সরল রেখার ঢাল বা গ্র্যাডিয়েন্ট কিসের সাথে সম্পর্কিত?

সরল রেখার সমীকরণের সহগের সাথে।

পয়েন্টের সংখ্যা

রেখার দৈর্ঘ্য

সরল রেখার সমীকরণকে গ্রাফে চিত্রায়িত করার জন্য কি প্রয়োজন?

ঢাল এবং y-অক্ষের ছেদন।

শুধুমাত্র ছেদন

একটি পয়েন্ট

শুধুমাত্র ঢাল

সরল রেখা পরস্পর লম্ব হলে কি হয়?

তাদের ঢাল একে অপরের বিপরীতমুখী।

তাদের ঢাল সমান

তাদের কোনো সম্পর্ক নেই

তাদের ছেদন সমান

যদি দুটি রেখার সমান্তরাল হতে চায়, তবে তাদের কি শর্ত থাকতে হয়?

ঢাল সমান হতে হবে।

ঢাল অনির্দিষ্ট হতে হবে।

ছেদন সমান হতে হবে।

ঢাল বিপরীত হতে হবে।

একটি রেখার গ্রাফে X-অক্ষ এবং Y-অক্ষের উপর ছেদন বের করার জন্য কি লাগে?

দুটি পয়েন্টের সমন্বয়।

শুধু একটি পয়েন্ট

ছেদন ছাড়া কিছুই লাগে না

The Straight Lines

Create a quiz over the following topic: Visual Art: Elements of Art, Music, Dance, and Drama A. Elements of Visual Art: There are seven primary elements of art (line, shape, form, space, color, value, texture), the components from which any artwork can be built. Any artwork that can stand the test of time will contain these elements. Element 1 – Line Line is the most fundamental concept in art. This element leads the viewer’s eye around the artwork, communicating the piece’s meaning to the viewer. Without this element, none of the other elements could exist. At its most basic foundation, a line is simply a moving dot. When these dots overlap, the line is solid. When they do not overlap, the line is dotted or dashed. These “incomplete” lines can represent movement or hidden material behind the primary figure. Repeated lines create patterns, and these patterned lines create a rhythm for the work. Lines can be: • Curved • Zigzag • Horizontal • Vertical • Diagonal • Implied • Gesture • Varied thicknesses • Varied lengths Examples of lines and their meaning in art: Thick Lines – give emphasis and advance Thin Lines – recede and cause the eye to “lose interest” Straight Lines – rarely found in nature, thus are inorganic. Straight lines are dynamic and mechanistic. Curved Lines – gently change directions and have no sharp angles, suggesting calmness – Curved lines are more readily found in nature and are thus considered organic lines Works with pronounced curved lines include Van Gogh’s The Starry Night (1889). Note the movement across the sky.

Let's Make Shapes! A line connects two points. A line is longer than it is wide. Lines can be short, and lines can be long. Lines can be straight, and lines can be curved. You can bend lines to make a shape. You can join straight lines together to make a shape. You can join curved lines together to make a shape. There are many kinds of shapes. Circles, squares, rectangles, and triangles are geometric shapes. We can use geometric shapes to draw many things. When a line goes all the way around, it makes a circle. You can use a circle, three small circles, and a curved line to make a face. On another piece of paper, draw a circle. Then make it a mouse with eyes, ears, and whiskers. Use lines and more circles. If we cut a circle in half, we get two half-circles. You can use four half-circles to draw a caterpillar. On another piece of Then make it into a fish paper, draw a half-circle. with eyes, a tail, and fins. When a line turns a corner three times, it makes a triangle. Triangles have three sides and three corners. You can use triangles to make a face on a pumpkin. On another piece of paper, Then make it into a tree draw a triangle. with leaves and a trunk. When a line turns a corner four times, it makes a square. A square has four sides and four corners. Each side is the same length. You can use squares and half-circles to make a truck. On another piece of paper, draw a square. Then make it into a dog by adding ears, a tail, and legs. Use curved lines and straight lines. A rectangle has four sides, just like a square. Two sides are the same length. The other two sides are another length. You can use rectangles, circles, squares and lines to draw a bus. On another piece of paper, draw a rectangle. Then make it a house with a roof, two windows, and a door. Use a triangle and three rectangles. Now, on another piece of paper, make a picture using all of the shapes: circles, squares, triangles, and rectangles.

