Tüm alıştırma soruları

Soru 481Soru →

An airport authority is installing a security barrier around a new rectangular radar facility. The facility measures $40$ yards in length and $32$ yards in width. The design for the security barrier requires a heavy-duty steel post at each of the four corners, with additional posts placed exactly every $8$ feet along all four sides. How many steel posts are required in total to enclose the facility?

Cevabı ve açıklamayı göster

Cevap: 54

Cevap

54 posts are required in total.

The correct answer is found by first ensuring all units match. Converting the dimensions to feet gives a length of 120 feet and a width of 96 feet. The total perimeter is 432 feet. Dividing this continuous perimeter by the 8-foot spacing requirement yields exactly 54 posts.

Adım Adım Çözüm

1

Convert the given dimensions from yards to feet.

Length = 40 * 3 = 120 feet. Width = 32 * 3 = 96 feet.

The post spacing is provided in feet, so all measurements must be converted to the same unit before calculating the perimeter.

2

Calculate the total perimeter of the rectangular facility.

Perimeter = 2 * (120 + 96) = 2 * 216 = 432 feet.

The security barrier encloses the entire outer boundary of the facility, which corresponds to its perimeter.

3

Determine the total number of posts required.

Total posts = 432 / 8 = 54.

For any closed loop, the total number of equally spaced posts equals the total perimeter divided by the distance between the posts.

Anahtar Kavram

Calculating perimeter of a rectangle, unit conversions, and dividing a perimeter into equal segments.

Soru 482Soru →

What value of

m

makes the equation

12m - 7 = 41

true?

Cevabı ve açıklamayı göster

Cevap: 4

Cevap

4

Applying the correct sequence of inverse operations (first adding 7, then dividing by 12) yields exactly 4.

Adım Adım Çözüm

1

Add 7 to both sides of the equation.

12m = 48

This is the first inverse operation needed to isolate the variable term.

2

Divide both sides by 12.

m = 4

This inverse operation isolates

m

, giving the final solution.

Anahtar Kavram

Solving two-step linear equations using inverse operations

Tahmini Süre:30s

Soru 483Soru →

A rectangular microchip has a length of $8.0 \times 10^{-3}$ meters and a width of $4.5 \times 10^{-3}$ meters. Calculate the area of the microchip in square meters and express the result in proper scientific notation as $a \times 10^n$ (where $1 \le a < 10$ ). What is the value of the coefficient $a$ ?

Cevabı ve açıklamayı göster

Cevap: 3.6

Cevap

The coefficient

a

is 3.6.

The correct answer is derived by multiplying the coefficients (8.0 × 4.5 = 36), adding the exponents (-3 + -3 = -6), and normalizing the preliminary result of 36 × 10^-6 by moving the decimal left by one place. This creates a proper coefficient of 3.6 and changes the exponent to -5.

Adım Adım Çözüm

1

Set up the multiplication for area

Area =

(8.0 \times 10^{-3}) \times (4.5 \times 10^{-3})

The area of a rectangle is found by multiplying its length by its width.

2

Multiply the coefficients

8.0 \times 4.5 = 36

When multiplying terms in scientific notation, the numerical coefficients are multiplied together.

3

Multiply the powers of 10

10^{-3} \times 10^{-3} = 10^{-6}

When multiplying identical bases, their exponents are added:

-3 + (-3) = -6

.

4

Combine into preliminary result

36 \times 10^{-6}

Bring the multiplied coefficient and combined power of 10 together.

5

Normalize to proper scientific notation

3.6 \times 10^{-5}

Proper scientific notation requires the coefficient

a

to satisfy

1 \le a < 10

. Moving the decimal one place left on 36 increases the exponent by 1 (

-6 + 1 = -5

).

6

Extract the coefficient

a

3.6

The question specifically asks for the value of the coefficient

a

in the final

a \times 10^n

format.

