we have

$y^\prime=me^{mx},~~~~~y^{\prime\prime}=m^2e^{mx}.$

Substituting these values in the given differential equation, we have

$m^2e^{mx}-e^{mx}=0\\\\\Rightarrow (m^2-1)e^{mx}=0\\\\\Rightarrow m^2-1=0~~~~~~~~~~~~~~~~~~~~~~~~~~[\textup{since }e^{mx}\neq0]\\\\\Rightarrow m^2=1\\\\\Rightarrow m=\pm1.$

So, the general solution of the given equation is

$y(x)=Ae^x+Be^{-x},$ where A and B are constants.

This gives, after differentiating with respect to x that

$y^\prime(x)=Ae^x-Be^{-x}.$

The given conditions implies that

$y(0)=2\\\\\Rightarrow A+B=2~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

and

$y^\prime(0)=-\dfrac{1}{2}\\\\\\\Rightarrow A-B=-\dfrac{1}{2}~~~~~~~~~~~~~~~~~~~~~~~~(ii)$

Adding equations (i) and (ii), we get

$2A=2-\dfrac{1}{2}\\\\\\\Rightarrow 2A=\dfrac{3}{2}\\\\\\\Rightarrow A=\dfrac{3}{4}.$

From equation (i), we get

$\dfrac{3}{4}+B=2\\\\\\\Rightarrow B=2-\dfrac{3}{4}\\\\\\\Rightarrow B=\dfrac{5}{4}.$

Substituting the values of A and B in the general solution, we get

$y(x)=\dfrac{3}{4}e^x+\dfrac{5}{4}e^{-x}.$

Thus, the required solution of the given IVP is

$y(x)=\dfrac{3}{4}e^x+\dfrac{5}{4}e^{-x}.$

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3 years ago

What is the median of the following numbers? 4, 5, 5, 2, 1, 3, 4, 5, 4, 4, 4, 7

Katen [24]

Answer:

Step-by-step explanation:

Rewrite is order going from least to greatest.

1, 2, 3, 4, 4, 4, 4, 4, 5, 5, 5, 7

Find the middle number.

Because there are an even amount of numbers you have to take the two middle numbers which are 4 and 4 add them which gives you 8 and then divide that by 2( because you added two numbers.)

Therefore the answer is 4

3 0

2 years ago