7.2.1 Critical Angle 1. The critical angle is the angle of incidence at which the refracted ray: A. Bends toward the normal B. Bends away from the normal C. Travels along the boundary D. Is totally reflected Answer: C 7.2.2 Snell’s Law & Critical Angle 2. Which formula correctly represents the critical angle c when light travels from medium 1 to medium 2? A. n1cos⁡c=n2 B. n2sin⁡c=n1 C. n1sin⁡c=n2 D. n1sin⁡c=n2sin⁡90∘ Answer: D 7.2.3 Total Internal Reflection 3. Total internal reflection occurs only when: A. Light travels from air to glass B. Angle of incidence is less than the critical angle C. Light travels from a denser to a rarer medium D. Refractive index of the second medium is greater Answer: C 4. Which condition is not required for total internal reflection? A. Light must travel from a denser medium B. Angle of incidence must exceed the critical angle C. Refractive index of second medium must be lower D. Light must strike at 90° Answer: D 7.2.4 Ray Diagrams & Angle Calculations 5. A ray in water (n = 1.33) hits the surface at 40°. Critical angle = 48.8°. What happens? A. Refraction only B. Total internal reflection C. No refraction D. Light stops Answer: A 7.2.5 Snell’s Law in Glass Blocks & Prisms 6. A ray enters glass (n = 1.5) from air at 30°. Which statement is correct? A. It bends away from the normal B. It bends toward the normal C. It travels straight D. It undergoes total internal reflection Answer: B 7. In a prism, the deviation of light occurs mainly because: A. Light slows down in glass B. Light speeds up in glass C. Light reflects internally D. Light cannot pass through glass Answer: A 7.2.6 Mirages 8. A mirage appears on a hot road because: A. Light reflects off the sky B. Light refracts through layers of air with different densities C. Light undergoes dispersion D. Light travels in straight lines only Answer: B 7.2.7 Dispersion Through a Prism 9. Dispersion occurs because: A. All colors refract equally B. Different wavelengths refract differently C. The prism reflects light D. White light cannot be refracted Answer: B 7.2.8 Rainbow Formation 10. A rainbow is formed due to: A. Refraction only B. Total internal reflection only C. Dispersion only D. Refraction + TIR + dispersion Answer: D 7.2.9 Optical Fibers 11. Optical fibers work mainly due to: A. Refraction B. Diffraction C. Total internal reflection D. Dispersion Answer: C 12. Which is an advantage of optical fibers? A. High signal loss B. Immune to electromagnetic interference C. Very heavy D. Slow data transmission Answer: B

CONCEPT OF INTEGERS What are INTEGERS? Integers are whole numbers that describe opposite ideas in mathematics. Integers can either be negative (-), positive (+) or zero. The integer zero is neutral. It is neither positive nor negative, but is an integer. Integers can be represented on a number line, which can help us understand the value of the integer. POSITIVE INTEGERS Are numbers to the right of zero. Are valued greater than zero. Express ideas of up, a gain or a profit. The sign for a positive integer is (+), however the sign is not always needed. Meaning +3 is the same value as 3. NEGATIVE INTEGERS Are numbers to the left of zero. Are valued less than zero. Express ideas of down or a loss. The sign for a negative integer is (-). This sign is always needed. Opposite Numbers/Integers – are the pairs of integers that have the same absolute value or have the same distance away from zero. ABSOLUTE VALUE The distance of a number from the origin (0) regardless of direction is called absolute value. The absolute value of a number is never negative. The symbol for absolute value is two straight lines surrounding the number or expression for which you wish to indicate absolute value. Examples: I 4 I = 4, +4 is read “ the absolute value of 4 is 4 “ I -3 I = 3, -3 is read “ the absolute value of -3 is 3” - I 3 I = -3, means “ the negative of the absolute value of 3 is -3 “ COMPARING AND ARRANGING INTEGERS Integers can be compared using a number line. As you move to the left along the number line, the integers decrease in value. On the other hand, integers increase in value as you move to the right along the number line. To arrange integers in ascending order is to arrange them from least to greatest. This means that when you use the number line, the smallest the integer is to the left of 0 on the number line. To arrange integers in descending order is to arrange them from greatest to least. This means that when you use the number line, the largest the integer is to the right of 0 on the number line. This is read as “nine is greater than negative 12.” This is read as “negative thirteen is less than negative 5.” This is read as “negative eight is greater than negative 18.”