Anahtar Kavram

Multiplying and Normalizing Values in Scientific Notation

Soru 484Soru →

The expression $(2y - 7)^2$ is expanded into the standard polynomial form $ay^2 + by + c$ . What is the value of the coefficient $b$ ?

Cevabı ve açıklamayı göster

Cevap: -28

Cevap

-28

Expanding the perfect square binomial

(2y - 7)^2

requires multiplying

(2y - 7)

by itself. Using the distributive property, the outer product is

(2y)(-7) = -14y

and the inner product is

(-7)(2y) = -14y

. Combining these like terms gives a total middle term of

-28y

. Because the required polynomial form is

ay^2 + by + c

, the value of the coefficient

b

is exactly -28.

Adım Adım Çözüm

1

Rewrite the expression as a product of two binomials.

(2y - 7)(2y - 7)

Writing the binomial twice makes it easier to correctly apply the distributive property (FOIL method) and avoid missing the middle terms.

2

Distribute the terms.

4y^2 - 14y - 14y + 49

Multiplying the First terms, Outer terms, Inner terms, and Last terms ensures that every term in the first binomial is multiplied by every term in the second binomial.

3

Combine the like terms.

4y^2 - 28y + 49

The middle terms,

-14y

and

-14y

, have the same variable raised to the same power, so their coefficients can be added together.

4

Identify the target coefficient.

-28

The standard polynomial form is given as

ay^2 + by + c

. The value of

b

corresponds to the coefficient of the

y

term.

Anahtar Kavram

Expanding Perfect Square Binomials

Soru 485Soru →

A plumber has a copper pipe that is $14.5$ inches long. She cuts off a piece that is $3.75$ inches long. What is the length of the remaining pipe in inches?

Cevabı ve açıklamayı göster

Cevap: 10.75

Cevap

10.75

Subtracting the cut piece (

3.75

inches) from the total length (

14.5

inches) gives the remaining length. Aligning the decimals properly as

14.50 - 3.75

results in exactly

10.75

.

Adım Adım Çözüm

1

Identify the operation needed

Subtraction:

14.5 - 3.75

Cutting a piece off means reducing the total length of the pipe.

2

Align the decimals for subtraction

14.50 - 3.75

To subtract decimals correctly, align the place values by lining up the decimal points. Add a placeholder zero to

14.5

to make it

14.50

.

3

Perform the subtraction

10.75

Subtracting

3.75

from

14.50

yields

10.75

.

Anahtar Kavram

Decimal Subtraction and Alignment

Tahmini Süre:45s

Soru 486Soru →

Given the expression $7x - 2y^2$ , what is its numerical value when $x = 5$ and $y = 3$ ?

Cevabı ve açıklamayı göster

Cevap: 17

Cevap

17

The expression evaluates to 17 by successfully substituting the values into the variables and properly applying the order of operations.

Adım Adım Çözüm

1

Substitute the values

x = 5

and

y = 3

into the algebraic expression.

7(5) - 2(3)^2

Variables must be replaced with their numerical values before evaluating.

2

Calculate the exponent.

7(5) - 2(9)

According to the order of operations (PEMDAS), exponents must be evaluated before multiplication.

3

Perform the multiplication operations.

35 - 18

Multiplication is evaluated before subtraction.

4

Subtract the resulting numbers.

17

This final arithmetic step yields the evaluated expression.

Anahtar Kavram

Evaluating Algebraic Expressions

Soru 487Soru →

An industrial bakery has a large container holding $10\frac{3}{8}$ gallons of vegetable oil. On Monday morning, a baker uses $3\frac{1}{2}$ gallons for a batch of muffins. In the afternoon, they use an additional $2\frac{3}{4}$ gallons for bread dough. How many gallons of vegetable oil remain in the container? (Enter your answer as a decimal.)

Cevabı ve açıklamayı göster

Cevap: 4.125

Cevap

4.125

Converting all fractions to a common denominator of 8 yields

10\frac{3}{8}

total,

3\frac{4}{8}

used first, and

2\frac{6}{8}

used second. Total used is

6\frac{2}{8}

. Subtracting this from

10\frac{3}{8}

leaves

4\frac{1}{8}

. Converting

\frac{1}{8}

to a decimal yields 0.125, making the final answer 4.125.

