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3 years ago

Which of the following best describes

Mathematics

2 answers:

Papessa [141]3 years ago

7 0

Answer:

Please add the picture

Step-by-step explanation:

If it point upward right: positive

if it point downward: negative

If it is just a horizontal line : zero

qwelly [4]3 years ago

6 0

Answer:

A. Positive I'm sorry if I got this wrong answer

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Otis bought a flashlight for $8 and a sleeping bag for $55 he sales tax was 7% which means 0.07 times the price find the amount

Basile [38]

Answer:

$4.41

Step-by-step explanation:

We have been given that Otis bought a flashlight for $8 and a sleeping bag for $55 he sales tax was 7% which means 0.07 times the price.

To find the amount of sales tax, we will add cost of sleeping bag and flashlight and multiply the sum by 0.07.

$\$55+\$8=\$63$

$\text{Amount of sales tax}=\$63\times 0.07$

$\text{Amount of sales tax}=\$4.41$

Therefore, Otis paid an amount of $4.41 in sales tax.

The 2nd way is that we can find sales tax of each product separately and then add the amount of sales of two items as:

$\$8\times 0.07=\$0.56$

$\$55\times 0.07=\$3.85$

$\$0.56+\$3.85=\$4.41$

Therefore, Otis paid an amount of $4.41 in sales tax.

3 0

3 years ago

Find the length of the curve. R(t) = cos(8t) i + sin(8t) j + 8 ln cos t k, 0 ≤ t ≤ π/4

arsen [322]

we are given

$R(t)=cos(8t)i+sin(8t)j+8ln(cos(t))k$

now, we can find x , y and z components

$x=cos(8t),y=sin(8t),z=8ln(cos(t))$

Arc length calculation:

we can use formula

$L=\int\limits^a_b {\sqrt{(x')^2+(y')^2+(z')^2} } \, dt$

$x'=-8sin(8t),y=8cos(8t),z=-8tan(t)$

now, we can plug these values

$L=\int _0^{\frac{\pi }{4}}\sqrt{(-8sin(8t))^2+(8cos(8t))^2+(-8tan(t))^2} dt$

now, we can simplify it

$L=\int _0^{\frac{\pi }{4}}\sqrt{64+64tan^2(t)} dt$

$L=\int _0^{\frac{\pi }{4}}8\sqrt{1+tan^2(t)} dt$

$L=\int _0^{\frac{\pi }{4}}8\sqrt{sec^2(t)} dt$

$L=\int _0^{\frac{\pi }{4}}8sec(t) dt$

now, we can solve integral

$\int \:8\sec \left(t\right)dt$

$=8\ln \left|\tan \left(t\right)+\sec \left(t\right)\right|$

now, we can plug bounds

and we get

$=8\ln \left(\sqrt{2}+1\right)-0$

so,

$L=8\ln \left(1+\sqrt{2}\right)$ ..............Answer

5 0

3 years ago

Find the coordinates of P so that P partitions segment AB in the part-to-whole ratio of 1 to 5 with A(-9, 3) and B(1, 8). Explai

ycow [4]

For both problems, we can use the section formula.

1) $P=\left(\frac{(1)(1)+(5)(-9)}{6}, \frac{(1)(8)+(5)(3)}{6} \right)=\boxed{\left(-\frac{22}{3}, \frac{23}{6} \right)}$

2) $Z=\left(\frac{(2)(7)+(1)(1)}{3}, \frac{((2)(5)+(1)(2)}{3} \right)=\boxed{(5, 4)}$

4 0

2 years ago

Solve the system of equations

DanielleElmas [232]

Answer:

<em>Simplifies to x=3/4y+2</em>

2x+5y=-9

Simplifies to -5/2y+-9/2

4 0

3 years ago

Express secΦ in terms of tanΦ

Sunny_sXe [5.5K]

Answer:

$\sec\theta=\sqrt{1+\tan^2\theta}$

Step-by-step explanation:

The trigonometric identity is :

$\sec^2\theta-\tan^2\theta=1\\\\or\\\\\sec^2\theta=1+\tan^2\theta$

We need to express secθ in terms of tanθ.

The above equation becomes,

$\sec\theta=\sqrt{1+\tan^2\theta}$

Hence, this is the required solution.

5 0

3 years ago