Show that <img src="https://tex.z-dn.net/?f=%5Csqrt%7B20%7D%20%3D2%5Csqrt%7B5%7D" id="TexFormula1" title="\sqrt{20} =2\sqrt{5}"

4(2y-7)=64+12y<br> 2y-7=16+3y<br> 5y=23<br> Y=4.6<br> Is this equivalent? <br> (Explain)

ratelena [41]

Yes it is equivalent because you need to isolate the y so divide by 5 on both sides and 23 divided by 5 is 4.6

8 0

3 years ago

7. During the Middle Ages, people often used grains, scruples, and drahms to measure the weights of different medicines. If 120

Serjik [45]

Answer:

5 drahms.

Step-by-step explanation:

From the question given above, the following data were obtained:

120 grains = 6 scruples

6 scruples = 2 drahms

300 grains (in drahms) =..?

From the above data,

120 grains = 6 scruples

6 scruples = 2 drahms

Therefore,

120 grains = 2 drahms

Thus, we can obtain 300 grains in drahms as follow:

120 grains = 2 drahms

Therefore,

300 grains = 300 grains × 2 drahms /120 grains

300 grains = (300 × 2)/120 drahms

300 grains = 5 drahms

Therefore, 300 grains is equivalent to 5 drahms.

5 0

3 years ago

A police helicopter is flying at 150 mph at a constant altitude of 0.5 mile above a straight road. The pilot uses radar to deter

natali 33 [55]

Answer:

a) (see attached picture)

b) d, h, velocity of helicopter, dd/dt

in the direction oposite to the movement of the helicopter.

Step-by-step explanation:

In order to solve this problem we must start by drawing a diagram that will represent the situation (see attached picture). As you may see, there is a right triangle being formed by the helicopter, the car and the graound. We can use this to build the equation we are going to use to model the problem.

$d^{2}=h^{2}+x^{2}$

we can use this equation to find the value of x at that very time, so we can do that by solving the equation for x, so we get:

$x=\sqrt{d^{2}-h^{2}}$

and substitute the given values:

$x=\sqrt{(1)^{2}-(0.5)^{2}}$

which yields:

x=0.866mi

we know that the height of the helicopter is going to be constant, so we rewrite the equation as:

$d^{2}=(0.5)^{2}+x^{2}$

$d^{2}=0.25+x^{2}$

Next, we can go ahead and differentiate the equation so we get:

$2d\frac{dd}{dt}=2x\frac{dx}{dt}$

which can be simplified to:

$d\frac{dd}{dt}=x\frac{dx}{dt}$

we can next solve the equation for dx/dt so we get:

$\frac{dx}{dt}=\frac{d}{x}*\frac{dd}{dt}$

so we can now substitue te provided values so we get:

$\frac{dx}{dt}=\frac{1}{0.866}*-190$

so we get:

$\frac{dx}{dt}=-219.40mph$

the negative sign means that the x-value is decreasing.

now, this problem deals with relative velocities, so we get that:

Velocity of car about the helicopter = Velocity of the car - Velocity of the helicopter. Or:

$V_{ch}=V_{c}-V_{h}$

so we can solve this for the actual velocity of the car, so we get:

$V_{c}=V_{ch}+V_{h}$

so we get:

$V_{c}=-219.40mph+150mph$

which yields:

$V_{c}=-69.4mph$

So it has a velocity of 69.4mph in a direction oposite to the helicopter's movement.

4 0

3 years ago

The previous triangular prism had a surface area of 288 square units. What happens to the surface area of your prism when you do

melisa1 [442]

If all four dimensions of triangular prism having surface area as 288 is doubled than new surface area will be four times than the initial prism that is 1152 square unit.

<h3><u>Solution:</u></h3>

Given that

Surface area of a triangular prism = 288 square unit

Need to evaluate new surface area if all four measurement of triangular prism is double.

Relation between surface area and the four dimensions of the triangular prism is given by following formula

Surface Area of triangular prism = bh + 2ls + lb

Where h is height of the prism , b is length of base of the prim , l is length of the prism and s is side length of the prism.

Given that Area of triangular prism = 288 square unit

=> bh + 2ls +lb = 288

Doubling the four dimensions means replace b by 2b, l by 2l , s by 2s and h by 2h in formula of Surface area of triangular prism.

$\text { We get Surface area of new triangular prism }=2 b \times 2 h+2 \times 2 l \times 2 s+2 l \times 2 b$

$\begin{array}{l}{=4 \times b h+4 \times 2 l s+4 \times l b} \\\\ {=4(b h+2 l s+l b)}\end{array}$

=> Surface area of new triangular prism = 4 (bh + 2ls +lb)

=> Surface area of new triangular prism = 4 x 288 = 1152 square unit.

Hence we can conclude that if all four dimensions of triangular prism having surface area as 288 is doubled than new surface area will be four times than the initial prism that is 1152 square unit.

8 0

2 years ago

Read 2 more answers

Wes makes 35,000 a year at his job he is going to recieve 3% how much will he make aafter the raise

N76 [4]

First find what 3% of his salary is
35000*0.03= 1,050

Add the 3% to his original salary
35000+1050= 36,050

3 0

3 years ago