Adım Adım Çözüm

1

Find a common denominator for all the fractions involved.

The common denominator for 8, 2, and 4 is 8.

Fractions must have the same denominator before they can be added or subtracted.

2

Convert the amounts of oil used into mixed numbers with the common denominator of 8.

3\frac{1}{2} = 3\frac{4}{8}

and

2\frac{3}{4} = 2\frac{6}{8}

.

This prepares the values for addition.

3

Add the amounts used together to find the total amount of oil removed.

3\frac{4}{8} + 2\frac{6}{8} = 5\frac{10}{8} = 6\frac{2}{8}

We must consolidate the used portions before subtracting from the total.

4

Subtract the total oil used from the original amount in the container.

10\frac{3}{8} - 6\frac{2}{8} = 4\frac{1}{8}

Subtracting the total used gives the remaining oil.

5

Convert the final mixed number to a decimal format.

4\frac{1}{8} = 4 + (1 \div 8) = 4.125

The question explicitly requires the answer to be entered as a decimal.

Anahtar Kavram

Adding and subtracting mixed numbers with unlike denominators

Soru 488Soru →

Calculate the precise value of $k$ that makes the following algebraic equation true:

5(2k - 3) = 3k + 13

Cevabı ve açıklamayı göster

Cevap: 4

Cevap

4

The correct value is found by distributing the 5, gathering all variable terms on one side and constants on the other, and finally dividing by the variable's coefficient.

Adım Adım Çözüm

1

Apply the distributive property on the left side of the equation.

10k - 15 = 3k + 13

To eliminate the parentheses and expose the variable terms for grouping.

2

Subtract

3k

from both sides.

7k - 15 = 13

To collect all terms containing the variable

k

on one side of the equation.

3

Add

15

to both sides.

7k = 28

To isolate the variable term by moving constants to the opposite side.

4

Divide both sides by

7

.

k = 4

To solve for the final value of

k

.

Anahtar Kavram

Solving linear equations with variables on both sides using the distributive property.

Soru 489Soru →

Given $x = -4$ and $y = 3$ , what is the exact value of the expression $3|x - y| - |y^2 - x^2|$ ?

Cevabı ve açıklamayı göster

Cevap: 14

Cevap

14

By correctly substituting the variables, following the order of operations, and applying the definition of absolute value, the expression simplifies to

3(7) - 7

, which evaluates precisely to

14

.

Adım Adım Çözüm

1

Substitute the given values for

x

and

y

into the expression.

3|-4 - 3| - |(3)^2 - (-4)^2|

Variable substitution is the first step in evaluating an algebraic expression.

2

Simplify the expression inside the first absolute value bars.

|-4 - 3| = |-7|

Absolute value bars act as grouping symbols, so operations inside them must be performed first.

3

Evaluate the exponents inside the second absolute value bars.

|(3)^2 - (-4)^2| = |9 - 16|

Following the order of operations, exponents are evaluated before subtraction.

4

Simplify the expression inside the second absolute value bars.

|9 - 16| = |-7|

Complete the subtraction inside the grouping symbols.

5

Apply the absolute value function to both simplified terms.

3(7) - 7

The absolute value of any non-zero real number is its positive counterpart:

|-7| = 7

.

6

Perform the final multiplication and subtraction.

21 - 7 = 14

Multiplication is performed before subtraction according to the standard order of operations.

Anahtar Kavram

Evaluating algebraic expressions involving absolute value, exponents, and signed numbers.

Tahmini Süre:1m 30s

Soru 490Soru →

A hiker plans to complete a trail that is $15\frac{3}{4}$ miles long. If she hikes at a consistent average speed of $3\frac{1}{2}$ miles per hour, how many hours will it take her to complete the entire trail?

