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3 years ago

Which equation shows the volume of the rectangular prism as a product of its edge lengths?

Mathematics

1 answer:

Anettt [7]3 years ago

6 0

Answer:

Top right option

Step-by-step explanation:

multiplying the digits, you get the volume, which is 3/4

Answered by GAUTHMATH

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Cara evaluated the expression below.

s2008m [1.1K]

Answer:

Cara multiplied only 4 and 7 together and did not multiply 4 and 13.

Step-by-step explanation:

Let us evaluate the given expression step by step,

$\frac{4(7-13)}{3} +(-4)^{2} -2(6-2)\\$

We can evaluate this expression in two ways; either by subtracting -13 from 7 and then multiply by 4 or by multiplying 4 to 7 and -13.

$\frac{28-52}{3} +16-2(4)$

$\frac{-24}{3} +16-8$

$-8+16-8=-16+16=0$

Now let us see where Cara made an error. We can see Cara just multiplied only 4 and 7 together and did not multiply 4 to 13.

Therefore, Cara made error in her first step.

5 0

3 years ago

Read 2 more answers

Question (c)! How do I know that t^5-10t^3+5t=0?<br> Thanks!

astra-53 [7]

(a) By DeMoivre's theorem, we have

$(\cos\theta+i\sin\theta)^5=\cos5\theta+i\sin5\theta$

On the LHS, expanding yields

$\cos^5\theta+5i\cos^4\theta\sin\theta-10\cos^3\theta\sin^2\theta-10i\cos^2\theta\sin^3\theta+5\cos\theta\sin^4\theta+i\sin^4\theta$

Matching up real and imaginary parts, we have for (i) and (ii),

$\cos5\theta=\cos^5\theta-10\cos^3\theta\sin^2\theta+5\cos\theta\sin^4\theta$
$\sin5\theta=5\cos^4\theta\sin\theta-10\cos^2\theta\sin^3\theta+\sin^5\theta$

(b) By the definition of the tangent function,

$\tan5\theta=\dfrac{\sin5\theta}{\cos5\theta}$
$=\dfrac{5\cos^4\theta\sin\theta-10\cos^2\theta\sin^3\theta+\sin^5\theta}{\cos^5\theta-10\cos^3\theta\sin^2\theta+5\cos\theta\sin^4\theta}$

$=\dfrac{5\tan\theta-10\tan^3\theta+\tan^5\theta}{1-10\tan^2\theta+5\tan^4\theta}$
$=\dfrac{t^5-10t^3+5t}{5t^4-10t^2+1}$

(c) Setting $\theta=\dfrac\pi5$ , we have $t=\tan\dfrac\pi5$ and $\tan5\left(\dfrac\pi5\right)=\tan\pi=0$ . So

$0=\dfrac{t^5-10t^3+5t}{5t^4-10t^2+1}$

At the given value of $t$ , the denominator is a non-zero number, so only the numerator can contribute to this reducing to 0.

$0=t^5-10t^3+5t\implies0=t^4-10t^2+5$

Remember, this is saying that

$0=\tan^4\dfrac\pi5-10\tan^2\dfrac\pi5+5$

If we replace $\tan^2\dfrac\pi5$ with a variable $x$ , then the above means $\tan^2\dfrac\pi5$ is a root to the quadratic equation,

$x^2-10x+5=0$

Also, if $\theta=\dfrac{2\pi}5$ , then $t=\tan\dfrac{2\pi}5$ and $\tan5\left(\dfrac{2\pi}5\right)=\tan2\pi=0$ . So by a similar argument as above, we deduce that $\tan^2\dfrac{2\pi}5$ is also a root to the quadratic equation above.

(d) We know both roots to the quadratic above. The fundamental theorem of algebra lets us write

$x^2-10x+5=\left(x-\tan^2\dfrac\pi5\right)\left(x-\tan^2\dfrac{2\pi}5\right)$

Expand the RHS and match up terms of the same power. In particular, the constant terms satisfy

$5=\tan^2\dfrac\pi5\tan^2\dfrac{2\pi}5\implies\tan\dfrac\pi5\tan\dfrac{2\pi}5=\pm\sqrt5$

But $\tanx>0$ for all $0$ , as is the case for $x=\dfrac\pi5$ and $x=\dfrac{2\pi}5$ , so we choose the positive root.

3 0

3 years ago

Old Faithful in Yellowstone National Park shoots water 60 feet into the air that casts a shadow of 42 feet. What is the height o

Rudiy27

It will be 90 feet considering the water triangle as shown as the figure

5 0

2 years ago

A local pizzeria sold 65 pizzas yesterday. Suppose the actual number of pizzas sold today was 60. Describe

Rudik [331]

We need to find the difference first. 65 - 60 = 5. Now we must find what percent 5 is of 65. It is 7,7%. The number decreased, and so it is a 7,7% decrease.

7 0

3 years ago

Determine whether the following sequence is geometric. If so, find the common ratio.

Shtirlitz [24]

Answer:

a) r = 5

b) false

Step-by-step explanation:

study about GP

8 0

3 years ago