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swat32
2 years ago
14

Can someone please help me with this ​

Mathematics
1 answer:
Readme [11.4K]2 years ago
3 0

Answer:

7) 28.8 in

8) 80.6 mm

9) 68.3 cm

(All answers to the nearest tenth)

Step-by-step explanation:

7) The traingle is a right-angled triangle since the 4 angles of a rectangle are right angles.

Applying Pythagoras' Theorem,

x²= 16² +24²

x²= 832

x= √832

x= 28.8 in (nearest tenth)

8) Applying Pythagoras' Theorem,

x² +40²= 90²

x²= 8100 -1600

x²= 6500

x= 80.6 mm (nearest tenth)

9) See the attached picture for better understanding.

1st picture shows the simplified diagram of the question, indicating where line x lies in the rectangular prism.

Now, if we cut the prism into half diagonally so that we obtain 2 equal triangular prism, we would obtain 2 prisms that look like the one drawn in picture 2.

Now zoom in to the blue face of the prism, we would get a triangle as shown in picture 3.

Let's find the value of y.

Applying Pythagoras' Theorem,

y²= 40² +54²

y²= 4516

y= √4516

Look at picture 2 again at focus at the pink shaded triangle. It has been re-drawn in picture 4.

Now we know that y= √4516.

Applying Pythagoras' Theorem,

x²= (√4515)² +12²

x²= 4660

x= √4660

x= 68.3 cm (nearest tenth)

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(5) Find the Laplace transform of the following time functions: (a) f(t) = 20.5 + 10t + t 2 + δ(t), where δ(t) is the unit impul
Aloiza [94]

Answer

(a) F(s) = \frac{20.5}{s} - \frac{10}{s^2} - \frac{2}{s^3}

(b) F(s) = \frac{-1}{s + 1} - \frac{4}{s + 4} - \frac{4}{9(s + 1)^2}

Step-by-step explanation:

(a) f(t) = 20.5 + 10t + t^2 + δ(t)

where δ(t) = unit impulse function

The Laplace transform of function f(t) is given as:

F(s) = \int\limits^a_0 f(s)e^{-st} \, dt

where a = ∞

=>  F(s) = \int\limits^a_0 {(20.5 + 10t + t^2 + d(t))e^{-st} \, dt

where d(t) = δ(t)

=> F(s) = \int\limits^a_0 {(20.5e^{-st} + 10te^{-st} + t^2e^{-st} + d(t)e^{-st}) \, dt

Integrating, we have:

=> F(s) = (20.5\frac{e^{-st}}{s} - 10\frac{(t + 1)e^{-st}}{s^2} - \frac{(st(st + 2) + 2)e^{-st}}{s^3}  )\left \{ {{a} \atop {0}} \right.

Inputting the boundary conditions t = a = ∞, t = 0:

F(s) = \frac{20.5}{s} - \frac{10}{s^2} - \frac{2}{s^3}

(b) f(t) = e^{-t} + 4e^{-4t} + te^{-3t}

The Laplace transform of function f(t) is given as:

F(s) = \int\limits^a_0 (e^{-t} + 4e^{-4t} + te^{-3t} )e^{-st} \, dt

F(s) = \int\limits^a_0 (e^{-t}e^{-st} + 4e^{-4t}e^{-st} + te^{-3t}e^{-st} ) \, dt

F(s) = \int\limits^a_0 (e^{-t(1 + s)} + 4e^{-t(4 + s)} + te^{-t(3 + s)} ) \, dt

Integrating, we have:

F(s) = [\frac{-e^{-(s + 1)t}} {s + 1} - \frac{4e^{-(s + 4)}}{s + 4} - \frac{(3(s + 1)t + 1)e^{-3(s + 1)t})}{9(s + 1)^2}] \left \{ {{a} \atop {0}} \right.

Inputting the boundary condition, t = a = ∞, t = 0:

F(s) = \frac{-1}{s + 1} - \frac{4}{s + 4} - \frac{4}{9(s + 1)^2}

3 0
3 years ago
Is these correct bro
iren [92.7K]

Answer:

yes

Step-by-step explanation:

if my eyes are good then yes

3 0
3 years ago
What is the intersection of AD and CD? Explain.
timofeeve [1]

Answer:

Point D

Step-by-step explanation:

AD and CD are a line

The intersection of two lines is a point

The two lines intersect at point D

8 0
3 years ago
CAN SOMEONE PLEASE HELP ME WITH THIS ONE I DONT KNOW IF I’m right or no
Arturiano [62]

Answer:

Your right

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
Rewrite the 4cm: 8km as a ratio in the form 1: n
Delicious77 [7]

Answer:

1 : 200000

Step-by-step explanation:

4 cm ⇒ 8 km

4 cm ⇒ 8 × 1000m

4cm ⇒ 8000m

4 cm ⇒ 8000 × 100 cm

4 cm ⇒ 800000cm

4 : 800000

\frac{ 4 \:\::\:\ 800000}{4}

1 : 200000

Therefore,

1 : n

1 : 200000

Hope this helps you.

Let me know if you have any other questions :-)

5 0
2 years ago
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