Cevabı ve açıklamayı göster

Cevap: 4.5

Cevap

4.5

The correct answer is found by converting the total distance (

15\frac{3}{4}

) and the speed (

3\frac{1}{2}

) into improper fractions (

\frac{63}{4}

and

\frac{7}{2}

), and then dividing the distance by the speed. This translates to

\frac{63}{4} \times \frac{2}{7}

, which cross-simplifies perfectly to

\frac{9}{2}

or

4.5

hours.

Adım Adım Çözüm

1

Convert the mixed numbers into improper fractions.

15\frac{3}{4} = \frac{63}{4}

and

3\frac{1}{2} = \frac{7}{2}

Fraction arithmetic requires mixed numbers to be in improper fraction form before dividing.

2

Set up the division equation to solve for time.

Time =

\frac{63}{4} \div \frac{7}{2}

Time is calculated by dividing total distance by the average speed.

3

Change the division to multiplication by using the reciprocal of the divisor.

\frac{63}{4} \times \frac{2}{7}

Dividing by a fraction is mathematically equivalent to multiplying by its reciprocal.

4

Multiply the fractions and simplify the result.

\frac{63 \times 2}{4 \times 7} = \frac{126}{28} = \frac{9}{2} = 4.5

Simplifying the fraction yields the exact number of hours.

Anahtar Kavram

Dividing mixed numbers by converting to improper fractions and multiplying by the reciprocal.

Tahmini Süre:1m 0s

Soru 491Soru →

When the algebraic expression $(4x - 3)(2x^2 + 5x - 1)$ is fully expanded and simplified into standard polynomial form, what is the value of the coefficient of the $x$ term?

Cevabı ve açıklamayı göster

Cevap: -19

Cevap

-19

The correct answer is

-19

because the

x

term is exclusively formed by the sum of the products

(4x)(-1)

and

(-3)(5x)

, which equals

-4x - 15x = -19x

.

Adım Adım Çözüm

1

Identify the goal.

We need to find the coefficient of the

x

term in the product of

(4x - 3)

and

(2x^2 + 5x - 1)

.

Focusing only on the terms that produce an

x

term saves time compared to expanding the entire polynomial expression.

2

Find the first partial product that results in an

x

term.

Multiply the

x

term from the binomial (

4x

) by the constant term from the trinomial (

-1

) to get

-4x

.

An

x

term multiplied by a constant results in an

x

term.

3

Find the second partial product that results in an

x

term.

Multiply the constant term from the binomial (

-3

) by the

x

term from the trinomial (

5x

) to get

-15x

.

A constant multiplied by an

x

term results in an

x

term.

4

Combine the partial products.

-4x + (-15x) = -19x

To find the total

x

term in the expanded polynomial, all like terms must be combined.

5

Identify the final coefficient.

The coefficient of

-19x

is

-19

.

The coefficient is the numerical multiplier of the variable.

Anahtar Kavram

Multiplying Polynomials and Combining Like Terms

Soru 492Soru →

A pottery studio has a storage bin containing $15\frac{1}{4}$ pounds of dry clay. An instructor removes $4\frac{5}{8}$ pounds of the clay for a beginner class and another $3\frac{1}{2}$ pounds for an advanced class. Later that day, a new shipment arrives, and $5\frac{7}{8}$ pounds of clay are added to the bin. How many pounds of clay are in the bin now?

Cevabı ve açıklamayı göster

Cevap: 13

Cevap

13

The correct answer is found by establishing a common denominator for all fractions, correctly borrowing a whole number to subtract the first amount of clay, subtracting the second amount, and then adding the final shipment to yield exactly 13 pounds.

Adım Adım Çözüm

1

Find a common denominator for all fractions.

15\frac{1}{4} = 15\frac{2}{8}

and

3\frac{1}{2} = 3\frac{4}{8}

.

Fractions must have the same denominator before they can be added or subtracted.

2

Subtract the amount of clay used for the beginner class from the total.

