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3 years ago

What is the height of a triangle when the area is 36 cm and the base is 6 cm

Mathematics

2 answers:

pentagon [3]3 years ago

6 0

Answer:

h = 12 cm

Step-by-step explanation:

Use the formula for area of a triangle A = (1/2)bh, where b is the base, and h is the height.

Plug in the given information of A = 36, and b = 6, then solve for h

36 = (1/2)(6)h

36 = 3h (one half of 6 is 3 (1/2)(6) = 3 )

12 = h (divide both sides by 3 to isolate h)

LekaFEV [45]3 years ago

6 0

The height of the triangle is 20 cm.

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What is the approximate number of hours in 72 days on Saturn

Anon25 [30]

A planet's day is the time it takes the planet to rotate or spin once on its axis. Saturn rotates faster than Earth so a day on Saturn is shorter than a day on Earth. A day on Saturn is 10.656 hours long while a day on Earth is 23.934 hours long.

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4 years ago

Read 2 more answers

Becky and luke bought the same kind of pencils and erasers . Becky spent $1.45 for 2 pencils and 3 erasers . Luke spent $2.65 fo

ivann1987 [24]

Answer: the cost of each pencil is $0.5

the cost of each eraser is $0.15

Step-by-step explanation:

Let x represent the cost of one pencil.

Let y represent the cost of one eraser.

Becky spent $1.45 for 2 pencils and 3 erasers. This means that

2x + 3y = 1.45- - - - - - - - - -1

Luke spent $2.65 for 5 pencils and 1 eraser. This means that

5x + y = 2.65- - - - - - - - - -2

Multiplying equation 1 by 1 and equation 2 by 3, it becomes

2x + 3y = 1.45

15x + 3y = 7.95

Subtracting, it becomes

- 13x = - 6.5

x = - 6.5/- 13

x = 0.5

Substituting x = 0.5 into equation 2, it becomes

5 × 0.5 + y = 2.65

2.5 + y = 2.65

y = 2.65 - 2.5

y = 0.15

6 0

3 years ago

Si una empresa obtiene un préstamo de S/3000 a seis años de plazo, con una tasa de interés compuesto del 15 % anual capitalizabl

Debora [2.8K]

Answer:

VF= $3.281,42

Interes= 3.281,42 - 3.000= $281.42

Step-by-step explanation:

Dada la siguiente información:

Prestamo (P)= $3.000

Tasa (i)= 0,015/2= 0,0075

Cantidad de periodos (n)= 6*2= 12 semestres

Para calcular el valor final del prestamos, tenemos que usar la siguiente formula:

VF= P*(1 + i)^n

VF= 3.000*1,0075^12

VF= $3.281,42

Interes= 3.281,42 - 3.000= $281.42

8 0

3 years ago

Consider the function f(x)equalscosine left parenthesis x squared right parenthesis. a. Differentiate the Taylor series about 0

dybincka [34]

I suppose you mean

$f(x)=\cos(x^2)$

Recall that

$\cos x=\displaystyle\sum_{n=0}^\infty(-1)^n\frac{x^{2n}}{(2n)!}$

which converges everywhere. Then by substitution,

$\cos(x^2)=\displaystyle\sum_{n=0}^\infty(-1)^n\frac{(x^2)^{2n}}{(2n)!}=\sum_{n=0}^\infty(-1)^n\frac{x^{4n}}{(2n)!}$

which also converges everywhere (and we can confirm this via the ratio test, for instance).

a. Differentiating the Taylor series gives

$f'(x)=\displaystyle4\sum_{n=1}^\infty(-1)^n\frac{nx^{4n-1}}{(2n)!}$

(starting at $n=1$ because the summand is 0 when $n=0$ )

b. Naturally, the differentiated series represents

$f'(x)=-2x\sin(x^2)$

To see this, recalling the series for $\sin x$ , we know

$\sin(x^2)=\displaystyle\sum_{n=0}^\infty(-1)^{n-1}\frac{x^{4n+2}}{(2n+1)!}$

Multiplying by $-2x$ gives

$-x\sin(x^2)=\displaystyle2x\sum_{n=0}^\infty(-1)^n\frac{x^{4n}}{(2n+1)!}$

and from here,

$-2x\sin(x^2)=\displaystyle 2x\sum_{n=0}^\infty(-1)^n\frac{2nx^{4n}}{(2n)(2n+1)!}$

$-2x\sin(x^2)=\displaystyle 4x\sum_{n=0}^\infty(-1)^n\frac{nx^{4n}}{(2n)!}=f'(x)$

c. This series also converges everywhere. By the ratio test, the series converges if

$\displaystyle\lim_{n\to\infty}\left|\frac{(-1)^{n+1}\frac{(n+1)x^{4(n+1)}}{(2(n+1))!}}{(-1)^n\frac{nx^{4n}}{(2n)!}}\right|=|x|\lim_{n\to\infty}\frac{\frac{n+1}{(2n+2)!}}{\frac n{(2n)!}}=|x|\lim_{n\to\infty}\frac{n+1}{n(2n+2)(2n+1)}$

The limit is 0, so any choice of $x$ satisfies the convergence condition.

3 0

4 years ago

A product comes in cans labeled "38 oz". A random sample of 10 cans had the following weights:

KiRa [710]

Answer:

b. 35.9, 39.1 ounces

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

barX=37.465 represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s=2.27 represent the sample standard deviation

n=10 represent the sample size

Confidence interval

The confidence interval for the mean is given by the following formula:

barX +- t*[(s)/(sqrt{n))] (1)

In order to calculate the critical value t we need to find first the degrees of freedom, given by:

df=n-1=10-1=9

Since the Confidence is 0.95 or 95%, the value of alpha=0.05 and \alpha/2 =0.025, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,9)".And we see that t_(alpha/2)=2.26

Now we have everything in order to replace into formula (1):

37.465-2.26[(2.27)/(sqrt{10))]=35.9

37.465+2.26[(2.27)/(sqrt{10))]=39.1

So on this case the 95% confidence interval would be given by (35.9;39.1)

7 0

3 years ago