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3 years ago

I'm having a hard time completing Task 2 of d. and e. Please answer them.

Mathematics

1 answer:

My name is Ann [436]3 years ago

8 0

Step-by-step explanation:

In part (d), we are shown how the sum of consecutive integers can be found. The sum is:

S = n (x + y) / 2

where n is the number of integers, x is the first integer, and y is the last integer.

We want to use this formula to find the sum of the numbers 101-110. We know there are 10 numbers between 101 and 110, so n = 10.

S = 10 (101 + 110) / 2

S = 1055

We used deductive reasoning to find the answer.

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devlian [24]

Answer:

It always has a solution until you get to imaginary numbers.

Plug in a=b for a=2

2≥2 which is true! so it will always have a solution.

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3 years ago

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Ahat [919]

Answer:

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Step-by-step explanation:

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3 years ago

(cotx+cscx)/(sinx+tanx)

Butoxors [25]

Answer: $\bold{\dfrac{cot(x)}{sin(x)}}$

<u>Step-by-step explanation:</u>

Convert everything to "sin" and "cos" and then cancel out the common factors.

$\dfrac{cot(x)+csc(x)}{sin(x)+tan(x)}\\\\\\\bigg(\dfrac{cos(x)}{sin(x)}+\dfrac{1}{sin(x)}\bigg)\div\bigg(\dfrac{sin(x)}{1}+\dfrac{sin(x)}{cos(x)}\bigg)\\\\\\\bigg(\dfrac{cos(x)}{sin(x)}+\dfrac{1}{sin(x)}\bigg)\div\bigg[\dfrac{sin(x)}{1}\bigg(\dfrac{cos(x)}{cos(x)}\bigg)+\dfrac{sin(x)}{cos(x)}\bigg]\\\\\\\bigg(\dfrac{cos(x)}{sin(x)}+\dfrac{1}{sin(x)}\bigg)\div\bigg(\dfrac{sin(x)cos(x)}{cos(x)}+\dfrac{sin(x)}{cos(x)}\bigg)$

$\text{Simplify:}\\\\\bigg(\dfrac{cos(x)+1}{sin(x)}\bigg)\div\bigg(\dfrac{sin(x)cos(x)+sin(x)}{cos(x)}\bigg)\\\\\\\text{Multiply by the reciprocal (fraction rules)}:\\\\\bigg(\dfrac{cos(x)+1}{sin(x)}\bigg)\times\bigg(\dfrac{cos(x)}{sin(x)cos(x)+sin(x)}\bigg)\\\\\\\text{Factor out the common term on the right side denominator}:\\\\\bigg(\dfrac{cos(x)+1}{sin(x)}\bigg)\times\bigg(\dfrac{cos(x)}{sin(x)(cos(x)+1)}\bigg)$

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4 years ago

Solving Linear Equations Unit Test 16 of 20Items Item 16 Gold has a density of 0.70 pounds per cubic inch and copper has a densi

mina [271]

Answer:

1 ft³ of gold will weigh 1209.6 pounds

1 ft³ of copper will weigh 559 pounds.

Step-by-step explanation:

We know the formula for:

Density = Mass/Volume

Hence, making mass the subject of the formula:

Mass = Density × Volume

From the question we are told:Volume of each metal = 1 ft³

1) Metal: Gold

Density of Gold = 0.70 pounds per cubic inch(lb/in³)

We convert the Volume of gold from ft³ to in³

The Volume of gold given in the question = 1 cubic foot = 1 ft³

1 cubic foot = 1728 cubic inches

Hence, the volume of Gold = 1728 in³

Mass of Gold = Density of Gold × Volume of Gold

Mass of Gold = 0.70Ib/in³ × 1728 in³

= 1209.6 lb(pounds)

2) Metal : Copper

Density of copper given in the question = 8.96 grams per cubic centimeter

Ib = pounds

We convert this density in g/cm³ to ib/in³

453.5g = 1 Ib

8.96g = a Ib

Cross Multiply

= 453.5g × a Ib =8.96g × 1 Ib

= a Ib = 8.96g × 1 Ib/453.5g

a Ib = 0.0197574421 Ib

Density of Copper = 0.0197574421 Ib/cm³

28,316.8 cm³ = 1 ft³

1 cm³ = b ft³

b ft³ = 1 cm³ × 1 ft³/28,316.8cm³

b ft³ = 0.0000353147 ft³

1 cm³ = 0.0000353147 ft³

We have to convert the density of Copper from Ib/cm³ to Ib/ft³

0.0197574421 Ib/cm³ = 0.0197574421 Ib/0.0000353147 ft³

559.46793026 Ib/ft³

Volume of copper = 1ft³

Mass = Density × Volume

Mass of copper = 559.46793026 Ib/ft³ × 1 ft³

= 559.46793026 Ib or pounds

≈ 559 pounds

Therefore , the weight of gold is 1209.6 pounds and the weight of copper will be 559 pounds.

3 0

3 years ago

Please answer my question <br> I WILL MARK BRANLIEST, AND ANSWER ONE OF YOUR QUESTIONS!!!!

ankoles [38]

Answer:

y = (4/3)x - 50

Step-by-step explanation:

Step 1 :

Identify the independent and dependent variables.

The independent variable (x) is the square footage of floor space.

The dependent variable (y) is the monthly rent.

Step 2 :

Write the information given in the problem as ordered pairs.

The rent for 600 square feet of floor space is $750 :

(600, 750)

The rent for 900 square feet of floor space is $1150 :

(900, 1150)

Step 3 :

Find the slope.

m = (y₂ - y₁) / (x₂ - x₁)

Substitute (600, 750) for (x₁, y₁) and (900, 1150) for (x₂, y₂).

m = (1150 - 750) / (900 - 600)

m = 400 / 300

m = 4/3

Step 4 :

Find the y-intercept.

Use the slope 4/3 and one of the ordered pairs (600, 750).

Slope-intercept form :

y = mx + b

Plug m = 4/3, x = 600 and y = 750.

750 = (4/3)(600) + b

750 = (4)(200) + b

750 = 800 + b

-50 = b

Step 5 :

Substitute the slope and y-intercept.

Slope-intercept form

y = mx + b

Plug m = 4/3 and b = -50

y = (4/3)x + (-50)

y = (4/3)x - 50

7 0

4 years ago

Read 2 more answers