15\frac{2}{8} - 4\frac{5}{8} = 14\frac{10}{8} - 4\frac{5}{8} = 10\frac{5}{8}

pounds.

Since

\frac{2}{8}

is smaller than

\frac{5}{8}

, we borrow 1 from 15 to properly execute the subtraction.

3

Subtract the amount of clay used for the advanced class from the new total.

10\frac{5}{8} - 3\frac{4}{8} = 7\frac{1}{8}

pounds.

This accounts for the second removal of clay.

4

Add the newly shipped clay to the remaining amount.

7\frac{1}{8} + 5\frac{7}{8} = 12\frac{8}{8}

pounds.

The new shipment increases the total inventory.

5

Simplify the final mixed number.

13

pounds.

\frac{8}{8}

is equal to 1 whole, so

12 + 1 = 13

.

Anahtar Kavram

Addition and subtraction of mixed numbers with unlike denominators, requiring whole-number borrowing.

Tahmini Süre:1m 15s

Soru 493Soru →

When the expression $(3x - 4)(2x + 5) - x(x - 2)$ is fully expanded and simplified into standard polynomial form, what is the value of the coefficient of $x$ ?

Cevabı ve açıklamayı göster

Cevap: 9

Cevap

9

Expanding the binomials gives

6x^2 + 7x - 20

. Distributing

-x

gives

-x^2 + 2x

. Combining like terms results in

5x^2 + 9x - 20

. The question asks for the coefficient of

x

, which is the number multiplying the

x

term: 9.

Adım Adım Çözüm

1

Multiply the binomials

(3x - 4)

and

(2x + 5)

.

6x^2 + 15x - 8x - 20

, which simplifies to

6x^2 + 7x - 20

.

To expand the first part of the expression using the distributive property (FOIL).

2

Distribute

-x

across the binomial

(x - 2)

.

-x^2 + 2x

.

To expand the second part of the expression, ensuring the negative sign is applied to both terms inside the parentheses.

3

Combine the expanded parts.

(6x^2 + 7x - 20) + (-x^2 + 2x) = 5x^2 + 9x - 20

.

To simplify the full expression into standard polynomial form by grouping like terms.

4

Identify the coefficient of

x

.

The coefficient of

x

in

5x^2 + 9x - 20

is

9

.

This answers the specific question asked.

Anahtar Kavram

Multiplying polynomials and combining like terms

Soru 494Soru →

A machinist needs to drill a hole completely through a steel block that is $3\frac{3}{4}$ inches thick. The drill bit advances through the steel at a constant rate of $\frac{3}{16}$ of an inch per second. How many seconds will it take to drill completely through the block?

Cevabı ve açıklamayı göster

Cevap: 20

Cevap

It will take 20 seconds to drill completely through the block.

To find the time required, the total thickness of the block must be divided by the distance the drill advances per second. Converting

3\frac{3}{4}

to

\frac{15}{4}

and dividing by

\frac{3}{16}

is calculated by multiplying by the reciprocal:

\frac{15}{4} \times \frac{16}{3} = 20

.

Adım Adım Çözüm

1

Convert the mixed number to an improper fraction.

3\frac{3}{4} = \frac{15}{4}

Fraction multiplication and division are performed using improper fractions rather than mixed numbers.

2

Set up the division equation to solve for time.

Time = Distance

\div

Rate =

\frac{15}{4} \div \frac{3}{16}

The time required is equal to the total distance (thickness) divided by the rate of progress.

3

Rewrite the division problem as multiplication by the reciprocal.

\frac{15}{4} \times \frac{16}{3}

Dividing by a fraction is mathematically equivalent to multiplying by its reciprocal.

4

Simplify the fractions by cross-canceling, then multiply.

5 \times 4 = 20

Cross-canceling common factors (15 and 3, 16 and 4) before multiplying makes the final calculation simpler.

