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3 years ago

A local city collects 8% sales tax. If the

Mathematics

1 answer:

vivado [14]3 years ago

3 0

If you take the total, and multiply it by the sales tax (.08) then you will get $17.28
(216x.08)

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The total surface area of a cube is 294 cm ² work out the volume of the cube

mihalych1998 [28]

$\text{ Total Surface Area of cube, with Side $a$ is } 6a^2 \\ \text{ (six times the area of each face)} \\ 6a^2=294 \ m^2 \\ a^2= \frac{294}{6} \\ a^2=\frac{49\times6}{6} \\ a^2=49 \\ a=\sqrt{49} \\ a=7 \ m \\ \text{Volume of cube with Side $a$ is } a^3 \\ V= 7^3=49\times7 \\ \text{volume of the cube is } 343 \ m^3$

6 0

4 years ago

Read 2 more answers

Evaluate x divided 4 for x=48

scoray [572]

You have to divide 48 by 4. How many times does 4 go into 48.....................12 times.

3 0

3 years ago

Hii can someone help with this pls :)

BlackZzzverrR [31]

Answer:

$R(x,y) = (0.8,-1.2)$

Step-by-step explanation:

The coordinates of QS are:

$Q(x_1,y_1) = (-2,-6)$

$S(x_2,y_2) = (5,6)$

The ratio is represented as:

$R_{m:n} = 2:3$

Required

Find the coordinates of R

The coordinates of R is calculated by:

$R(x,y) = (\frac{mx_2 + nx_1}{m+n},\frac{my_2 + ny_1}{m+n})$

Substitute values for m, n, x's and y's

$R(x,y) = (\frac{2 * 5 + 3 * -2}{2+3},\frac{2*6 + 3*-6}{2+3})$

$R(x,y) = (\frac{4}{5},\frac{-6}{5})$

$R(x,y) = (0.8,-1.2)$

None of the options is correct

6 0

2 years ago

Prove : sin²θ + cos²θ = 1 thankyou ~

Gnom [1K]

Answer:

See below

Step-by-step explanation:

Here we need to prove that ,

$\sf\longrightarrow sin^2\theta + cos^2\theta = 1$

Imagine a right angled triangle with one of its acute angle as $\theta$ .

The side opposite to this angle will be perpendicular .
Also we know that ,

$\sf\longrightarrow sin\theta =\dfrac{p}{h} \\$

$\sf\longrightarrow cos\theta =\dfrac{b}{h}$

And by Pythagoras theorem ,

$\sf\longrightarrow h^2 = p^2+b^2 \dots (i)$

Where the symbols have their usual meaning.

Now , taking LHS ,

$\sf\longrightarrow sin^2\theta +cos^2\theta$

Substituting the respective values,

$\sf\longrightarrow \bigg(\dfrac{p}{h}\bigg)^2+\bigg(\dfrac{b}{h}\bigg)^2\\$

$\sf\longrightarrow \dfrac{p^2}{h^2}+\dfrac{b^2}{h^2}\\$

$\sf\longrightarrow \dfrac{p^2+b^2}{h^2}$

From equation (i) ,

$\sf\longrightarrow\cancel{ \dfrac{h^2}{h^2}}\\$

$\sf\longrightarrow \bf 1 = RHS$

Since LHS = RHS ,

Hence Proved !

I hope this helps.

5 0

2 years ago

5. A yacht is cruising at 20 knots at bearing of 185° when a 15 knot wind starts to blow at a bearing of 290°. Find the directio

kicyunya [14]

Answer:

Direction of the boat is 43.05° and the speed is 21.66 knot

Step-by-step explanation:

yacht speed = 20 knots

yacht bearing = 185° = 85° below the negative horizontal x-axis

wind speed = 15 knots

wind bearing = 290° = 20° above the negative horizontal x-axis

we find the x and y components of the boat velocities

for yacht,

x component = -20 cos 85° = -1.74 knots

y component = -20 sin 85° = -19.92 knots

for the wind,

x component = -15 cos 20° = -14.09 knots

y component = 15 sin 20° = 5.13 knots

total x component Vx = -1.74 + (-14.09) = -15.83 knots

total y component Vy = -19.92 + 5.13 = -14.79 knots

Resultant speed of the boat = $\sqrt{Vx^{2} + Vy^{2} }$

==> $\sqrt{15.83^{2} + 14.79^{2} }$ = 21.66 knot

direction of boat = $tan^{-1} \frac{Vy}{Vx}$

==> $tan^{-1} \frac{14.79}{15.83}$ = 43.05°

3 0

3 years ago