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3 years ago

What is the length of the diagonal of the square shown below?

Mathematics

1 answer:

amid [387]3 years ago

5 0

Answer:

$7\sqrt{2}$

Step-by-step explanation:

Given is a picture of a square with each side = 7 units

Since a square is right angled we have the diagonal bisecting the square into two isosceles right triangles.

Use Pythagorean theorem to get the diagonal length.

Hence diagonal = $\sqrt{7^2+7^2} =7\sqrt{2}$

Alternate method:

Find the length of the diagonal of a square, multiply the length of one side by the square root of 2: If the length of one side is x, then diagonal will have length as

$x\sqrt{2}$

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Sergio039 [100]

$\bf ~~~~~~\textit{initial velocity} \\\\ \begin{array}{llll} ~~~~~~\textit{in feet} \\\\ h(t) = -16t^2+v_ot+h_o \end{array} \quad \begin{cases} v_o=\stackrel{}{\textit{initial velocity of the object}}\\\\ h_o=\stackrel{}{\textit{initial height of the object}}\\\\ h=\stackrel{}{\textit{height of the object at "t" seconds}} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ h=-16t^2+\stackrel{\stackrel{v_o}{\downarrow }}{65}t$

now, take a look at the picture below, so for 2) and 3) is the vertex of this quadratic equation, 2) is the y-coordinate and 3) the x-coordinate.

$\bf \textit{vertex of a vertical parabola, using coefficients} \\\\ h=\stackrel{\stackrel{a}{\downarrow }}{-16}t^2\stackrel{\stackrel{b}{\downarrow }}{+65}t\stackrel{\stackrel{c}{\downarrow }}{+0} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left( -\cfrac{65}{2(-16)}~~,~~0-\cfrac{65^2}{4(-16)} \right) \implies \left( \cfrac{65}{32}~,~0- \cfrac{4225}{-64}\right)$

$\bf \left( \cfrac{65}{32}~,~0+ \cfrac{4225}{64}\right)\implies \left( \stackrel{seconds}{2\frac{1}{32}}~~,~~ \stackrel{feet~hight}{66\frac{1}{64}}\right)$

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3 years ago

A group of students wanted to investigate the claim that the average number of text messages sent yesterday by

Likurg_2 [28]

First we need to write the null and alternate hypothesis for this case.

Let x be the average number of text message sent. Then

Null hypothesis: x = 100
Alternate hypothesis: x > 100

The p value is 0.0853

If p value > significance level, then the null hypothesis is not rejected. If p value < significance level, then the null hypothesis is rejected.

If significance level is 10%(0.10), the p value will be less than 0.10 and we reject the null hypothesis and CAN conclude that:
The mean number of text messages sent yesterday was greater than 100.

If significance level is 5%(0.05), the p value will be greater than 0.05 and we cannot reject the null hypothesis and CANNOT conclude that:
The mean number of text messages sent yesterday was greater than 100.

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3 years ago

Paul is saving for a down payment to buy a house. The account earns 13% interest compound quarterly, and he wants to have $15,00

Tatiana [17]

Answer:

The principal must be = $8991.88

Step-by-step explanation:

Formula for compound interest is:

$A = P(1 + \frac{r}{n})^{nt}$

Where A is the amount after 't' years.

P is the principal amount

n is the number of times interest is compounded each year.

r is the rate of interest.

Here, we are given that:

Amount, A = $15000

Rate of interest = 13 % compounded quarterly i.e. 4 times every year

Number of times, interest is compounded each year, n = 4

Time, t = 4 years.

To find, Principal P = ?

Putting all the given values in the formula to find P.

$15000 = P(1 + \frac{13}{400})^{4\times 4}\\\Rightarrow 15000 = P(1 + 0.0325)^{16}\\\Rightarrow 15000 = P(1.0325)^{16} \\\Rightarrow 15000 = P \times 1.66817253\\\Rightarrow P = \dfrac{15000}{1.66817253}\\\Rightarrow P \approx \$8991.88$

So, <em>the principal must be = $8991.88</em>

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3 years ago