Anahtar Kavram

Fraction Division and Applied Rates

Tahmini Süre:50s

Soru 495Soru →

Given the values $x = \frac{1}{2}$ , $y = -4$ , and $z = -2$ , determine the value of the expression $4x^2y - yz^3$ .

Cevabı ve açıklamayı göster

Cevap: -36

Cevap

-36

The correct answer is derived by substituting the variables accurately, applying the exponents (especially noting that a negative base to an odd power remains negative), and strictly following the order of operations to multiply and then subtract.

Adım Adım Çözüm

1

Substitute

x = \frac{1}{2}

,

y = -4

, and

z = -2

into the expression.

4(\frac{1}{2})^2(-4) - (-4)(-2)^3

Variable substitution must be done exactly as given to prepare for evaluation.

2

Evaluate the terms with exponents.

(\frac{1}{2})^2 = \frac{1}{4}

and

(-2)^3 = -8

. The expression becomes

4(\frac{1}{4})(-4) - (-4)(-8)

.

According to the order of operations (PEMDAS), exponents must be resolved before multiplication.

3

Perform the multiplication operations from left to right.

4(\frac{1}{4})(-4) = 1(-4) = -4

and

(-4)(-8) = 32

. The expression is now

-4 - 32

.

Multiplication is the next step in the order of operations. Note that multiplying two negative numbers results in a positive product.

4

Perform the final subtraction.

-4 - 32 = -36

Subtracting a positive number from a negative number moves further left on the number line.

Anahtar Kavram

Evaluating algebraic expressions using rational numbers, negative bases, and the correct order of operations.

Tahmini Süre:1m 0s

Soru 496Soru →

If the polynomial expression $(3x - 5)$ is multiplied by the expression $(Ax^2 + 2x - 7)$ , the resulting simplified polynomial has an $x^2$ coefficient of $-19$ . What is the value of the constant $A$ ?

Cevabı ve açıklamayı göster

Cevap: 5

Cevap

5

The

x^2

terms in the product of

(3x - 5)

and

(Ax^2 + 2x - 7)

are generated by multiplying the

x

terms together

(3x \cdot 2x = 6x^2)

and by multiplying the constant by the

x^2

term

(-5 \cdot Ax^2 = -5Ax^2)

. Setting their sum equal to

-19x^2

gives the equation

6 - 5A = -19

. Solving for

A

yields

A = 5

.

Adım Adım Çözüm

1

Identify combinations that yield an

x^2

term

The

x^2

terms come from multiplying

(3x)

by

(2x)

and

(-5)

by

(Ax^2)

.

To find the coefficient of a specific term without expanding the entire polynomial, only multiply the terms whose exponents sum to the target power.

2

Calculate the partial products

(3x)(2x) = 6x^2

and

(-5)(Ax^2) = -5Ax^2

These represent the only contributions to the

x^2

term in the final expanded polynomial.

3

Formulate an equation for the coefficient

6 - 5A = -19

The sum of the partial

x^2

coefficients must equal the total

x^2

coefficient given in the problem.

4

Solve the linear equation for

A

-5A = -25 \rightarrow A = 5

Isolating the variable

A

provides the final answer.

Anahtar Kavram

Multiplying Polynomials

Soru 497Soru →

A military field generator consumes diesel fuel at a rate of $3.25$ gallons per hour. The generator's fuel tank initially contains $50.4$ gallons of fuel. If the generator runs continuously for $8.4$ hours, how many gallons of fuel remain in the tank?

Cevabı ve açıklamayı göster

Cevap: 23.1

Cevap

23.1

To find the remaining fuel, you first need to determine the total amount used. Multiplying the hourly rate of

3.25

gallons by

8.4

hours gives

27.3

gallons consumed. Subtracting this from the initial

50.4

gallons (

50.4 - 27.3

) leaves exactly

23.1

gallons.

Adım Adım Çözüm

1

Calculate the total amount of fuel consumed by the generator during the run time.