What are INTEGERS? Integers are whole numbers that describe opposite ideas in mathematics. Integers can either be negative (-), positive (+) or zero. The integer zero is neutral. It is neither positive nor negative, but is an integer. Integers can be represented on a number line, which can help us understand the value of the integer. POSITIVE INTEGERS Are numbers to the right of zero. Are valued greater than zero. Express ideas of up, a gain or a profit. The sign for a positive integer is (+), however the sign is not always needed. Meaning +3 is the same value as 3. NEGATIVE INTEGERS Are numbers to the left of zero. Are valued less than zero. Express ideas of down or a loss. The sign for a negative integer is (-). This sign is always needed. Opposite Numbers/Integers – are the pairs of integers that have the same absolute value or have the same distance away from zero. ABSOLUTE VALUE The distance of a number from the origin (0) regardless of direction is called absolute value. The absolute value of a number is never negative. The symbol for absolute value is two straight lines surrounding the number or expression for which you wish to indicate absolute value. Examples: I 4 I = 4, +4 is read “ the absolute value of 4 is 4 “ I -3 I = 3, -3 is read “ the absolute value of -3 is 3” - I 3 I = -3, means “ the negative of the absolute value of 3 is -3 “ COMPARING AND ARRANGING INTEGERS Integers can be compared using a number line. As you move to the left along the number line, the integers decrease in value. On the other hand, integers increase in value as you move to the right along the number line. To arrange integers in ascending order is to arrange them from least to greatest. This means that when you use the number line, the smallest the integer is to the left of 0 on the number line. To arrange integers in descending order is to arrange them from greatest to least. This means that when you use the number line, the largest the integer is to the right of 0 on the number line. This is read as “nine is greater than negative 12.” This is read as “negative thirteen is less than negative 5.” This is read as “negative eight is greater than negative 18.” R

What are INTEGERS? Integers are whole numbers that describe opposite ideas in mathematics. Integers can either be negative (-), positive (+) or zero. The integer zero is neutral. It is neither positive nor negative, but is an integer. Integers can be represented on a number line, which can help us understand the value of the integer. POSITIVE INTEGERS Are numbers to the right of zero. Are valued greater than zero. Express ideas of up, a gain or a profit. The sign for a positive integer is (+), however the sign is not always needed. Meaning +3 is the same value as 3. NEGATIVE INTEGERS Are numbers to the left of zero. Are valued less than zero. Express ideas of down or a loss. The sign for a negative integer is (-). This sign is always needed. Opposite Numbers/Integers – are the pairs of integers that have the same absolute value or have the same distance away from zero. ABSOLUTE VALUE The distance of a number from the origin (0) regardless of direction is called absolute value. The absolute value of a number is never negative. The symbol for absolute value is two straight lines surrounding the number or expression for which you wish to indicate absolute value. Examples: I 4 I = 4, +4 is read “ the absolute value of 4 is 4 “ I -3 I = 3, -3 is read “ the absolute value of -3 is 3” - I 3 I = -3, means “ the negative of the absolute value of 3 is -3 “ COMPARING AND ARRANGING INTEGERS Integers can be compared using a number line. As you move to the left along the number line, the integers decrease in value. On the other hand, integers increase in value as you move to the right along the number line. To arrange integers in ascending order is to arrange them from least to greatest. This means that when you use the number line, the smallest the integer is to the left of 0 on the number line. To arrange integers in descending order is to arrange them from greatest to least. This means that when you use the number line, the largest the integer is to the right of 0 on the number line. This is read as “nine is greater than negative 12.” This is read as “negative thirteen is less than negative 5.” This is read as “negative eight is greater than negative 18.”

