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2 years ago

Urgent!

Mathematics

1 answer:

Rzqust [24]2 years ago

6 0

$\sqrt[3]{8^x}=(8^x)^{\frac{1}{3}}=8^{\frac{x}{3}}$

Answer C

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Calculate the length b to two decimal places.

Andrej [43]

Answer:

B. 21.64

Step-by-step explanation:

We have been given a triangle and we are asked to find the length of AC (b).

We will use law of cosines to find the length of side AC.

$c^{2}=a^{2}+b^{2}-2ab \text{ cos }\theta$

Upon substituting our given values in the formula we will get,

$(AC)^{2}=15^{2}+12^{2}-2\times 15\times 12 \text{ cos}(106)$

$(AC)^{2}=225+144-360\text{ cos}(106)$

$(AC)^{2}=369-360(-0.275637355817)$

$(AC)^{2}=369+99.22944809412$

$(AC)^{2}=468.22944809412$

Upon taking square root of both sides of our equation we will be get,

$AC=\sqrt{468.22944809412}$

$AC=21.6386101238993629\approx 21.64$

Therefore, the length of b is 21.64 and option B is the correct choice.

6 0

2 years ago

It x, y, and z are positive intergers and 3x = 4y = 7z, then the least possible value of x + y + z is???

Dmitry [639]

$3x = 4y = 7z \\ \Rightarrow \begin{cases}3x - 4y = 0 \\4y - 7z = 0 \\ 7z - 3x = 0\end{cases} \\ \Leftrightarrow \begin{cases}x = \frac{4}{3} y\\4y - 7z = 0 \\ 7z - 3( \frac{4}{3}y) = 0\end{cases} \\ \Leftrightarrow \begin{cases}x = \frac{4}{3} y\\4y - 7z = 0 \\ 7z - 4y= 0\end{cases} \\ \Leftrightarrow \begin{cases}x = \frac{4}{3} y\\ y \\ z = \frac{4}{7}y \end{cases} \\ x,y,z\: are\: intergers\Rightarrow y=LCM(3,7)=21\Rightarrow x = 28,z = 12 \\ \Rightarrow x + y + z = 61$

5 0

2 years ago

Find the interval(s) of upward concavity on this accumulation function.

maxonik [38]

$\displaystylef(x)=\int_{0}^{x^2}\sec^2(\sqrt{x})dx \\=\int_{0}^{\sqrt{x^2}}\sec^2(u)\cdot2udu \\=2\int_{0}^{\sqrt{x^2}}\sec^2(u)du \\=2\Big[u\tan(u)-\int\tan(u)du\Big]_{0}^{\sqrt{x^2}} \\=2\Big[u\tan(u)+\ln\Big(\mathrm{abs}(\cos(u))\Big)\Big]_0^x \\=2\Big(x\tan(x)+\dfrac{1}{2}\ln\Big(\cos^2(x)\Big)\Big) \\=2x\tan(x)+\ln(\cos^2(x))$

Hope this helps.

6 0

3 years ago

Barry types at a constant rate of 50 words per minute, and has already typed 229 words. Which function

dangina [55]

Answer:

For me

Step-by-step explanation:

I think it's A because x is unknown and per minutes meaning 50 times the x plus the 229

8 0

3 years ago

Ship A receives a distress signal from the southwest, and ship B receives a distress from the same vessel from the north. At wha

Fiesta28 [93]

I've attached an image showing the coordinates of Ship A and Ship B.

Answer:

distressed vessel is located at (1, 1.5)

Step-by-step explanation:

From the image attached, we can see that;

Coordinate of ship A is (3, 4)

Coordinate of ship B is (1, 1)

Now, we are told that Ship A receives a distress signal from the southwest, and ship B receives a distress from the same vessel from the north.

This means that the distressed ship is somewhere in between ship A & B.

To solve this, we will extend the arrow line from Ship A in that same SW direction and we will do the same for ship B in the same North direction. Their point of intersection is where the distressed ship is located.

Now, if we do that, we will see that they will intersect at the point; (1, 1.5)

Thus,distressed vessel is located at (1, 1.5)

5 0

3 years ago