3.25 \times 8.4 = 27.3

gallons

The total fuel consumed is found by multiplying the hourly consumption rate by the total number of hours the generator operates.

2

Calculate the remaining fuel by subtracting the consumed fuel from the initial amount.

50.4 - 27.3 = 23.1

gallons

The fuel left in the tank is the difference between the starting volume and the volume that was burned.

Anahtar Kavram

Solving multi-step practical arithmetic problems involving decimal multiplication and decimal subtraction.

Tahmini Süre:1m 0s

Soru 498Soru →

An industrial pump dispenses $3.45$ liters of a chemical per cycle. A tank initially contains $150.8$ liters of the chemical. If the pump runs for $14$ cycles to remove the chemical from the tank, and then a technician manually adds $5.25$ liters back into the tank, how many liters of chemical remain in the tank?

Cevabı ve açıklamayı göster

Cevap: 107.75

Cevap

107.75

The final volume is accurately found by multiplying the removal rate by the number of cycles to determine the total removed amount, subtracting that from the initial volume, and finally adding the manually returned amount while maintaining proper decimal alignment.

Adım Adım Çözüm

1

Calculate the total volume of chemical removed by the pump.

14 \times 3.45 = 48.3

The pump runs for 14 cycles, removing 3.45 liters each time, so multiplication is required to find the total removal.

2

Subtract the removed volume from the initial tank volume.

150.8 - 48.3 = 102.5

Removing the chemical decreases the total volume available in the tank.

3

Add the volume of the chemical manually poured back into the tank.

102.5 + 5.25 = 107.75

Adding chemical increases the total volume to its final amount.

Anahtar Kavram

Solving multi-step practical problems involving the multiplication, subtraction, and addition of decimals.

Tahmini Süre:1m 0s

Soru 499Soru →

A sample of mineral oil has a density of $0.8\text{ g/cm}^3$ and a volume of $50\text{ cm}^3$ . What is the mass of the oil sample in grams?

Cevabı ve açıklamayı göster

Cevap: 40

Cevap

40 g

The mass of a substance is determined by multiplying its density by its volume:

\text{Mass} = \text{Density} \times \text{Volume} = 0.8\text{ g/cm}^3 \times 50\text{ cm}^3 = 40\text{ g}

.

Adım Adım Çözüm

1

State the formula for calculating mass from density and volume

\text{Mass} = \text{Density} \times \text{Volume}

Density represents mass per unit volume (

\text{Density} = \frac{\text{Mass}}{\text{Volume}}

); rearranging this relationship isolates mass.

2

Substitute the given values into the equation and compute the result

\text{Mass} = 0.8\text{ g/cm}^3 \times 50\text{ cm}^3 = 40\text{ g}

Multiplying the density (

0.8\text{ g/cm}^3

) by the total volume (

50\text{ cm}^3

) yields the total mass in grams.

Anahtar Kavram

The relationship between mass, volume, and density as physical properties of matter

Tahmini Süre:45s

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A $12\text{ V}$ direct-current car battery is connected to a circuit powering a single headlight with a resistance of $4\,\Omega$ . What is the electric current, in amperes, flowing through the headlight?

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Cevap: 3

Cevap

The electric current flowing through the headlight is 3 amperes.

According to Ohm's law, electric current (

I

) equals voltage (

V

) divided by resistance (

R

). Dividing a voltage of

12\text{ V}

by a resistance of

4\,\Omega

yields an electric current of

3\text{ A}

.

Adım Adım Çözüm

1

Identify the relationship between voltage, current, and resistance using Ohm's law.

V = I \times R

, which rearranges to

I = \frac{V}{R}

.

Ohm's law governs the relationship between electric potential difference, current flow, and resistance in a DC circuit.

2

Substitute the given values into the formula and solve for current.

I = \frac{12\text{ V}}{4\,\Omega} = 3\text{ A}

Dividing the electromotive force (voltage) by the total circuit resistance yields the resulting electric current.

Anahtar Kavram

Ohm's Law (

V = IR

)

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