The following days are a jumble of gunfire, digging, gobbled food, soldiers running in and out of the forest in small groups, distant explosions, stray shells, bandaged heads and unexpected lulls. On the very first day, before dawn, I am ordered into one of the newly dug trenches. I huddle there, squeezing my magic buttons and singing songs to the dog. When the fighting stops, the dog disappears, but a new companion takes his place. A strange little soldier crawls along the trench toward me. ‘Private Sasha!’ he cries. ‘I’ve been looking for you all day long!’ He’s old, like a grandfather, a dedushka. He has a black patch over one eye, a tape measure around his neck and a row of pins threaded into his sleeve. Hanging from his belt is the most enormous pair of scissors I have ever seen and I wonder if he uses them as a weapon. He doesn’t tell me his name, so in my head he becomes Dedushka. Dedushka squats, cups his hand to his ear, peers over the top of the trench and smiles. ‘It’s safe to be upright . . . for now.’ He helps me to my feet, dusts me off and commands me to stand as tall and straight as I can. Then he measures me. Everything from head to toe – even my toes! He writes numbers in a little notebook, strings his tape measure back around his neck, salutes and hurries away. It’s all very strange, and I wonder if Dedushka has been bumped on the head during the battle and is now a little bit muddled. I should have given him a hug before he left. I chase after him but stop when I’m hit by a shovelful of flying dirt. Sleepy Bear is digging a cave! ‘Are you going to hibernate?’ I ask. Sleepy Bear chuckles. ‘No, although that would be wonderful! I could do with a lo-o-o-ong sleep.’ He sighs and closes his eyes. He doesn’t open them again and I realise that he has gone to sleep. Standing up! I shake his arm, and he opens his eyes and keeps talking. ‘No, I’m not hibernating. I’m digging a little nook where I can sleep and eat. I’ll hang up my raincape as a door that can open and close so it feels just like a real home . . . except for the lice . . . and the bad smells . . . and the bombs that make the walls shake and crumble.’ He points further along the trench to where other soldiers are digging. ‘We’re all making little houses in the ground.’ ‘Like rabbits and moles,’ I say. Sleepy Bear chuckles. ‘Yes! And soldiers who need to hide from German bullets and bombs.’ He stops digging to roll a cigarette. ‘Should I be making a house?’ I ask. ‘I want to hide from German bullets and bombs, too.’ Sleepy Bear flops to the ground, lights his cigarette, closes his eyes and takes a deep puff. I wait for him to answer, but, instead, he begins to snore! I poke him in the side. He snorts and he murmurs, ‘I think someone has already built you a house, Sasha. Keep going along this beautiful village street and you are sure to find it.’ He falls asleep once more. I kiss his dusty cheek and whisper, ‘Thank you, Sleepy Bear.’ A little way along, I see Cook in a cloud of smoke. He has lit a fire, right here in the middle of the trench, and is stirring a cauldron full of kasha. He squats as he stirs. ‘What are you doing?’ I ask. ‘Cooking supper, of course!’ he cries. ‘But why are you doing it here?’ Cook points his spoon at the ground above the trenches. ‘Because if I do it up there, my pot will be filled with holes from German bullets and all of the kasha will leak out onto the ground. It’s bad enough that our supplies can’t get through German lines and there’s nothing to cook but buckwheat for kasha. But if we lost the kasha, too . . .’ ‘Hungry soldiers,’ I say. Cook nods. ‘And grumpy!’ ‘Like Boris!’ I gasp. ‘Even worse,’ warns Cook. I picture the kasha pot full of bullet holes. And then I realise that if the kasha pot were full of holes, then Cook would be, too. I wrap my arms around Cook’s neck and say, ‘I think this is a very good place for cooking our supper.’ I kiss his smoky cheek and run along. At the end of the trench, I find the biggest hole of all. It’s wide and deep and as busy as a beehive in a blossom tree. Above, a group of soldiers is rolling logs into place for a roof, while below, typewriters rattle and pencils scratch and papers flutter and voices crackle out of five different radios. Their words tangle together to tell a strange wartime fairy tale about German guns and a loving father called Stalin and a Red Army regiment that is lost in the deep, dark forest and a wicked beast called Hitler and a delivery of vegetables that was hit by a bomb and blown into a million tiny pieces too small even to make soup. In the middle of it all, wrestling with a rumpled map, his rifle still slung over his shoulder, is Major Scruff. ‘Major Scruff!’ I run and jump into his arms. ‘Is this our new home?’ ‘Yes, Sasha. I suppose it is.’ ‘Is it safe from German bullets and bombs?’ I ask. He stares at me. ‘Were you scared in the trenches today, Sasha?’ ‘No,’ I reply. ‘I had magic buttons and a dog and some songs to sing. Were you scared in the forest, Major Scruff?’ ‘Yes,’ he says. ‘Poor Major Scruff!’ I press my hand against his cheek. The dark, rough stubble is grubby with grit and his eyelids are taking a long time to open after every blink. ‘You need a shave and a nap!’ I scold. He chuckles. ‘I am too tired to shave and too busy to nap.’ I scrunch my nose while I consider his problem. ‘I know!’ I cry. ‘You nap and I will shave your whiskers. That will be two jobs tumbled into one!’ And so that’s what we do. Major Scruff slumps into a chair and snoozes while I lather his face with soapy water and shave his whiskers. The soap suds travel from his face, up into his hair and down the front of his uniform, and I have to shave his jaw and chin three times because I keep missing bits, but I finally get it all done. I am just wiping his cheeks dry when the dog appears. He licks my hand, then stretches up and licks soap suds from Major Scruff’s ear. Major Scruff wakes with a start. He feels his newly shaved face and cries, ‘Wonderful, Sasha! I feel smooth, clean, rested and ready for action.’ He ruffles my hair. ‘We must do this again tomorrow. Although next time, you might wake me with a gentle shake of the shoulder instead of licking my ear.’

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