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Find the possible values for s in the inequality 12s – 20 ≤ 50 – 3s – 25.

Margaret [11]

◆ INEQUALITIES ◆

$given \: expression \: \: - \\ \\ 12s - 20 \leqslant 50 - 3s - 25 \\ \\ 12s - 20 \leqslant 25 - 3s \\ \\ adding \: 20 \: both \: sides \: \: , \: \\ we \: get \: - \\ \\ 12 s \leqslant 45 - 3s \\ \\ 12s + 3s \leqslant 45 \\ \\ 15s \leqslant 45 \\ s \leqslant \frac{45}{15} \\ \\ \\ s \leqslant 3 \: \: \: \: \: \: ans.$

8 0

3 years ago

Express the quotient of z1 and z2 in standard form given that <img src="https://tex.z-dn.net/?f=z_%7B1%7D%20%3D%20-3%5Bcos%28%5C

Lesechka [4]

Answer:

Solution : $-\frac{3}{4}-\frac{3}{4}i$

Step-by-step explanation:

$-3\left[\cos \left(\frac{-\pi }{4}\right)+i\sin \left(\frac{-\pi \:}{4}\right)\right]\:\div \:2\sqrt{2}\left[\cos \left(\frac{-\pi \:\:}{2}\right)+i\sin \left(\frac{-\pi \:\:\:}{2}\right)\right]$

Let's apply trivial identities here. We know that cos(-π / 4) = √2 / 2, sin(-π / 4) = - √2 / 2, cos(-π / 2) = 0, sin(-π / 2) = - 1. Let's substitute those values,

$\frac{-3\left(\frac{\sqrt{2}}{2}-\frac{\sqrt{2}}{2}i\right)}{2\sqrt{2}\left(0-1\right)i}$

= $-3\left(\frac{\sqrt{2}}{2}-\frac{\sqrt{2}}{2}i\right)$ ÷ $2\sqrt{2}\left(0-1\right)i$

= $3\left(-\frac{\sqrt{2}i}{2}+\frac{\sqrt{2}}{2}\right)$ ÷ $-2\sqrt{2}i$

= $\frac{3\left(1-i\right)}{\sqrt{2}}$ ÷ $2\sqrt{2}i$ = $-3-3i$ ÷ $4$ = $-\frac{3}{4}-\frac{3}{4}i$

As you can see your solution is the last option.

3 0

3 years ago

Javier has four cylindrical models. The heights, radii, and diagonals of the vertical cross-sections of the models are shown in

Ronch [10]

The model in which the lateral surface meets the base at right angle is : Model 1.

<h3>What is a lateral surface?</h3>

The lateral surface of an object is all surfaces of that object excluding its base and top.

Analysis:

To know the exact model, we check for the models in which their dimensions form a Pythagorean triplet otherwise a right-angled triangle.

For Pythagorean triplet, the square of the diagonal must be equal to the sum of squares of the other two sides.

Model 1

Diagonal = 50cm, radius = 14cm, lateral height = 48cm

$(50)^{2}$ = $(14)^{2}$ + $(48)^{2}$

2500 = 196 + 2304

2500 = 2500. Forms Pythagorean triplet

Model 2

Diagonal= 37cm, radius = 6cm lateral height = 35cm

$(37)^{2}$ = $(35)^{2}$ + $(6)^{2}$

1369 = 1225 +36

1369 $\neq$ 1261

Model 3

Diagonal = 60cm, radius = 20cm lateral height = 40cm

$(60)^{2}$ = $(20)^{2}$ + $(40)^{2}$

3600 = 400 + 1600

3600 $\neq$ 2000

Model 4

Diagonal = 30cm, radius = 24cm, lateral height = 9cm

$(30)^{2}$ = $(24)^{2}$ + $(9)^{2}$

900 = 576 + 81

900 $\neq$ 657

Therefore the lateral surface model 1 meets the base at right angle

In conclusion, the lateral surface of model 1 meets the base at right angles as the dimensions form a right-angled triangle.

Learn more about Pythagorean triplet: brainly.com/question/20894813

#SPJ1

5 0

2 years ago

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HELP PLEASE

Gnesinka [82]

Answer: $x^2=8y$

Step-by-step explanation:

Let the given parabolic mirror opens upwards and vertex=(0,0)

Focus point of the parabolic mirror is located 2 inches from the vertex of the mirror. ∴ p=2

Since, the parabola opens upward, then the equation of the parabola is of the form $x^2=4py$

Substitute the value of p=2 in this, we get the equation of the parabolic mirror

$x^2=4(2)y\\\Rightarrow\ x^2=8y$

Hence, the equation of the parabola that models the cross section of the mirror is $x^2=8y$

7 0

3 years ago

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A crew you’re supervising is installing a circular patio. In order to purchase the materials, they need to compute the area. The

lawyer [7]

Answer:

it would be 37.69 square yards the answer that was given is off by .01

Step-by-step explanation:

you multiply 12 times pi (3.14) = 37.69

8 0

4 years ago

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